Code of Maine Rules
05  DEPARTMENT OF EDUCATION
071  EDUCATION  GENERAL
Chapter 132  LEARNING RESULTS: PARAMETERS FOR ESSENTIAL INSTRUCTION
Current through 202339, September 27, 2023
SUMMARY: The Maine Department of Education Regulation 132  The Maine Learning Results: Parameters for Essential Instruction establishes parameters for essential teaching and learning in grades PreKindergarten through Diploma across eight content areas and supports the goals outlined in the Guiding Principles. The Maine Learning Results: Parameters for Essential Instruction will inform the blueprint for item development of the largescale State assessments aligned to the federal accountability standards found in Maine Department of Education Regulation 131  The Federal, State, and Local Accountability Standards. High school, middle school, and elementary school programming in Maine's publicly supported schools must be aligned to the knowledge and skills described in the Maine Learning Results: Parameters for Essential Instruction.
The Maine Department of Education Regulation 132  The Maine Learning Results: Parameters for Essential Instruction augments and expands upon the content standards for federal accountability (Maine Department of Education Regulation 131: The Maine Federal, State, and Local Accountability Standards) by describing details for essential teaching and learning for eight content areas. These learning goals identify the knowledge and skills required for college, career and citizenship in the 21st century.
THE GUIDING PRINCIPLES  The knowledge and skills described in the Maine Department of Education Regulation 132 support Maine students in achieving the goals established in Maine's Guiding Principles. The Guiding Principles state that each Maine student must leave school as:
A. A clear and effective communicator who:
B. A selfdirected and lifelong learner who:
C. A creative and practical problem solver who: [1995, c. 649, § 1 (new).]
D. A responsible and involved citizen who:
E. An integrative and informed thinker who:
CAREER AND LIFE READY STANDARDS INTRODUCTION
Life and Career Ready standards in Maine include an emphasis on multiple pathways toward meaningful careers and focus on life skills and experiences that will allow students to pivot as economic needs change and personal interests evolve. They have been crafted to allow flexibility and variation in focus and implementation, while ensuring all students exhibit key skills required to successfully navigate the changing career landscape.
Maine's economic future depends on a wellprepared, resilient, adaptable and skilled workforce. To achieve this, schools must creatively offer relevant opportunities that include interactive experiences and allow for direct exposure between students and a variety of career options. Schools must partner with local communities to bridge the gap between traditional K12 education and ongoing career development. Networking with local community partners can provide opportunities which may include internships/preapprenticeships, job shadows, workbased learning options, early college courses, service learning, volunteering, guest speakers, field trips, and firsttime work experiences.
These standards are a dynamic approach that frame multiple pathways for our students as they progress through grades K12 and begin their post high school journey. To meet the needs of all youth, institutions need to examine educational practices and strategies, understanding the need to prepare students to experience and explore a variety of roles within their communities and recognizing students will choose to enter the workforce in different ways.
Outline of Life and Career Ready
Standards Strand A: SelfKnowledge and Life Skills
Standard A. 1 SelfKnowledge Standard A. 2 Life Skills Standard A. 3 Problem SolvingStrand B: Aspirations
Standard B.1 Exploring OpportunitiesStrand C: Building Pathways for the Future
Standard C.1 Planning Standard C.2 Career Awareness and AdaptabilityHow to Represent the Life and Career Ready Standards and Performance Expectations
Strand 
A. SelfKnowledge and Life Skills 

Standard 
A.1 SelfKnowledge Students demonstrate an understanding of their own capabilities, characteristics, attitudes and how these attributes impact their future choices, including local, state, national, and global opportunities. 

Childhood 

Performance Expectations 
Kindergarten 
Grade 1 
Grade 2 
Students demonstrate and reflect on likes and dislikes. 
Students demonstrate and reflect on likes and dislikes that impact future choices. 
Students demonstrate and reflect on personal characteristics and attitudes that impact future choices. 

Performance Expectations 
Grade 3 
Grade 4 
Grade 5 
Students demonstrate and reflect on personal characteristics, attitudes, and interests that develop life skills and lead to career readiness. 
Students demonstrate and reflect on personal characteristics, attitudes, and interests that develop life skills and lead to career readiness with a local community focus. 
Students demonstrate and reflect on personal characteristics, attitudes, and interests that develop life skills and lead to career readiness with a state of Maine focus. 

Early Adolescence 

Performance Expectation 
Grades 68 

Students demonstrate and reflect on personal characteristics, attitudes, and interests that develop life skills and lead to career readiness, emphasizing national and global awareness. 

Adolescence 

Performance Expectation 
Grades 9Diploma 

Students demonstrate and reflect on personal characteristics, attitudes, and interests that develop life skills and assist in making post high school career and life decisions. 
Strand 
A. SelfKnowledge and Life Skills 

Standard 
A.2 Life Skills Students demonstrate positive interpersonal and life skills and understand how they are important to success in relationships, school, work, and community. 

Childhood 

Performance Expectations 
Kindergarten 
Grade 1 
Grade 2 
Students demonstrate and reflect on social skills that influence interpersonal relationships in positive ways in the classroom. a. Get along with others b. Follow established expectations for observing and listening. 
Students demonstrate and reflect on social skills that influence interpersonal relationships in positive ways in the classroom. a. Accept and give constructive feedback. 
Students demonstrate and reflect on social skills that influence interpersonal relationships in positive ways in the classroom. a. Use effective communication to manage conflict. 

Performance Expectations 
Grade 3 
Grade 4 
Grade 5 
Students demonstrate and reflect on social skills that influence interpersonal relationships in positive ways in school. a. Be a responsible member or leader of a team. 
Students demonstrate and reflect on social skills that influence interpersonal relationships in positive ways in school and the local community. a. Exhibit ethical behavior. 
Students demonstrate and reflect on skills that influence interpersonal relationships in positive ways in school and the Maine community. a. Use strategies to cope with interpersonal issues. b. Use organizational skills and time management strategies. 
Strand 
A. SelfKnowledge and Life Skills 
Standard 
A.2 Life Skills Students demonstrate positive interpersonal and life skills and understand how they are important to success in relationships, school, work, and community. 
Early Adolescence 

Performance Expectation 
Grades 68 
Students demonstrate and reflect on skills that influence interpersonal relationships in positive ways in school, work, and the regional and national community. a. Work independently to solve problems. b. Work as a productive member or leader of a team. c. Demonstrate the ability to resolve conflicts and to negotiate acceptable solutions. 

Adolescence 

Performance Expectation 
Grades 9Diploma 
Students demonstrate and reflect on skills that influence interpersonal relationships in positive ways in school, work, and the global community. a. Use a variety of communication skills in a responsible manner. b. Exhibit ethical behavior, including responsibility for self and others. c. Understand and exhibit professionalism in changing situations and environments. 
Strand 
A. SelfKnowledge and Life Skills 

Standard 
A.3 Problem Solving Students are engaged community members who identify problems and apply skills to resolve problems within local and global communities 

Childhood 

Performance Expectations 
Kindergarten 
Grade 1 
Grade 2 
Students use and analyze communication skills in their classroom. 
Students use and analyze problemsolving skills in their classroom. 
Students use and analyze communication and problemsolving skills in their school. 

Performance Expectations 
Grade 3 
Grade 4 
Grade 5 
Students integrate and analyze communication, collaboration, and problemsolving skills in their school. 
Students integrate and analyze communication, collaboration, and problemsolving skills in their local community. 
Students apply skills to analyze and creatively solve problems that impact their schools and local communities. 

Early Adolescence 

Performance Expectation 
Grades 68 

Students evaluate and develop problemsolving skills and resolve problems within the community. a. Evaluate skills and understand gaps in skill sets. b. Develop creative solutions to meet local and global needs. 

Adolescence 

Performance Expectation 
Grades 9Diploma 

Students evaluate and implement strategies to manage multiple roles and responsibilities as involved members of their local and global communities. a. Evaluate responsibilities and potential impact as students, community members and employees. b. Engage in issues impacting local and global communities. 
Strand 
B. Aspirations 

Standard 
B.1 Exploring Opportunities Students understand their options and can navigate choices and experiences concerning interests and future opportunities. 

Childhood 

Performance Expectations 
Kindergarten 
Grade 1 
Grade 2 
Students engage in new experiences and ask questions to promote creativity and curiosity about their interests. 
Students use resources, seeking help proactively and asking questions when needed, to promote creativity and curiosity about their interests. 
Students recognize and analyze available resources, using strategies described by others to promote creativity and curiosity about their interests. 

Performance Expectations 
Grade 3 
Grade 4 
Grade 5 
Students integrate communication, collaboration, and problemsolving skills to identify and reflect on interests. 
Students analyze and apply learning strategies to discover emerging questions and pursue new interests. 
Students use learning strategies and available resources to explore future opportunities. 

Early Adolescence 

Performance Expectation 
Grades 68 

Students use and analyze resources to purposely and creatively explore a variety of post high school options. 

Adolescence 

Grades 9Diploma 

Performance Expectation 
Students articulate a variety of post high school options based on individualized, indepth exploration. 
Strand 
C. Building Pathways for the Future 

Standard 
C.1 Planning Students develop goals and implement career and life plans. 

Childhood 

Performance Expectations 
Kindergarten 
Grade 1 
Grade 2 
Students participate in the development of classroom guidelines. 
Students reflect upon and adjust classroom guidelines with guidance. 
Students develop an awareness of goals and goalsetting practices. 

Performance Expectations 
Grade 3 
Grade 4 
Grade 5 
Students engage in the goalsetting process. 
Students reflect upon and adjust individual academic goals. 
Students use feedback and experiences to develop, implement, and adjust goals. a. Demonstrate ability to learn from mistakes. 

Early Adolescence 

Performance Expectation 
Grades 68 

Students develop, implement, and adjust goals as they relate to potential future paths. a. Demonstrate awareness of available academic opportunities, course levels, alternate options, and timelines. b. Draw on curiosity to seek out meaningful career exploration opportunities in interactive settings. 

Adolescence 

Performance Expectation 
Grades  9Diploma 

Students develop, take steps to implement, and reflect on individualized, post high school plans. a. Analyze educational achievement and performance strategies as it relates to future choices, adapting plans as needed. b. Seek out meaningful career exploration opportunities, both individually and in smallgroup interactive settings. c. Understand the financial impact of post high school credentialing programs, using that awareness to inform plans. 
Strand 
C. Building Pathways for the Future 

Standard 
C.2 Career Awareness and Adaptability Students integrate personal aptitudes and interests, changing employment trends, community and societal needs, and current economic conditions into ongoing career plans, adapting as necessary. 

Childhood 

Performance Expectations 
Kindergarten 
Grade 1 
Grade 2 
Students explore jobs/careers and how these roles contribute to the community. 
Students explore jobs/careers of individual interest and how these roles contribute to the community. 
Students connect classroom learning with workplace skills and roles in the community. 

Performance Expectations 
Grade 3 
Grade 4 
Grade 5 
Students explore the concept of career clusters. 
Students identify and reflect on skills and education related to various career clusters. 
Students identify and reflect on skills and education requirements of occupations within and across career clusters of interest to them. 

Early Adolescence 

Performance Expectation 
Grades 68 

Students consider personal aptitudes, evolving personal interests and current employment trends, locally and globally, as they develop future plans. a. Identify horizontal and vertical opportunities (within career cluster hierarchies) related to personal aptitudes and interests and the skills needed for potential career options. b. Recognize that career planning to attain career goals is a lifelong process. c. Use knowledge of career clusters to develop and adapt career plans. 

Adolescence 

Performance Expectation 
Grades 9Diploma 

Students are aware of changing career and economic trends and can adapt their personal plan to meet situational needs, personal aptitudes and interests. a. Reflect on personal growth and alternative perspectives. b. Analyze and adjust approach, timeline, and plan as needed. c. Explore credentialing requirements. d. Plan strategically (informed by changing career and economic trends) and choose learning experiences/courses/classes that strengthen knowledge and skills needed for individual next steps after high school. 
ENGLISH LANGUAGE ARTS STANDARDS INTRODUCTION
Literacy is a basic human right, achievable by all students. Today's learners need to know how to read, write, speak, and communicate effectively in order to survive in an everchanging and challenging global society. English Language Arts/Literacy is the foundation for learning in all of the content areas. The literacy continuum develops across an individual's lifetime, but literacy does not reside solely in the individual person; it requires and creates relationships with others through communication and interaction. Literacy is a developmental process that empowers students to become lifelong, effective learners and communicators.
The Maine Learning Results English Language Arts/Language standards are organized into four strands: Language, Speaking and Listening, Reading, and Writing. Each strand represents a body of knowledge and skills that students need to become lifelong learners. These strands are further broken down into standards that identify enduring understandings and skills that transfer across contexts, content areas, and grade levels. As students progress through the curriculum, the standards are broken down into Performance Expectations that are grouped by grade level through grade 5 and then are banded 68 and 9Diploma. The Performance Expectations define skills and establish measurable articulations of what the student understands and can do.
The standards reference "Various Text Types" rather than emphasizing any one particular genre. Teachers are encouraged to use a variety of text types, including literature and informational texts in multiple formats. The skills outlined by the standards are designed so that students can receive literacy instruction with each text they encounter across all disciplines.
Guiding Principles
The Guiding Principles steer education in Maine and are reflected and embedded throughout the English Language Arts/Literacy standards. Examples of how students can show evidence of those guiding principles in English Language Arts/Literacy may include (but are not limited to) the following suggestions:
A. Clear and effective communicator: Students participate in a range of evidencebased discussions and generate detailed writing that are both used to communicate ideas clearly with others.
B. A selfdirected and lifelong learner: Students apply knowledge in new contexts and demonstrate flexibility including the ability to learn, unlearn and relearn.
C. A creative and practical problem solver: Students use inquiry and writing processes that require adaptation to feedback through the use of reflection, sometimes persevering through multiple attempts.
D. A responsible and involved citizen: Students demonstrate ethical behavior, particularly during the discussion of ideas, maintaining awareness of, and respect for, multiple and diverse perspectives.
E. An integrative and informed thinker: Students frequently read, evaluate, and synthesize information and ideas from multiple sources, incorporating it into both oral and written communication.
LANGUAGE
Throughout the developmental continuum in English Language Arts/Literacy and across all content areas, language is the core of understanding and comprehension. Context is key. Human understanding is founded in communication and language, and organic experiences are the most effective means of learning language skills. While the language standards are presented separately from reading, writing, speaking, and listening, they are best utilized and presented as embedded skills within the other strands. A balance must be found between direct instruction of standards, like vocabulary acquisition and spelling, and integrated instruction of standards, like vocabulary use and nuance.
These standards are not a checklist, but key components of reading, writing, speaking, and listening instruction, and they should be treated as such. Frequent, intentional reference to and instruction in these skills is essential to teaching students to be clear communicators in every medium and field.
Each language standard may contain multiple concepts, at different levels of complexity. In early adolescence and adolescence grade spans, these are best taught in order as listed, even across grade levels, to provide students with the foundational knowledge required for success as they progress, not just through school, but through life. Developing facility with the language standards is key to building comprehension and fluency with increasingly complex texts and communications.
Strand 
LANGUAGE: CONVENTIONS OF STANDARD ENGLISH 

Standard 1 
Demonstrate command of the conventions of Standard English grammar and usage when writing or speaking. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Use frequently occurring nouns and verbs. b. Form regular plural nouns orally by adding /s/ or /es/ (e.g., dog, dogs; wish, wishes). c. Understand and use question words (interrogatives) (e.g., who, what, where, when, why, how). d. Use the most frequently occurring prepositions (e.g., to, from, in, out, on, off, for, of, by, with). e. Produce and expand complete sentences in shared language activities. 
a. Use common, proper, and possessive nouns. b. Use singular and plural nouns with matching verbs in basic sentences (e.g., He hops; We hop). c. Use personal, possessive, and indefinite pronouns (e.g., I, me, my; they, them, their; anyone, everything). d. Use verbs to convey a sense of past, present, and future (e.g., Yesterday I walked home; Today I walk home; Tomorrow I will walk home). e. Use frequently occurring adjectives. f. Use frequently occurring conjunctions (e.g., and, but, or, so, because). g. Use determiners (e.g., articles, demonstratives). h. Use frequently occurring prepositions (e.g., during, beyond, toward). i. Produce and expand complete simple and compound declarative, interrogative, imperative, and exclamatory sentences in response to prompts. 
a. Use collective nouns (e.g., group). b. Form and use frequently occurring irregular plural nouns (e.g., feet, children, teeth, mice, fish). c. Use reflexive pronouns (e.g., myself, ourselves). d. Form and use the past tense of frequently occurring irregular verbs (e.g., sat, hid, told). e. Use adjectives and adverbs; choose between them depending on what is to be modified. f. Produce, expand, and rearrange complete simple and compound sentences (e.g., The boy watched the movie; The little boy watched the movie; The action movie was watched by the little boy). 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Explain the function of nouns, pronouns, verbs, adjectives, and adverbs in general and their functions in particular sentences. b. Form and use regular and irregular plural nouns. c. Use abstract nouns (e.g., childhood). d. Form and use regular and irregular verbs. e. Form and use the simple (e.g., I walked; I walk; I will walk) verb tenses. f. Ensure subjectverb and pronounantecedent agreement. g. Form and use comparative and superlative adjectives and adverbs, and choose h. between them depending on what is to be modified. i. Standards for Language 3 j. Use coordinating and subordinating conjunctions. k. Produce simple, compound, and complex sentences. 
a. Use relative pronouns (who, whose, whom, which, that) and relative adverbs (where, when, why). b. Form and use the progressive (e.g., I was walking; I am walking; I will be walking) verb tenses. c. Use modal auxiliaries (e.g., can, may, must) to convey various conditions. d. Order adjectives within sentences according to conventional patterns (e.g., a small red bag rather than a red small bag). e. Form and use prepositional phrases. f. Produce complete sentences, recognizing and correcting inappropriate fragments and runons.* g. Correctly use frequently confused words (e.g., to, too, two; there, their). 
a. Explain the function of conjunctions, prepositions, and interjections in general and their function in particular sentences. b. Form and use the perfect (e.g., I had walked; I have walked; I will have walked) verb tenses. c. Use verb tense to convey various times, sequences, states, and conditions. d. Recognize and correct inappropriate shifts in verb tense. e. Use correlative conjunctions (e.g., either/or, neither/nor). 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Ensure that pronouns are in the proper case (subjective, objective, possessive). b. Use intensive pronouns (e.g., myself, ourselves). c. Recognize and correct inappropriate shifts in pronoun number and person. d. Recognize and correct vague pronouns (i.e., ones with unclear or ambiguous antecedents). e. Recognize variations from standard English in their own and others' writing and speaking and identify and use strategies to improve expression in conventional language. f. Explain the function of phrases and clauses in general and their function in specific sentences. g. Choose among simple, compound, complex, and compoundcomplex sentences to signal differing relationships among ideas. h. Place phrases and clauses within a sentence, recognizing and correcting misplaced and dangling modifiers i. Explain the function of verbals (gerunds, participles, infinitives) in general and their function in particular sentences. j. Form and use verbs in the active and passive voice. k. Form and use verbs in the indicative, imperative, interrogative, conditional, and subjunctive mood. l. Recognize and correct inappropriate shifts in verb voice and mood. 

Grade Span 
Adolescence 

Grades 9Diploma 

a. Use parallel structure. b. Use various types of phrases (noun, verb, adjectival, adverbial, participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations. c. Apply the understanding that usage is a matter of convention, can change over time, and is sometimes contestable. d. Resolve issues of complex or contested usage, consulting references as needed. 
Strand 
LANGUAGE: CONVENTIONS OF STANDARD ENGLISH 

Standard 2 
Demonstrate command of the conventions of Standard English capitalization, punctuation, and spelling when writing. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Capitalize the first word in a sentence and the pronoun I. b. Recognize and name end punctuation. c. Write a letter or letters for most consonant and shortvowel sounds (phonemes). d. Spell simple words phonetically, drawing on knowledge of soundletter relationships. 
a. Capitalize dates and names of people. b. Use end punctuation for sentences. c. Use commas in dates and to separate single words in a series. d. Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words. e. Spell untaught words phonetically, drawing on phonemic awareness and spelling conventions. 
a. Capitalize holidays, product names, and geographic names. b. Use commas in greetings and closings of letters. c. Use an apostrophe to form contractions and frequently occurring possessives. d. Generalize learned spelling patterns when writing words (e.g., cage> badge; boy> boil). e. Consult reference materials, including beginning dictionaries, as needed to check and correct spellings. 

Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Capitalize appropriate words in titles. b. Use commas in addresses. c. Use commas and quotation marks in dialogue. d. Form and use possessives. e. Use conventional spelling for highfrequency and other studied words and for adding suffixes to base words (e.g., sitting, smiled, cries, happiness). f. Use spelling patterns and generalizations (e.g., word families, positionbased spellings, syllable patterns, ending rules, meaningful word parts) in writing words. g. Consult reference materials, including beginning dictionaries, as needed to check and correct spellings. 
a. Use correct capitalization. b. Use commas and quotation marks to mark direct speech and quotations from a text. c. Use a comma before a coordinating conjunction in a compound sentence. d. Spell gradeappropriate words correctly, consulting references as needed. 
a. Use punctuation to separate items in a series. b. Use a comma to separate an introductory element from the rest of the sentence. c. Use a comma to set off the words yes and no (e.g., Yes, thank you), to set off a tag question from the rest of the sentence (e.g., It's true, isn't it?), and to indicate direct address (e.g., Is that you, Steve?). d. Use underlining, quotation marks, or italics to indicate titles of works. e. Spell gradeappropriate words correctly, consulting references as needed. 

Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Spell correctly. b. Use punctuation (commas, parentheses, dashes) to set off nonrestrictive/parenthetical elements. c. Use a comma to separate coordinate adjectives (e.g., It was a fascinating, enjoyable movie but not He wore an old[,] green shirt). d. Use punctuation (comma, ellipsis, dash) to indicate a pause or break. e. Use an ellipsis to indicate an omission. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
a. Use a semicolon (and perhaps a conjunctive adverb) to link two or more closely related independent clauses. b. Use a colon to introduce a list or quotation. c. Observe hyphenation conventions. d. Spell correctly. 
Strand 
LANGUAGE: KNOWLEDGE OF LANGUAGE 

Standard 3 
Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style in writing and speaking, and to comprehend more fully when reading or listening. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Use knowledge of language and its conventions when speaking or listening. 
Use knowledge of language and its conventions when writing, speaking, reading, or listening. 
Use knowledge of language and its conventions when writing, speaking, reading, or listening. a. Compare formal and informal uses of English. 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Use knowledge of language and its conventions when writing, speaking, reading, or listening. a. Choose words and phrases for effect. b. Recognize and observe differences between the conventions of spoken and written standard English. 
Use knowledge of language and its conventions when writing, speaking, reading, or listening. a. Choose words and phrases to convey ideas precisely. b. Choose punctuation for effect. c. Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., smallgroup discussion). 
Use knowledge of language and its conventions when writing, speaking, reading, or listening. a. Expand, combine, and reduce sentences for meaning, reader/listener interest, and style. b. Compare and contrast the varieties of English (e.g., dialects, registers) used in stories, dramas, or poems. 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Vary sentence patterns for meaning, reader/listener interest, and style. b. Maintain consistency in style and tone. c. Choose language that expresses ideas precisely and concisely, recognizing and eliminating wordiness and redundancy. d. Use verbs in the active and passive voice and in the conditional and subjunctive mood to achieve particular effects (e.g., emphasizing the actor or the action; expressing uncertainty or describing a state contrary to fact). 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
a. Write and edit work so that it conforms to the guidelines in a style manual appropriate for the discipline and writing task. b. Vary syntax for effect, consulting references for guidance as needed; apply an understanding of syntax to the study of complex texts when reading. 
Strand 
LANGUAGE: VOCABULARY ACQUISITION AND USE 

Standard 4 
Use context clues, analyze meaningful word parts, and consult general and specialized reference materials as appropriate to determine or clarify the meaning of unknown and multiplemeaning words and phrases from grade level content. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Determine or clarify the meaning of unknown and multiplemeaning words and phrases based on kindergarten reading and content. a. Identify new meanings for familiar words and apply them accurately (e.g., knowing duck is a bird and learning the verb to duck). b. Use the most frequently occurring inflections and affixes (e.g., ed, s, re, un, pre, ful, less) as a clue to the meaning of an unknown word. 
Determine or clarify the meaning of unknown and multiplemeaning words and phrases based on grade 1 reading and content, choosing flexibly from an array of strategies. a. Use sentencelevel context as a clue to the meaning of a word or phrase. b. Use frequently occurring affixes as a clue to the meaning of a word. c. Identify frequently occurring root words (e.g., look) and their inflectional forms (e.g., looks, looked, looking). 
Determine or clarify the meaning of unknown and multiplemeaning words and phrases based on grade 2 reading and content, choosing flexibly from an array of strategies. a. Use sentencelevel context as a clue to the meaning of a word or phrase. b. Determine the meaning of the new word formed when a known prefix is added to a known word (e.g., happy/unhappy, tell/retell). c. Use a known root word as a clue to the meaning of an unknown word with the same root (e.g., addition, additional). d. Use knowledge of the meaning of individual words to predict the meaning of compound words (e.g., birdhouse, lighthouse, housefly; bookshelf, notebook, bookmark). d. Use glossaries and beginning dictionaries, both print and digital, to determine or clarify the meaning of words and phrases. 

Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Determine or clarify the meaning of unknown and multiplemeaning words and phrases based on grade 3 reading and content, choosing flexibly from a range of strategies. a. Use sentencelevel context as a clue to the meaning of a word or phrase. b. Determine the meaning of the new word formed when a known affix is added to a known word (e.g., agreeable/disagreeable, comfortable/uncomfortable, care/careless, heat/preheat). c. Use a known root word as a clue to the meaning of an unknown word with the same root (e.g., company, companion). d. Use glossaries or beginning dictionaries, both print and digital, to determine or clarify the precise meaning of key words and phrases. 
Determine or clarify the meaning of unknown and multiplemeaning words and phrases based on grade 4 reading and content, choosing flexibly from a range of strategies. a. Use context (e.g., definitions, examples, or restatements in text) as a clue to the meaning of a word or phrase. b. Use common, gradeappropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., telegraph, photograph, autograph). c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases. 
Determine or clarify the meaning of unknown and multiplemeaning words and phrases based on grade 5 reading and content, choosing flexibly from a range of strategies. a. Use context (e.g., cause/effect relationships and comparisons in text) as a clue to the meaning of a word or phrase. b. Use common, gradeappropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., photograph, photosynthesis). c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases. 

Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Use context (e.g., the overall meaning of a sentence or paragraph; a word's position or function in a sentence) as a clue to the meaning of a word or phrase. b. Use common, gradeappropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., audience, auditory, audible in 6th grade; belligerent, bellicose, rebel in 7th grade; precede, recede, secede in 8th grade). c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses) to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech. d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary). 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
a. Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word's position or function in a sentence) as a clue to the meaning of a word or phrase. b. Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., conceive, conception, conceivable). c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses) to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, its etymology, or its usage. d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary). 
Strand 
LANGUAGE: VOCABULARY ACQUISITION AND USE 

Standard 5 
Demonstrate understanding of figurative language, word relationships, and nuances in word meanings sufficient for reading, writing, speaking, and listening. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
With guidance and support from adults, explore word relationships and nuances in word meanings. a. Sort common objects into categories (e.g., shapes, foods) to gain a sense of the concepts the categories represent. b. Demonstrate understanding of frequently occurring verbs and adjectives by relating them to their opposites (antonyms). c. Identify reallife connections between words and their use (e.g., note places at school that are colorful). d. Distinguish shades of meaning among verbs differing in manner (e.g., look, peek, glance, stare, glare, scowl) and adjectives differing in intensity (e.g., large, gigantic) by defining or choosing them or by acting out the meanings. 
With guidance and support from adults, demonstrate an understanding of word relationships and nuances in word meanings. a. Sort words into categories (e.g., colors, clothing) to gain a sense of the concepts the categories represent. b. Define words by category and by one or more key attributes (e.g., a duck is a bird that swims; a tiger is a large cat with stripes). c. Identify reallife connections between words and their use (e.g., note places at home that are cozy). d. Distinguish shades of meaning among verbs differing in manner (e.g., look, peek, glance, stare, glare, scowl) and adjectives differing in intensity (e.g., large, gigantic) by defining or choosing them or by acting out the meanings. 
Demonstrate understanding of word relationships and nuances in word meanings. a. Identify reallife connections between words and their use (e.g., describe foods that are spicy or juicy). b. Distinguish shades of meaning among closely related verbs (e.g., toss, throw, hurl) and closely related adjectives (e.g., thin, slender, skinny, scrawny). 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Demonstrate understanding of word relationships and nuances in word meanings. a. Distinguish the literal and nonliteral meanings of words and phrases in context (e.g., take steps). b. Identify reallife connections between words and their use (e.g., describe people who are friendly or helpful). c. Distinguish shades of meaning among related words that describe states of mind or degrees of certainty (e.g., knew, believed, suspected, heard, wondered). 
a. Demonstrate understanding of figurative language, word relationships, and nuances in word meanings. b. Explain the meaning of simple similes and metaphors (e.g., as pretty as a picture) in context. c. Recognize and explain the meaning of common idioms, adages, and proverbs. d. Demonstrate understanding of words by relating them to their opposites (antonyms) and to words with similar but not identical meanings (synonyms). 
Demonstrate understanding of figurative language, word relationships, and nuances in word meanings. a. Interpret figurative language, including similes and metaphors, in context. b. Recognize and explain the meaning of common idioms, adages, and proverbs. c. Use the relationship between particular words (e.g., synonyms, antonyms, homographs) to better understand each of the words. 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Interpret figures of speech (e.g. personification in 6th grade; allusions in 7th grade; verbal irony, puns in 8th grade) in context. b. Use the relationship between particular words (e.g., cause/effect, part/whole, item/category in 6th grade; synonym/antonym, analogy in 7th grade) to better understand each of the words. c. Distinguish among the connotations of words with similar denotations (e.g., stingy, scrimping, economical, unwasteful, thrifty in 6th grade; refined, respectful, polite, diplomatic, condescending in 7th grade; bullheaded, willful, firm, persistent, resolute in 8th grade). 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
a. Interpret figures of speech (e.g., euphemism, oxymoron, hyperbole, paradox) in context and analyze their role in the text. b. Analyze nuances in the meaning of words with similar denotations. 
Strand 
LANGUAGE: VOCABULARY ACQUISITION AND USE 

Standard 6 
Acquire and use accurately a range of general academic and domainspecific words and phrases sufficient for reading, writing, speaking, and listening; demonstrate independence in gathering vocabulary knowledge when encountering an unknown term important to comprehension or expression. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Use words and phrases acquired through conversations, reading and being read to, and responding to texts. 
Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using frequently occurring conjunctions to signal simple relationships (e.g., because). 
Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using adjectives and adverbs to describe (e.g., When other kids are happy that makes me happy). 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Acquire and use accurately gradeappropriate conversational, general academic, and domainspecific words and phrases, including those that signal spatial and temporal relationships (e.g., After dinner that night we went looking for them). 
Acquire and use accurately gradeappropriate general academic and domainspecific words and phrases, including those that signal precise actions, emotions, or states of being (e.g., quizzed, whined, stammered) and that are basic to a particular topic (e.g., wildlife, conservation, and endangered when discussing animal preservation). 
Acquire and use accurately gradeappropriate general academic and domainspecific words and phrases, including those that signal contrast, addition, and other logical relationships (e.g., however, although, nevertheless, similarly, moreover, in addition). 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
Acquire and use accurately gradeappropriate general academic and domainspecific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
Acquire and use accurately general academic and domainspecific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression. 
SPEAKING AND LISTENING
Speaking and listening are essential components in our schools, our homes, our communities, and our places of work. Direct, interpersonal communication is the cornerstone of human relationships, and nowhere is this more clearly articulated than in dialogue, discussion, presentation, and debate. Successful students must be able to communicate in multiple mediums, through conversations, interviews, digital presentations, and countless daytoday interactions that build understanding of their world and the perspectives of their peers. Key to success in our modern world is interaction with diverse others and everchanging groups, and creating and following community guidelines and rules, which is critical practice for civic responsibility later in life.
Speaking and listening standards do not stand alone; like all Language Arts skills, they are interconnected. Early speaking and listening skills in primary grades are foundational to close reading skills in later grades, and throughout school and life the ability to understand, analyze, and evaluate others' words helps everyone develop a richer and deeper awareness of human motivation and purpose.
Strand 
SPEAKING AND LISTENING: COMPREHENSION AND COLLABORATION 

Standard 1 
Prepare for and participate in conversations across a range of topics, types, and forums, building on others' ideas and expressing their own. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Participate in collaborative conversations about kindergarten topics and texts with peers and adults in small and larger groups. b. Follow agreedupon rules for discussions (e.g., listening to others and taking turns speaking about the topics and texts under discussion). c. Continue a conversation through multiple exchanges. 
a. Participate in collaborative conversations about grade 1 topics and texts with peers and adults in small and larger groups. b. Follow agreedupon rules for discussions (e.g., listening to others with care, speaking one at a time about the topics and texts under discussion). c. Build on others' talk in conversations by responding to the comments of others through multiple exchanges. d. Ask questions to clear up any confusion about the topics and texts under discussion. 
a. Participate in collaborative conversations about grade 2 topics and texts with peers and adults in small and larger groups. b. Follow agreedupon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion). c. Build on others' talk in conversations by linking their comments to the remarks of others. d. Ask for clarification and further explanation as needed about the topics and texts under discussion. 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Engage effectively in a range of collaborative discussions (oneonone, in groups, studentled and teacherled) on grade 3 topics and texts, building on others' ideas and expressing their own clearly. b. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. c. Follow agreedupon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion). d. Ask questions to check understanding of information presented, stay on topic, and link their comments to the remarks of others. e. Explain their own ideas and understanding in light of the discussion. 
a. Engage effectively in a range of collaborative discussions (oneonone, in groups, studentled, and teacherled) on grade 4 topics and texts, building on others' ideas and expressing their own clearly. b. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. c. Follow agreedupon rules for discussions and carry out assigned roles. d. Pose and respond to specific questions to clarify or follow up on information and make comments that contribute to the discussion and link to the remarks of others. e. Review the key ideas expressed and explain their own ideas and understanding in light of the discussion. 
a. Engage effectively in a range of collaborative discussions (oneonone, in groups, studentled, and teacherled) on grade 5 topics and texts, building on others' ideas and expressing their own clearly. b. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. c. Follow agreedupon rules for discussions and carry out assigned roles. d. Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. e. Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Engage effectively in a range of collaborative discussions (oneonone, in groups, studentled, and teacherled) on grade 68 topics, texts, and issues, building on others' ideas and expressing their own clearly. b. Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion. c. Follow rules for collegial discussions and decisionmaking, set and track progress toward specific goals and deadlines, and define individual roles as needed. d. Pose questions that elicit elaboration, connect the ideas of several speakers, and respond to others' questions and comments with relevant evidence, observations, and ideas. e. Review the key ideas expressed and demonstrate understanding of multiple perspectives through paraphrasing and reflection. Acknowledge new information expressed by others, and, when warranted, modify, qualify, or justify their own views in light of the evidence presented. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
a. Participate effectively in a range of collaborative discussions (oneonone, in groups, studentled, and teacherled)on grades 9Diploma topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. b. Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, wellreasoned exchange of ideas. c. Work with peers to promote civil, democratic discussions and decisionmaking, set clear goals and deadlines, and establish individual roles as needed. d. Propel conversations by posing and responding to questions that probe reasoning and evidence. e. Respond thoughtfully to diverse perspectives; synthesize comments, claims, and evidence made on all sides of an issue; resolve contradictions when possible; and determine what additional information or research is required to deepen the investigation or complete the task. 
Strand 
SPEAKING AND LISTENING: COMPREHENSION AND COLLABORATION 

Standard 2 
Integrate and evaluate information presented in diverse media and formats, including point of view, reasoning, and use of evidence and rhetoric. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Confirm understanding of a text read aloud or information presented orally or through other media by asking and answering questions about key details to seek help if something is not understood. b. Ask and answer questions in order to seek help, gather information, or clarify something that is not understood. 
a. Ask and answer questions about key details in a text read aloud or information presented orally or through other media. b. Ask and answer questions about what a speaker says in order to gather additional information or clarify something that is not understood. 
a. Recount or describe key ideas or details from a text read aloud or information presented orally or through other media. b. Ask and answer questions about what a speaker says in order to clarify comprehension, gather additional information, or deepen understanding of a topic or issue. 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Determine the main ideas and supporting details of a text read aloud or information presented in diverse media and formats. b. Ask and answer questions about information from a speaker, offering appropriate elaboration and detail. 
a. Paraphrase portions of a text read aloud or information presented in diverse media and formats. b. Identify the reasons and evidence a speaker provides to support particular points. 
a. Summarize a written text read aloud or information presented in diverse media and formats. b. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Interpret information, analyze the main ideas and supporting details, and analyze the purpose of information presented in diverse formats. b. Explain how the presentation contributes to or clarifies a topic under study, and evaluate the motives (e.g., social, commercial, political) behind its presentation. c. Delineate a speaker's argument and specific claims, evaluate the soundness of the reasoning and sufficiency of the evidence, and identify when irrelevant evidence is introduced. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
a. Integrate multiple sources of information presented in diverse formats and media in order to make informed decisions and solve problems, evaluating the credibility and accuracy of each source and noting any discrepancies among the data. b. Evaluate the speaker's technique, including use of evidence, reasoning, stylistic and rhetorical elements, or other features appropriate to the task. 
Strand 
SPEAKING AND LISTENING: PRESENTATION OF KNOWLEDGE AND IDEAS 

Standard 3 
Present information and supporting evidence appropriate to task, purpose, and audience so listeners can follow the line of reasoning and incorporate multimedia when appropriate. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Describe familiar people, places, things, and events and, with prompting and support, provide additional detail. b. Add drawings or other visual displays to descriptions as desired to provide additional detail. 
a. Describe people, places, things, and events with relevant details, expressing ideas and feelings clearly. b. Add drawings or other visual displays to descriptions when appropriate to clarify ideas, thoughts, and feelings. 
a. Describe people, places, things, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speaking audibly in coherent sentences. b. Create audio/video recordings of stories or poems; add drawings or other visual displays to stories or recounts of experiences when appropriate to clarify ideas, thoughts, and feelings. 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Report on a topic or text, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speak clearly at an understandable pace. b. Create audio/video recordings of stories or poems that demonstrate fluid reading at an understandable pace; add visual displays when appropriate to emphasize or enhance certain facts or details. 
a. Report on a topic or text, tell a story, or recount an experience in an organized manner, using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace. b. Add audio/video recordings and visual displays to presentations when appropriate to enhance the development of main ideas or themes. 
a. Report on a topic or text or present an opinion, sequencing ideas logically and using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace. b. Include multimedia components (e.g., graphics, sound) and visual displays in presentations when appropriate to enhance the development of main ideas or themes. 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Present claims and findings, emphasizing salient points in a sequenced, focused, coherent manner with relevant evidence, sound and valid reasoning, and wellchosen details. b. Use appropriate eye contact, adequate volume, and clear pronunciation. c. When appropriate, integrate multimedia and visual displays into presentations to clarify information, strengthen claims and evidence, and add interest. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
a. Present information, findings, and supporting evidence, conveying a clear and distinct perspective so that listeners can follow the line of reasoning. b. Address alternative or opposing perspectives; the organization development, substance, and style are appropriate to purpose, audience, and a range of formal and informal tasks. c. Use appropriate eye contact, adequate volume, and clear pronunciation. d. Make strategic use of multimedia (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence. 
Strand 
SPEAKING AND LISTENING: PRESENTATION OF KNOWLEDGE AND IDEAS 

Standard 4 
Adapt speech to a variety of contexts, audiences, and communicative tasks. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Speak audibly and express thoughts, feelings, and ideas clearly. 
Produce complete sentences when appropriate to task and situation. (See grade 1 Language standards 1 and 3 for specific expectations.) 
Produce complete sentences when appropriate to task and situation in order to provide requested detail or clarification. (See grade 2 Language standards 1 and 3 for specific expectations.) 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Speak in complete sentences when appropriate to task and situation in order to provide requested detail or clarification. (See grade 3 Language standards 1 and 3 for specific expectations.) 
Differentiate between contexts that call for different registers (e.g. formal English for presenting ideas and informal discourse for smallgroup discussion) (See grade 4 Language standards 1 and 3 for specific expectations.) 
Adapt speech to a variety of contexts and tasks, demonstrating command of language in the appropriate register. (See grade 5 Language standards 1 and 3 for specific expectations.) 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
Adapt speech to a variety of contexts, demonstrating command of language in the appropriate register (See grades 68 Language standards 1 and 3 for specific expectations.) 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
Adapt speech to a variety of contexts, demonstrating a command of language in the appropriate register. (See grades 9Diploma Language standards 1 and 3 for specific expectations.) 
READING
The goal of all reading instruction is to help students become competent consumers of a wide variety of texts in diverse forms so that they can achieve independence, find meaning, and use literacy for lifelong learning, empowerment, and enjoyment.
A text is anything that can be read, heard or viewed. Texts may include words, images, objects, sounds, and symbols that convey messages from developers to consumers. They broadly encompass multiple purposes, audience appeal, and a wide variety of human experiences that create meaning for the reader. A student's experience with texts may range from cursive, print and digital fonts. When choosing texts, teachers must consider the qualities of complexity and the diversity of texts each student should experience.
The reading standards are designed progressively, using specificity and scaffolding to engage all readers in pursuing skills and experiences that contribute to personal, communal, and global needs and interests. This design promotes essential reading skills, allowing students to understand and enjoy a wide range of texts from a variety of perspectives. Teachers must employ a balance of researchbased instructional approaches and strategies designed to provide multiple opportunities for transfer of learning.
Strand 
READING: FOUNDATIONAL SKILLS/ PRINT CONCEPTS 

Standard 1 
Demonstrate understanding of the organization and basic features of print. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Follow words from left to right, top to bottom, and page by page. b. Recognize that spoken words are represented in written language by specific sequences of letters. c. Understand that words are separated by spaces in print. d. Recognize and name all upper and lowercase letters of the alphabet. 
Recognize the distinguishing features of a sentence (e.g., first word, capitalization, ending punctuation). 
Recognize the distinguishing features of a paragraph (e.g. indent). 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should assess where students are, determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to help students move toward proficiency. 
Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should assess where students are, determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to help students move toward proficiency. 
Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should assess where students are, determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to help students move toward proficiency. 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should assess where students are, determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to move students toward proficiency. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should assess where students are, determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to move students toward proficiency. 
Strand 
READING: FOUNDATIONAL SKILLS/ PHONOLOGICAL AWARENESS 

Standard 2 
Demonstrate understanding of words, syllables, and sounds (phonemes). 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Recognize and produce rhyming words. b. Count, pronounce, blend, and segment syllables in spoken words. c. Blend and segment onsets and rimes of singlesyllable spoken words. d. Isolate and pronounce the initial, medial vowel, and final sounds (phonemes) in threephoneme (consonantvowelconsonant, or CVC) words. (This does not include CVCs ending with /l/, /r/, or /x/.) e. Add or substitute individual sounds (phonemes) in simple, onesyllable words to make new words. 
a. Distinguish long from short vowel sounds in spoken singlesyllable words. b. Produce singlesyllable words by blending sounds (phonemes), including consonant blends. c. Isolate and pronounce initial, medial vowel, and final sounds (phonemes) in spoken single syllable words. d. Segment spoken singlesyllable words into their complete sequence of individual sounds (phonemes). 
Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should assess where students are, determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to move students toward proficiency. 

Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should assess where students are, determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to help students move toward proficiency. 
Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should assess where students are, determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to help students move toward proficiency. 
Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should assess where students are, determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to help students move toward proficiency. 

Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should assess where students are, determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to move students toward proficiency. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should assess where students are, determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to move students toward proficiency. 
Strand 
READING: FOUNDATIONAL SKILLS/ PHONICS AND WORD RECOGNITION 

Standard 3 
Know and apply gradelevel phonics and word analysis skills in decoding words. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Demonstrate basic knowledge of onetoone lettersound correspondences by producing the primary or many of the most frequent sound for each consonant. b. Associate the long and short sounds with common spellings (graphemes) for the five major vowels. c. Read common highfrequency words by sight (e.g., the, of, to, you, she, my, is, are, do, does). d. Distinguish between similarly spelled words by identifying the sounds of the letters that differ 
a. Know the spellingsound correspondences for common consonant digraphs. b. Decode regularly spelled one syllable words. c. Know final e and common vowel team conventions for representing long vowel sounds. d. Use knowledge that every syllable must have a vowel sound to determine the number of syllables in a printed word. e. Decode twosyllable words following basic patterns by breaking the words into syllables. f. Read words with inflectional endings. g. Recognize and read grade appropriate irregularly spelled words. 
a. Distinguish long and short vowels when reading regularly spelled onesyllable words. b. Know spellingsound correspondences for additional common vowel teams. c. Decode regularly spelled twosyllable words with long vowels. d. Decode words with common prefixes and suffixes. e. Identify words with inconsistent but common spellingsound correspondences. f. Recognize and read gradeappropriate irregularly spelled words. 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

a. Identify and know the meaning of the most common prefixes and derivational suffixes. b. Decode words with common Latin suffixes. c. Decode multisyllabic words. d. Read gradeappropriate irregularly spelled words. 
Use combined knowledge of all lettersound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context. 
Use combined knowledge of all lettersound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context. 

Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should assess where students are, determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to move students toward proficiency. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should assess where students are, determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to move students toward proficiency. 
Strand 
READING/KEY IDEAS AND DETAILS 

Standard 4 
Read various texts closely to determine what each text explicitly says and to make logical inferences; cite specific textual evidence to support conclusions drawn from the texts. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Ask and answer questions with prompting and support about who, what, when, where, and how. 
Ask and answer questions about who, what, when, where, and how. 
Ask and answer questions about who, what, when, where, how and why. 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers. 
Refer to details and examples in a text when explaining what the text says explicitly and when making inferences. 
Accurately quote details and examples from the text when explaining what the text says explicitly and when making inferences. 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
Cite several pieces of textual evidence that most strongly support an analysis of what the text says explicitly as well as inferences drawn from the text. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
Cite strong and thorough textual evidence to support analysis of various texts in ways that demonstrate what the text(s) says explicitly and implicitly, including attending to moments of textual inconsistency or ambiguity. 
Strand 
READING/KEY IDEAS AND DETAILS 

Standard 5 
Provide an accurate summary of various texts; determine the central idea(s) or theme(s) and analyze its development throughout each text. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Retell familiar texts with prompting and support, including details about who, what, when, where, and how. b. Retell key details of texts with prompting and support, including the main topic. 
a. Retell texts, including details about who, what, when, where, and how; demonstrate an understanding of the theme. b. Retell key details of texts, including the main topic. 
a. Retell texts, including details about who, what, when, where, how, and why; demonstrate understanding of the theme. b. Identify the main topic of a multiparagraph text and the central ideas of specific paragraphs. 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Retell texts, including details about who, what, when, where, why and how; explain how the theme is supported. b. Explain how the key details support the central idea of a text. 
a. Summarize texts, including details about who, what, when, where, how and why; explain how the theme is supported. b. Summarize texts, including how the key details support the central idea. 
a. Summarize texts, including theme and character development. b. Summarize texts, including how the key details support two or more central ideas. 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Provide an accurate summary of various texts; b. Determine theme(s) or central idea(s) and analyze how its development is conveyed over the course of the texts, including its relationship to specific supporting details. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
a. Provide accurate summaries of various texts that make clear the relationships among the key details and ideas. b. Determine the theme(s) or central idea(s) of various texts and analyze the development of the theme(s) or central idea(s) over the course of the texts, including how elements interact and build on one another, to provide a complex account or analysis. 
Strand 
READING: KEY IDEAS AND DETAILS 

Standard 6 
Analyze how and why individuals, events, and ideas develop and interact over the course of a text. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. With prompting and support, identify characters, settings, and major events in a story. b. With prompting and support, describe the connection between two individuals, events, ideas, or pieces of information in a text. 
a. Describe characters, settings, and major events in a story, including details about who, what, when, where, and how. b. Describe the connection between two individuals, events, ideas, or pieces of information in a text. 
a. Describe how characters in a story respond to major events and challenges. b. Describe the relationship between a series of events, ideas or concepts, using language that pertains to time, sequence, and cause/effect. 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Describe in depth a character, setting, or event in a story, drawing on specific details in the text (e.g., a character's thoughts, words, or actions). b. Explain the relationship between events, ideas or concepts, using language that pertains to time, sequence, and cause/effect, based on information from the text. 
a. Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events, drawing on specific details in the text. b. Explain the relationships or interactions between two or more individuals, events, ideas, or concepts, explicitly referring to specific information from the text. 
a. Analyze how two or more characters, settings, or events in a story are related, drawing on specific details in the text (e.g., how characters interact). b. Analyze relationships or interactions between individuals, events, ideas, or concepts throughout the text. 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
Analyze in detail how an author develops individuals/characters, events, ideas, elements and/or techniques to create interactions over the course of a text (or a series of texts). 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
Analyze the impact of an author's choices and determine how specific individuals/characters, elements and/or techniques, events, or ideas interact and develop over the course of the text (or a series of texts). 
Strand 
READING: CRAFT AND STRUCTURE 

Standard 7 
Interpret words and phrases as they are used in various texts, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. With prompting and support, ask and answer questions about unknown words in a text. b. With prompting and support, ask and answer questions about unknown words in a text. 
a. Identify words and phrases in a text that suggest feelings or appeal to the senses. b. Ask and answer questions to help determine or clarify the meaning of words and phrases in a text. 
a. Describe how words and phrases supply rhythm and meaning in a text. b. Use provided resources to determine meaning of words and phrases in a text. 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Determine the meaning of words and phrases as they are used in a text, distinguishing literal from figurative language. b. Use provided resources to determine meaning of domainspecific words and phrases. 
a. Determine the meaning of words and phrases including figurative language as they are used in a text. b. Draw on a variety of strategies to determine meaning of domainspecific words and phrases. 
a. Determine the meanings of words and phrases including figurative language and connotations as they are used in a text. b. Initiate strategies to determine meaning of domainspecific words and phrases. 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
Determine the meaning of figurative, connotative, and technical word meanings and phrases as they are used in various texts; analyze the impact of specific word choices and techniques on meaning and tone. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
Determine the meaning of figurative, connotative, and technical word meanings and phrases as they are used in various contexts and texts; analyze the impact of specific word choices on meaning and tone, including words with multiple meanings and/or language that is particularly evocative. 
Strand 
READING: CRAFT AND STRUCTURE 

Standard 8 
Analyze the structure of various texts, including how the features and components relate to each other and the whole. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Identify texts that tell stories. b. Identify texts that provide information. 
a. Explain major differences between texts that tell stories and texts that give information, drawing on various text types. b. Determine and use text features (e.g., headings, bold print, indexes, graphics, tables of contents, glossaries, links, icons) that help locate key facts or information in a text. 
a. Describe the overall structure of a text, including describing how the beginning introduces the story and the ending concludes the action. b. Explain how various text features (e.g., headings, bold print, indexes, graphics, tables of contents, glossaries, links, icons) are used to locate key facts or information in a text efficiently. 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Refer to parts of a text (e.g. chapters, scenes, or stanzas) and explain how each successive part builds on earlier sections. b. Use various text features (e.g., headings, bold print, indexes, graphics, tables of contents, glossaries, links, icons) to locate key facts or information in a text efficiently. 
a. Explain how individual parts of a text (e.g., chapters, scenes, or stanzas) work together to provide meaning to the text as a whole. b. Identify the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of a text and explain how the text features help support the overall structure. 
a. Explain how the text's structure supports its meaning and the author's purpose of the text as a whole. b. Compare and contrast the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in two or more texts on the same topic. 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
Analyze how the organization and structure of specific features and components in various texts develop ideas and/or meaning, contributing to the author's purpose for the text as a whole. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
a. Analyze the organization and structure of specific features and components in various texts b. Evaluate the effectiveness of text structures in conveying the overall meaning and/or purpose of the text as a whole. 
Strand 
READING: CRAFT AND STRUCTURE 

Standard 9 
Assess how perspective or purpose shapes the content and style of various texts. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. With prompting and support, name the author and illustrator of a story and define the role of each in telling the texts. b. With prompting and support, name the author and illustrator of a text and define the role of each in presenting the ideas or information in a text. 
a. Identify who is telling the story at various points in a text. b. Distinguish between information provided by pictures or other illustrations and information provided by the words in a text. 
a. Acknowledge differences in the points of view of characters b. Identify the main purpose of a text, including what the author wants to answer, explain, or describe. 

Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Distinguish the reader's personal point of view from that of the narrator or those of the characters. b. Distinguish the reader's personal point of view from that of the author of a text. 
a. Compare and contrast the point of view from which different texts are narrated, including the difference between first and thirdperson narrations. b. Compare and contrast primary and secondary sources of the same event or topic; describe the differences in perspective based on information in the texts. 
a. Describe how a narrator's or speaker's point of view influences how events are described in various contexts. b. Analyze multiple accounts and/or contexts of the same event or topic, noting important similarities and differences in the perspectives they represent based on information in the texts. 

Grade Span 
Early Adolescence 

Grades 68 

Analyze how and why authors from various contexts (e.g. diverse, intersectional, multicultural, religious) use perspective for intended purposes and/or audiences. 

Grade Span 
Adolescence 

Grades 9Diploma 

Analyze and evaluate how authors from various contexts (e.g. diverse, intersectional, multicultural, religious) use perspective and purpose to shape the intended content, style, and effect of various texts. 
Strand 
READING: INTEGRATION OF KNOWLEDGE AND IDEAS 

Standard 10 
Evaluate the argument and specific claims in various texts. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
With prompting and support, identify the reasons an author or character gives to support points in a text. 
Identify the reasons an author or character gives to support points in a text. 
Describe how reasons support specific points an author or character makes in a text. 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Explain how an author or character uses reasons and evidence to support a claim in a text. 
Explain how an author or character uses reasons and evidence to support a claim in a text, identifying which reasons and evidence support the claim(s). 
a. Trace the organization and development of a claim in a text. b. Determine the effectiveness of an author's or character's claim. 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Distinguish among fact, opinion, evidence, reasoning, and qualifying statements in a text. b. Evaluate the effectiveness of how an author or character develops the argument. c. Assess the validity and reasoning of the argument, considering if the argument is relevant and sufficient. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
a. Evaluate the effectiveness of how authors use literary and/or rhetorical strategies to develop arguments in various texts. b. Evaluate the premises, claims, and/or conclusions in various texts, verifying the information when possible and corroborating or challenging conclusions with other sources of information. 
Strand 
READING: INTEGRATION OF KNOWLEDGE AND IDEAS 

Standard 11 
Analyze and evaluate content presented in various texts (e.g. literary, historical, visual, artistic, quantitative, and technological). 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. With prompting and support, describe the relationship between illustrations and the text. b. With prompting and support, compare and contrast the experiences of characters in two or more familiar texts. c. With prompting and support, describe the relationship between the text and what person, place, thing, or idea the illustration depicts. d. With prompting and support, compare and contrast two texts on the same topic. 
a. Use illustrations and words in a text to describe its characters, setting, or events. b. Compare and contrast the experiences of characters in various texts. c. Use the illustrations and details in a text to describe its central idea. d. Compare and contrast two texts on the same topic. 
a. Use illustrations and words in a print or digital text to demonstrate understanding of its characters, setting, or plot. b. Compare and contrast two or more versions of the same story presented in diverse forms c. Explain how specific visuals contribute to and clarify the meaning of a text. d. Compare and contrast the information presented by two texts on the same topic. 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Explain how specific aspects of a text's illustrations contribute to the meaning of a text (e.g., create mood, emphasize aspects of a character or setting). b. Compare and contrast themes, settings, characters, and plots of stories. c. Use information gained from the text features and the words within to demonstrate an understanding of the whole text. d. Compare and contrast the key details presented in two texts on the same topic 
a. Compare and contrast between texts and other multimedia versions and how it influences the meaning and author's intent. b. Compare and contrast similar themes, topics, and patterns of events in texts. c. Interpret information presented in diverse forms and explain how the information contributes to an understanding of an idea or topic. 
a. Analyze how diverse forms and their features contribute to the meaning, tone, and author's intent of a text. b. Compare and contrast how two or more authors of the same text type interpret similar themes and topics. c. Draw on information presented in various texts in order to answer a question or to solve a problem. 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Analyze how two or more authors of various texts present information by emphasizing different interpretations of a theme and/or topic. b. Evaluate the advantages and disadvantages of an author's choice for using a specific form and/or text type. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
a. Evaluate and synthesize multiple sources of information and various texts (e.g., literary, visual, artistic, and quantitative) in order to achieve a specific purpose or to answer a question. b. Analyze how various authors or texts address similar themes or topics in order to build knowledge or to compare the approaches the authors take. c. Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of an idea or event, noting discrepancies among perspectives. 
Strand 
READING: FLUENCY 

Standard 12 
Read with sufficient accuracy and fluency to support comprehension 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Read emergentreader texts with purpose and understanding. 
a. Read various onlevel text with purpose and understanding. b. Read various onlevel text with accuracy, appropriate rate, and expression on successive readings. c. Use context to confirm or selfcorrect word recognition and understanding, rereading as necessary. 
a. Read various onlevel text with purpose and understanding. b. Read various onlevel text orally with accuracy, appropriate rate, and expression on successive readings. c. Use context to confirm or selfcorrect word recognition and understanding, rereading as necessary. 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Read various onlevel text with purpose and understanding. b. Read various onlevel text with accuracy, appropriate rate, and expression on successive readings c. Use context to confirm or selfcorrect word recognition and understanding, rereading as necessary. 
a. Read with sufficient accuracy and fluency to support comprehension. b. Read various onlevel text with purpose and understanding. c. Read various onlevel text with accuracy, appropriate rate, and expression on successive readings. d. Use context to confirm or selfcorrect word recognition and understanding, rereading as necessary. 
a. Read with sufficient accuracy and fluency to support comprehension. b. Read various onlevel text with purpose and understanding. c. Use context to confirm or selfcorrect word recognition. 
Grade Span 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Read with sufficient accuracy and fluency to support comprehension. b. Read various onlevel texts with purpose and understanding. c. Use context to confirm or selfcorrect word recognition. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
a. Read with sufficient accuracy and fluency to support comprehension. b. Read various onlevel texts with purpose and understanding. c. Use context to confirm or selfcorrect word recognition. 
WRITING
Writing is a lifelong, essential tool for communication. In order to prepare students for varied and evolving writing tasks, students should write routinely, in both long and short time frames, as a means of building writing stamina. Moreover, students should write in a breadth of modes and forms across all disciplines. This includes the foundational instruction of legible handwriting forms and skills such as printing, cursive, typing, as well as the use of technology to compose, where the use of formatting supports the task, audience, and purpose.
In order to manage the increasing complexity of what students read and write, educators provide guidance and support when developmentally appropriate, with the understanding that students need to develop autonomy and independence over time, particularly at the upper grade levels. To that end, the standards include a developmentally appropriate progression of performance expectations that includes all grade levels. The K5 performance expectations reflect a foundational level of skill acquisition, while the 68 and 9Diploma grade bands expect that writing grows in sophistication and complexity.
The strand of writing includes three standards, which have been arranged to reflect a traditional learning progression in the classroom, incorporating the use of technology when authentic to the task. Students begin with an exploration of a variety of texts/ideas, then use a process to refine, plan, and craft the communication of ideas, and finally compose with a style that reflects awareness of task, audience, and purpose. The standard and performance expectations for composing are consistent regardless of mode; therefore, the performance expectations for common modes (argument/opinion, informational/expository, and narrative) have been outlined in supporting documents.
Strand 
WRITING: Inquiry to Build and Present Knowledge 

Standard 1 
Use an inquiry process to gather relevant, credible information/evidence from a variety of sources (e.g., print, digital, discussions, etc.) that build understanding of and lead to conclusions about a subject under investigation while avoiding plagiarism. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Investigate questions by participating in shared research and writing projects. b. Gather information from provided sources and/or recall information from experiences in order to answer questions with guidance and support from adults. 
a. Investigate questions by participating in shared research and writing projects. b. Gather information from provided sources and/or recall information from experiences in order to answer questions with guidance and support from adults. 
a. Investigate questions by participating in shared research and writing projects. b. Gather information from provided sources and/or recall information from experiences in order to answer questions. 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Investigate questions by participating in research that builds knowledge about a topic. b. Gather information from a variety of sources and/or recall information from experiences in order to answer questions. c. Take brief notes on sources and sort information into provided categories. 
a. Investigate questions by participating in research that builds varied knowledge about a topic. b. Gather relevant information from a variety of sources and/or recall information from experiences in order to answer questions. c. Take notes on sources and sort information into provided categories. d. Provide a list of sources. 
a. Investigate and generate questions by participating in research that builds varied knowledge about a topic. b. Gather relevant information from a variety of sources and/or recall information from experiences in order to answer questions. c. Summarize or paraphrase notes on sources and sort information into provided categories. d. Provide a list of sources. 
Grade Span 
Early Adolescence 

Grade 68 

Performance Expectations 
a. Investigate selfgenerated questions by participating in inquiry that builds increasingly complex knowledge, refocusing inquiry as needed. b. Assess the credibility and accuracy of a variety of sources in order to gather relevant information that leads to conclusions. c. Take organized notes that purposefully quote, summarize, and/or paraphrase a variety of sources while avoiding plagiarism. d. Follow a standard format for citation (intext and a list of sources) that applies to task, audience, and purpose. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
a. Investigate selfgenerated questions by participating in sustained inquiry that builds increasingly complex knowledge or that solves a problem, refocusing inquiry and/or incorporating effective advanced searches as needed. b. Assess the credibility, accuracy, and usefulness of a variety of authoritative sources in order to synthesize relevant information that leads to logical, increasingly complex conclusions. c. Take organized notes that purposefully quote, summarize, and/or paraphrase a variety of sources while avoiding plagiarism and overreliance on any one source. d. Follow a standard format for citation (intext and a list of sources) that applies to task, audience, and purpose. 
Strand 
WRITING: Process and Production 

Standard 2 
Develop, strengthen, and produce polished writing by using a collaborative process that includes the ageappropriate use of technology. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. With guidance and support from adults, respond to questions and suggestions from peers and add details to strengthen writing as needed. b. With guidance and support from adults, explore a variety of digital tools to produce and publish writing, including peer collaboration. 
a. With guidance and support from adults, focus on a topic, respond to questions and suggestions from peers, and add details to strengthen writing as needed. b. With guidance and support from adults, use a variety of digital tools to produce and publish writing, including peer collaboration. 
a. With guidance and support from adults and peers, focus on a topic and strengthen writing as needed by revising and editing. b. With guidance and support from adults, use a variety of digital tools to produce and publish writing, including peer collaboration. 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. b. With guidance and support from adults, use technology to produce writing, as well as to interact and collaborate with others. c. Develop keyboarding skills. 
a. With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. b. With some guidance and support from adults, use technology to produce writing, as well as to interact and collaborate with others. c. Demonstrate sufficient command of keyboarding skills to produce sustained writing of increasing length. 
a. With guidance and support from peers and adults, develop and strengthen writing as needed by planning, composing, revising, editing, rewriting, reflecting, and/or trying a new approach. b. With some guidance and support from adults, use technology to produce writing, as well as to interact and collaborate with others. c. Demonstrate sufficient command of keyboarding skills to produce sustained writing of increasing length. d. 
Grade Span 
Early Adolescence 

Grade 68 

Performance Expectations 
a. With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, composing, revising, editing, rewriting, reflecting, and/or trying a new approach, focusing on how well purpose and audience have been addressed. b. Use technology to produce writing, as well as to interact and collaborate with others. c. Demonstrate and maintain command of keyboarding skills to produce sustained writing of increasing length. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
a. Develop and strengthen writing as needed by planning, composing, revising, editing, rewriting, reflecting, and/or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. b. Use technology and ongoing feedback, including new arguments and information, to produce increasingly dynamic writing products. c. Demonstrate and maintain command of keyboarding skills to produce sustained writing of increasing length. 
Strand 
WRITING: Composing for Audience and Purpose 

Standard 3 
Routinely produce a variety of clear and coherent writing in which the development, organization, and style are appropriate to task, audience, and purpose. 

Grade 
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Print many upper and lowercase letters. b. Use a combination of drawing and writing to communicate a topic. 
a. Print all upper and lowercase letters. b. Use a combination of drawing and writing to communicate a topic with details. 
Use a combination of drawing, and writing to communicate a topic with a beginning, middle (including details), and an end. 
Grade 
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Use a combination of illustrations and writing to produce pieces with introductions and bodies including details and conclusions. b. Develop the topic with relevant supporting details. c. Use developmentally appropriate linking words and phrases. d. Use precise vocabulary/word choice. e. Provide a sense of closure that is related to the ideas presented. 
a. Produce writing to communicate clearly and to organize increasingly complex pieces with introductions and bodies including details and conclusions. b. Develop the topic with relevant supporting details. c. Use developmentally appropriate linking words and phrases with increasing complexity. d. Use precise vocabulary/word choice. e. Provide a sense of closure that is related to the ideas presented. 
a. Produce writing to communicate clearly and organize increasingly complex pieces with introductions and bodies including details and conclusions. b. Develop the topic with relevant, logically ordered supporting details. c. Use developmentally appropriate linking words and phrases with increasing complexity. d. Use precise vocabulary/word choice. e. Provide a sense of closure that is related to the ideas presented. 
Grade Span 
Early Adolescence 

Grade 68 

Performance Expectations 
a. Compose clear and increasingly complex pieces with sections that are organized according to task, audience, and purpose. b. Develop and support the topic with relevant techniques and logically ordered details. c. Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas. d. Effectively use increasingly complex and precise language to establish an appropriate voice and tone. e. Provide a sense of closure that follows from, supports, and reflects the purpose of the piece. 

Grade Span 
Adolescence 

Grades 9Diploma 

Performance Expectations 
a. Compose clear and increasingly varied and complex pieces with purposefully designed sections that are organized to fully explore the depth and significance of ideas that are appropriate to task, audience, and purpose. b. Develop and support the topic with a variety of relevant techniques and by purposefully embedding the most significant details. c. Use appropriate and varied transitions, along with purposeful syntax, to create cohesion that clarifies relationships among increasingly complex ideas. d. Effectively use increasingly sophisticated, precise language to establish a highly developed voice and tone. e. Provide closure that enhances, supports, and reflects the purpose of the piece. 
HEALTH EDUCATION AND PHYSICAL EDUCATION
The Health Education and Physical Education Standards and performance expectations represent the essential knowledge and skills students need to be healthy individuals and lifelong learners. Being a lifelong learner involves the awareness and understanding of health and physical literacy. "Personal health literacy is the degree to which individuals have the ability to find, understand, and use information and services to inform health related decisions and actions for themselves and others." (US CDC). "Physical literacy is the ability to move with competence and confidence in a wide variety of physical activities in multiple environments that benefit the healthy development of the whole person" (SHAPE America). Social and emotional learning is naturally embedded in both health education and physical education. Students participate in an inclusive learning environment that values the interests of all Maine children through opportunities to learn and practice social and emotional skills and behaviors. Through achievement of the Health Education and Physical Education Standards, students will practice an active and balanced approach to life, take responsibility for their own wellness and contribute to the health and wellbeing of their own community.
Highly effective health education programsprovide students with knowledge and the skills to thrive physically, mentally, emotionally, and socially across their lifetime. Health education can assist students to be better consumers of information, manage the complex world around them and be more inclusive of others. Through an effective skillsbased health education curriculum, students will practice skills that protect, promote and enhance lifelong health.
Highly effective physical education programsprovide students with a variety of skills and knowledge that foster the confidence to be active for a lifetime. A physically literate individual is prepared with a foundation of knowledge and skill development, along with the tools to analyze their personal fitness. Students who participate in quality physical education on a regular basis understand the benefits of physical activity and how it contributes to a lifetime commitment to an active lifestyle.
Statutes
§ 4711. Elementary Course of Study, Mental Health and Reducing Stigma
§ 4712. Junior High or Middle School Course of Study, Mental Health and Reducing Stigma
§ 4723. Health and Physical Education including Affirmative Consent
§ 4502. School Approval Requirements 5b. Suicide Awareness Education And Training
§ 4502. School Approval Requirements  Child Sexual Abuse Prevention Education and Response
§ 6304. Automated external defibrillators and cardiopulmonary resuscitation
§ 6671. Youth Mental Health First Aid Training
§ 1902. Definitions, 1A Maine Comprehensive Family Life Education
§ 272. Tobacco Prevention and Control Program
Guiding Principles
The Guiding Principles guide education in Maine and should be reflected throughout the Health Education curriculum. Examples of how students can show evidence of those guiding principles in Health Education may include:
Strand Health Education 
Standard HE.1  Health Concepts 
Standard HE.2  Health Information, Products, and Services 
Standard HE.3  Health Promotion and Risk Reduction 
Standard HE.4  Influences on Health 
Standard HE.5  Communication and Advocacy Skills 
Standard HE.6  DecisionMaking and GoalSetting Skills 
Standard 1 
Health Concepts: Health literate students comprehend concepts related to health promotion and disease prevention to enhance health. 

Childhood 

Performance Expectations 
Kindergarten 
Grade 1 
Grade 2 
1.1 Health Concepts, Behaviors and Personal Health 
Students name basic healthy behaviors, including nutrition; personal health; and safety and injury prevention. 
Students name basic health terms and behaviors, including healthy relationships; nutrition; personal health; and safety and injury prevention. 
Students recognize healthy behaviors Including healthy relationships; nutrition; personal health; and safety and injury prevention. 
1.2 Dimensions of Health 
Students name the dimensions of health including physical and social health. 
Students identify dimensions of health including physical, mental, social, emotional and health. 
Students recognize the multiple dimensions of health including physical, mental, social and emotional.. 
1.3 Health Conditions 
Students list prevention strategies for common childhood communicable diseases. 
Students identify the transmission and prevention of common childhood communicable diseases. 
Students describe the transmission and prevention of common childhood communicable diseases. 
1.4 Environment and Personal Health 
Students list qualities of a safe and healthy school environment. 
Students identify ways a safe and healthy school environment can promote personal health. 
Students describe ways a safe and healthy school environment can promote personal health. 
1.5 Growth and Development 
Students name personal and public body parts. 
Students label personal and public body parts. 
Students recognize that the body changes throughout the lifespan. 
Performance Expectations 
Grade 3 
Grade 4 
Grade 5 
1.1 Health Concepts, Behaviors and Personal Health 
Students describe how healthy behaviors impact personal health, including healthy relationships; nutrition; safety and injury prevention; and substance use prevention. 
Students describe how healthy and unhealthy behaviors impact personal health, including healthy relationships; nutrition; safety and injury prevention; and substance use prevention. 
Students predict how healthy and unhealthy behaviors affect personal health, including healthy relationships; nutrition; safety and injury prevention; and substance use prevention. 
1.2 Dimensions of Health 
Students recall the dimensions of health including physical, mental, social and emotional. 
Students define the dimensions of health including physical, mental, social and emotional. 
Students explain the dimensions of health including physical, mental, social and emotional. 
1.3 Health Conditions 
Students identify ways to prevent and detect common childhood health conditions. 
Students identify ways to prevent, detect, treat, and/or manage common childhood health conditions. 
Students describe ways to prevent, detect, treat, and/or manage common childhood health conditions. 
1.4 Environment and Personal Health 
Students explain ways a safe and healthy environment can promote personal health. 
Students explain ways a safe and healthy environment can positively and negatively impact personal health. 
Students identify current health issues that relate to one's environment and the impact on personal health. 
1.5 Growth and Development 
Students recognize that bodies change at different rates. 
Students explore ways their bodies grow, change, and develop through adolescence. 
Students describe how their bodies grow, change, and develop physically, mentally, socially, and emotionally through adolescence. 
Early Adolescence 

Performance Expectation 
Grades 6  8 

1.1 Health Concepts, Behaviors and Personal Health 
Students explain the importance of assuming responsibility for behaviors and the impact it has on personal health related to healthy sexuality; nutrition; safety and injury prevention; and substance abuse prevention. 

1.2 Dimensions of Health 
Students explain the interrelationship of the dimensions of health including physical, mental, social and emotional. 

1.3 Health Conditions 
Students investigate causes of health conditions and ways to reduce, prevent, treat, and/or manage them. 

1.4 Environment and Personal Health 
Students determine how the environment and other factors impact personal health. 

Adolescence 

Performance Expectation 
Grades 9  Diploma 

1.1 Health Concepts, Behaviors and Personal Health 
Students analyze the impact of complex health issues on personal health related to healthy sexuality; nutrition; safety and injury prevention; and substance abuse prevention. 

1.2 Dimensions of Health 
Students analyze the impact of current health issues on the dimensions of health including physical, mental, social and emotional. 

1.3 Health Conditions 
Students analyze causes of health conditions and ways to reduce, prevent, treat, and/or manage them. 

1.4 Environment and Personal Health 
Students analyze how one's environment and other factors impact personal health. 
Standard 2 
Health Information, Products, and Services: Health literate students can demonstrate the ability to access valid health information, services, and products to enhance health. 

Childhood 

2.1 Reliability of Resources 
Students label trusted adults and professionals who can help promote health. 
Students identify trusted adults and professionals who can help promote health. 
Students describe the characteristics of trusted adults and professionals who can help promote health. 

2.2 Locating Health Resources 
Students identify school and community health helpers. 
Students identify the locations of school and community health helpers. 
Students describe ways to locate school and community health helpers. 

Performance Expectations 
Grade 3 
Grade 4 
Grade 5 

2.1 Reliability of Resources 
Students identify characteristics of reliable health information, products, and trusted adults. 
Students describe characteristics of reliable health information, products, and trusted adults. 
Students compare and contrast characteristics of reliable health information, products, and trusted adults. 

2.2 Locating Health Resources 
Students identify resources from home, school, and the community that provide reliable health information. 
Students explore resources from home, school, and the community that provide reliable health information. 
Students locate resources from home, school, and the community that provide reliable health information. 

Early Adolescence  
Performance Expectation 

2.1 Reliability of Resources 
Students analyze the reliability of health information, products, and services. 

2.2 Accessing Health Resources 
Students locate reliable health information, products, and services. 

Adolescence  
Performance Expectation 

2.1 Reliability of Resources 
Students evaluate the reliability and accessibility of health information, products, and services. 

2.2 Accessing Health Resources 
Students access reliable health information, products, and services. 

2.1 Reliability of Resources 
Students label trusted adults and professionals who can help promote health. 
Standard 3 
Health Promotion and Risk Reduction: Health literate students demonstrate the ability to practice healthenhancing behaviors and avoid or reduce health risks for self and others. 

Childhood 

Performance Expectations 
Kindergarten 
Grade 1 
Grade 2 

3.1 HealthEnhancing Behaviors and SelfManagement 
Students name healthenhancing behaviors to improve personal health including selfmanagement skills. 
Students describe healthenhancing behaviors to improve personal health including selfmanagement skills. 
Students apply healthenhancing behaviors to improve personal health including selfmanagement skills. 

3.2 Avoiding/Reducing Health Risks 
Students name behaviors to help avoid or reduce personal health risks. 
Students recognize behaviors to help avoid or reduce personal health risks. 
Students explain behaviors to help avoid or reduce personal health risks. 

Performance Expectations 
Grade 3 
Grade 4 
Grade 5 

3.1 HealthEnhancing Behaviors and SelfManagement 
Students examine healthenhancing behaviors to improve or maintain personal health including selfmanagement skills. 
Students explain healthenhancing behaviors to improve or maintain personal health including selfmanagement skills. 
Students demonstrate healthenhancing behaviors to improve or maintain personal health including selfmanagement skills. 

3.2 Avoiding/Reducing Health Risks 
Students examine a variety of behaviors to help avoid or reduce personal health risks to self and others. 
Students explain a variety of behaviors to help avoid or reduce personal health risks to self and others. 
Students demonstrate a variety of behaviors to help avoid or reduce health risks to self and others. 

Early Adolescence 

Performance Expectation 
Grades 6  8 

3.1 HealthEnhancing Behaviors and SelfManagement 
3.1.68a  Students explain the importance of assuming responsibility for personal health behaviors. 

3.1.68b  Students apply healthenhancing behaviors to improve or maintain the health of self and others, including selfmanagement skills. 

3.2 Avoiding/Reducing Health Risks 
Students demonstrate healthenhancing behaviors to avoid or reduce health risks to self and others. 

Adolescence 

Performance Expectation 
Grades 9  Diploma 

3.1 HealthEnhancing Behaviors and SelfManagement 
3.1.9Da  Students analyze the role of individual responsibility for enhancing health. 

3.1.9Db  Students evaluate healthenhancing behaviors to improve or maintain the health of self and others, including selfmanagement skills. 

3.2 Avoiding/Reducing Health Risks 
Students assess healthenhancing behaviors to avoid or reduce health risks to self and others. 
Standard 4 
Influences on Health: Health literate students analyze the influences of family, peers, culture, media, technology and other factors on health practices and behaviors. 

Childhood 

Performance Expectations 
Kindergarten 
Grade 1 
Grade 2 

4.1 Influences on Health Behaviors 
Students recognize people who influence their health behaviors. 
Students name people who influence their health behaviors. 
Students identify multiple influences on personal health behaviors including peers, family, and media. 

4.2 Effects of Health Behaviors 
Students recognize factors that influence health behaviors. 
Students identify factors that influence health behaviors. 
Students describe factors that influence health behaviors. 

Performance Expectations 
Grade 3 
Grade 4 
Grade 5 

4.1 Influences on Health Behaviors 
Students identify how a variety of factors influence personal health behaviors including peers, family, school, community, media, and technology. 
Students explore how a variety of factors influence personal health behaviors including peers, family, community, culture, media, technology, and social platforms. 
Students describe how a variety of factors influence personal health behaviors including peers, family, community, culture, media, technology, and social platforms. 

4.2 Effects of Health Behaviors 
Students list health behaviors that could influence future behaviors. 
Students identify how health behaviors could influence future behaviors. 
Students describe how health behaviors could influence future behaviors. 

Early Adolescence 

Performance Expectation 
Grades 6  8 

4.1 Influences on Health Behaviors 
Students analyze positive and negative influences on adolescent health practices and behaviors including peers, family, media, culture, community, technology, and social platforms. 

4.2 Compound Effects of Health Behaviors 
Students examine how healthenhancing and risky behaviors can influence the likelihood of engaging in more of the same behaviors. 

Adolescence 

Performance Expectation 
Grades 9  Diploma 

4.1 Influences on Health Behaviors 
Students evaluate positive and negative influences on health practices and behaviors including peers, family, media, culture, community, perception of norms, government, technology, and social platforms. 

4.2 Compound Effects of Health Behaviors 
Students analyze how healthenhancing and risky behaviors can influence the likelihood of engaging in more of the same behaviors. 
Standard 5 
Communication and Advocacy Skills: Health literate students demonstrate the ability to use interpersonal communication and advocacy skills to enhance personal, family, and community health. 

Childhood 

Performance Expectations 
Kindergarten 
Grade 1 
Grade 2 
5.1 Interpersonal Communication Skills 
Students name healthy and unhealthy ways to communicate. 
Students demonstrate healthy ways to communicate. 
Students describe verbal and nonverbal ways to communicate. 
5.2 Advocacy Skills 
Students name healthy ways to express their needs, wants, and feelings. 
Students recognize ways to ask for help to promote health for self and others. 
Students demonstrate ways to promote health for self and/or others. 
Performance Expectations 
Grade 3 
Grade 4 
Grade 5 
5.1 Interpersonal Communication Skills 
Students demonstrate effective communication skills to enhance personal health including written, facetoface and safe use of technology. 
Students demonstrate effective communication skills to enhance personal and family health including written, facetoface, and safe use of technology. 
Students demonstrate effective communication skills to enhance personal, family, and community health including written, facetoface, and safe use of technology. 
5.2 Advocacy Skills 
Students explore ways to promote health for self, others, and school. 
Students demonstrate ways to promote health for self, others, and school. 
Students demonstrate ways to share informed opinions to promote health for self and others. 
Early Adolescence 

Performance Expectation 
Grades 6  8 

5.1 Interpersonal Communication Skills 
Students apply effective interpersonal communication skills including affirmative consent, refusal and negotiation skills to enhance health and build relationships including written, facetoface, and safe use of technology. 

5.2 Advocacy Skills 
Students utilize advocacy skills for self and others to make positive health choices. 

Adolescence 

Performance Expectation 
Grades 9  Diploma 

5.1 Interpersonal Communication Skills 
Students analyze effective communication skills for self and others to enhance health and build relationships including affirmative consent, refusal and negotiation skills. 

5.2 Advocacy Skills 
Students analyze advocacy skills for self and others to make positive health choices. 
Standard 6 
DecisionMaking and GoalSetting Skills: Health literate students demonstrate the ability to make decisions and set goals to enhance health. 

Childhood 

Performance Expectations 
Kindergarten 
Grade 1 
Grade 2 
6. 1 DecisionMaking Skills 
Students name health situations where a decision is needed. 
Students identify health situations where a decision is needed. 
Students identify health situations where decisions can appropriately be made by the individual and when assistance is needed. 
6.2 GoalSetting Skills 
Students identify what health goals are. 
Students explore when health goals are useful. 
Students identify resources to help achieve a personal health goal. 
Performance Expectations 
Grade 3 
Grade 4 
Grade 5 
6.1 DecisionMaking Skills 
Students identify a decisionmaking process to enhance health. 
Students describe when to use a decisionmaking process to enhance health. 
Students apply a decision making process to enhance health. 
6.2 GoalSetting Skills 
Students identify the goalsetting process to enhance health. 
Students describe when to use a goalsetting process to enhance health. 
Students practice the goalsetting process to achieve a personal health goal. 
Early Adolescence 

Performance Expectation 
Grades 6  8 

6.1 DecisionMaking Skills 
Students apply decisionmaking skills to enhance health as an individual and through collaboration. 

6.2 GoalSetting Skills 
Students apply goalsetting skills to achieve a personal shortterm health goal. 

Adolescence 

Performance Expectation 
Grades 9  Diploma 

6.1 DecisionMaking Skills 
Students analyze decision making skills to enhance health outcomes. 

6.2 GoalSetting Skills 
Students analyze goalsetting skills to achieve short and/or longterm personal health goals. 
Strand Physical Education 
Standard PE. 1  Motor Skills and Movement Patterns 
Standard PE. 2  Concepts and Strategies 
Standard PE. 3  Fitness Education 
Standard PE. 4  Responsible Personal and Social Behavior 
Standard PE. 5  Recognition of the Value of Physical Activity 
Standard 1 
Motor Skills and Movement Patterns: Physically literate students demonstrate competency in a variety of motor skills and movement patterns. 

Childhood 

Performance Expectations 
Kindergarten 
Grade 1 
Grade 2 
1.1 Locomotor Skills 
Practices critical elements of locomotor skills. 
Uses recognizable forms of basic locomotor skills in different pathways, levels or directions. 
Executes a combination of locomotor skills in different pathways, levels or directions. 
1.2 Nonlocomotor Skills 
Practices critical elements of nonlocomotor skills. 
Uses recognizable forms of nonlocomotor skills to move and control the body. 
Executes more complex nonlocomotor skills to move and control the body. 
1.3 Locomotor and Nonlocomotor Combination Skills 
Replicates locomotor skills in response to teacher led creative movement sequence. 
Combines locomotor and nonlocomotor skills in a teacher designed movement sequence. 
Performs a rhythmic activity with correct response to simple rhythms. 
1.4 Manipulative Skills 
Practices critical elements of basic manipulative skills. 
Uses critical elements of basic manipulative skills. 
Executes a variety of manipulative skills while maintaining control of body and objects/ equipment. 
Performance Expectations 
Grade 3 
Grade 4 
Grade 5 
1.1 Locomotor Skills 
Demonstrates mature patterns of locomotor skills 
Demonstrates combinations of complex locomotor skills in various physical activity settings. 
Applies combinations of complex locomotor skills specific to individual, dual, and team activities. 
1.2 Nonlocomotor Skills: 
Demonstrates mature use of nonlocomotor skills. 
Demonstrates complex nonlocomotor skills in various activities. 
Applies combinations of complex nonlocomotor skills specific to individual, dual and team activities. 
1.3 Locomotor Nonlocomotor Combination Skills 
Performs teacherselected and developmentally appropriate dance steps and /or movement patterns. 
Combines locomotor movement patterns and dance steps to create and perform an original movement sequence. 
Combines locomotor skills and movement concepts with rhythm and patterns. 
1.4 Manipulative Skills 
Demonstrates critical elements of basic manipulative skills. 
Demonstrates maturing manipulative skills in a nondynamic environment. 
Applies maturing manipulative skills in individual, dual, and team activities. 
Early Adolescence 

Grades 6  8 

Performance Expectation 
Emerging 
Maturing 
Applying 
1.1 Movement and Rhythm 
Demonstrates rhythmic movement and patterns with emphasis in keeping the beat. 
Demonstrates rhythmic movement and patterns for different dances and activities. 
Exhibits command of rhythm and timing by creating a movement sequence as an individual or in a group. 
1.2 Game and Sport Skills 
Uses specialized skills that are refined and appropriate for modified game play. 
Demonstrates complex combinations of movements specific to at least two game, sport, or physical activities. 
Executes complex combinations of movements specific to at least two game, sport, or physical activities. 
1.3 Offensive and Defensive Skills 
Demonstrates basic offensive and defensive movement skills for games, sports or physical activities. 
Performs basic offensive and defensive movement skills for games, sports or physical activities. 
Applies offensive and defensive movement skills for at least two games, sports or physical activities that contribute to successful participation. 
1.4. Lifetime Activities 
Demonstrates basic skills in individual performance or outdoor lifetime activities. 
Performs basic skills in individual performance or outdoor lifetime activities. 
Applies skills in at least two individual performance or outdoor lifetime activities that contribute to successful participation. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
Level 1 
Level 2 

1.1 Movement and Rhythm 
Creates movement combinations in rhythmic activities with an emphasis on keeping to the beat. 
Performs movement combinations in rhythmic activities with an emphasis on keeping to the beat. 

1.2 Game and Sport Skills 
Applies basic and/or advanced skills to participate proficiently in at least three individual, dual, or team games, sports or physical activities. 
Refines basic and/or advanced skills to participate proficiently in at least three individual, dual, or team games, sports or physical activities. 

1.3 Lifetime Activities 
Demonstrates competency and/or refines activityspecific movement skills in a variety of lifetime activities. 
Refines activityspecific movement skills in a variety of lifetime activities. 
Standard 2 
Concepts and Strategies : Physically literate students apply knowledge of concepts, principles, strategies and tactics related to movement and performance. 

Childhood 

Performance Expectations 
Kindergarten 
Grade 1 
Grade 2 
2.1 Movement Concepts 
Demonstrates a variety of movements associated with basic motor performance. 
Utilizes basic motor movements in activity and game play. 
Demonstrates basic motor performance in conjunction with manipulative skills. 
2.2 Strategies and Tactics 
Uses teacher feedback to improve basic form and function. 
Uses teacher feedback to improve basic motor performance in conjunction with manipulative skills. 
Understands/explains the importance of feedback as it relates to improved motor performance. 
Performance Expectations 
Grade 3 
Grade 4 
Grade 5 
2.1 Movement Concepts 
Utilizes basic motor movements and manipulative skills during activity and games. 
Applies basic concepts of movement to improve individual (personal) performance. 
Assesses movement and game skills to provide feedback for improvement. 
2.2 Strategies and Tactics 
Demonstrates basic strategies and tactics for modified activities and games. 
Utilizes basic strategies and tactics for a variety of activities and games. 
Demonstrates basic offense and defense strategies in modified games and activities. 
Early Adolescence 

Grades 6  8 

Performance Expectations 
Emerging 
Maturing 
Applying 
2.1 Movement Concepts 
Applies advanced movement concepts to enhance game play/activities. 
Applies concepts from other content areas (i.e. physics, geometry) to movement skills. 
Utilizes complex movement principles to evaluate and improve performance. 
2.2 Strategies and Tactics 
Explains when and why strategies and tactics are utilized in game play and activities. 
Demonstrates game strategies and tactics at appropriate times and using appropriate methods. 
Applies appropriate game strategies and tactics during game play and activities. 
Adolescence 

Grades 9 Diploma 

Performance Expectations 
Level 1 
Level 2 

2.1 Movement Concepts 
Applies complex movement concepts to refine learned skills and acquire new, advanced skills 
Integrates increasing complex, contentspecific knowledge (biomechanics) with movement skills. 

2.2 Strategies and Tactics 
Applies/integrates appropriate game strategies and tactics during game play and activities. 
Creates and applies multiple offensive and defensive strategies for game play and activity. 
Standard 3 
Fitness Education: Physically literate students demonstrate the knowledge and skills to plan, execute, selfmonitor, achieve, and maintain a healthenhancing level of physical activity and/or fitness. 

Childhood 

Performance Expectations 
Kindergarten 
Grade 1 
Grade 2 
3.1 HealthRelated Fitness and Exercise. 
Identifies the physiological signs of moderate to vigorous physical activity, 
Identifies the physiological responses of moderate to vigorous physical activity. 
Identifies the physiological signs of moderate to vigorous physical activity and uses teachers' suggestions to modify intensity of the activity when needed. 
3.2 SkillRelated Fitness and Training 
Demonstrates control of body and space when performing skillrelated fitness components. 
Demonstrates control of body, movement, and space when performing skillrelated fitness components. 
Demonstrates control of body in space when performing skillrelated fitness components during game play and challenge activities. 
3.3 Training Principles for Fitness and Sport 
Participates in a teacherdirected workout that includes moderate to vigorous physical activities. 
Demonstrates proper technique when using one's own body as resistance. 
Classifies activities as light, medium, and/or difficult based on the response of the physiological responses of the body. 
3.4 Healthrelated and/or sport training and/or fitness plan 
Participates in a teacherdirected workout that includes moderate to vigorous physical activities. 
Participates in a teacherdirected workout that includes moderate to vigorous physical activities. 
Creates a simple workout plan using motor skill, movement concepts, healthrelated and/or skillrelated fitness components. 
3.5 Fitness, Sport, and Technology 
Participates in a teacherdirected skillrelated fitness, and/or dance/movement video resource at school. 
Participates in a teacherdirected skillrelated fitness, and/or dance/movement video resource at school. 
Participates in a teacherdirected skillrelated fitness, and/or dance/movement video resource at school and/or at home. 
3.6 Physical Activity, Community, 
Participates with family in activities that are enjoyable, challenging, fun and/or that allow for selfexpression. 
Participates with family or friends in activities that are enjoyable, challenging, fun and/or that allow for selfexpression. 
Identifies ways to be responsible for one's own fitness by choosing to be active at home or at school. 
Performance Expectations 
Grade 3 
Grade 4 
Grade 5 
3.1 HealthRelated Fitness and Exercise. 
Participates in exercises and/or activities and identifies muscle groups or body systems targeted. 
Participates in targeted activities to improve specific healthrelated fitness components demonstrating appropriate form, technique, and principles of exercise. 
Demonstrates appropriate form, technique, and principles and adjusts intensity to sustain activity 
3.2 SkillRelated Fitness and Training 
Participates in exercises and/or activities and identifies the skillrelated fitness component(s) targeted. 
Participates in exercises, movement patterns, and/or sport skill activities and identifies the skillrelated component(s) targeted. 
Uses one or more skillrelated fitness components used during exercise, movement patterns, or sport skill activities and identifies the skillrelated component targeted. 
3.3 Training Principles for Fitness and Sport 
Participates in workouts and identifies exercise and/or activities in each part of the workout. 
Participates in workouts and describes and/or explains body responses to physical activities 
Participates in workouts and describes and/or explains, measures and/or records body responses to physical activities. 
3.4 Healthrelated and/or sport training and/or fitness plan 
Uses movement or sport skills to create a simple workout that includes a warmup, workout, and cooldown. 
Creates and implements a workout plan using exercises and/or activities in one or more healthrelated components. 
Creates and implements a workout plan using exercises and/or activities utilizing skillrelated and/or healthrelated fitness components 
3.5 Fitness, Sport, and Technology 
Uses teacherdirected videoresources or apps to engage in fitness activities and/or skillpractice. 
Uses teacherdirected technology tools to engage in fitness or skillpractice activities at home or at school. 
Uses teacherdirected technology tools to measure or practice targeted lesson objectives. 
3.6 Physical Activity, Community, 
Participates actively in physical activities at recess. 
Participates in activities at school and/or outside of school, 
Identifies opportunities and participates in activities at school, outside of school, and in the community with family and friends. 
Early Adolescence 

Grades 6  8 

Performance Expectations 
Emerging 
Maturing 
Applying 
3.1 HealthRelated Fitness and Exercise. 
Demonstrates body positioning and/or technique when performing muscle strength, muscle endurance, and flexibility exercises. Identifies and/or classifies exercises and physical activities for each healthrelated fitness components 
Demonstrates proper body positioning and/or technique when executing muscle strength, muscle endurance, and flexibility exercises while engaged in healthrelated fitness activities (ex. Tabata, exercise circuit, etc.). Maintains a pace while walking, jogging, or running. 
Creates simple exercise routines and records workout data in a simple log. 
3.2 SkillRelated Fitness and Training 
Lists, defines, and explains skillrelated fitness components and uses components in exercises and/or games. 
Demonstrates improvements in skillrelated fitness exercises 
Creates a skillrelated fitness exercise circuit and records data in a personal log 
3.3 Training Principles for Fitness and Sport 
Uses training principles to improve fitness or sport performance. 
Uses measurement tools to identify intensity of exercise or activity 
Examines fitness data to improve fitness or sport performance 
3.4 Healthrelated and/or sport training and/or fitness plan 
Engages/follows a teacher created exercise plan demonstrating proper posture and technique when performing exercises. 
Designs and implements a personal fitness plan based on fitness or sport goals for physical education. 
Designs and implements a personal fitness plan for home based on fitness or sport goals. 
3.5 Fitness, Sport, and Technology 
Uses teacherdirected technology tools to engage in healthrelated fitness activities for skill practice or for enjoyment. 
Uses teacherdirected fitnessrelated technology tools to measure physical activity and/or practice lesson objectives. 
Selects and uses technology tools to monitor exercise programs or uses video resources to gain ideas to create a new exercise plan. 
3.6 Physical Activity, Community, 
Identifies and/or participates in physical activities at school, home, and/or in the community 
Participates in physical activities at school, home, and/or in the community 
Creates a plan to be active at home or in community activities. 
Adolescence 

Grades 9 Diploma 

Performance Expectations 
Level 1 
Level 2 

3.1 HealthRelated Fitness and Exercise. 
Executes with proper form and technique a wide variety of exercises in each of the healthrelated fitness components addressing all major muscle groups. Engages in cardiorespiratory activities. 
Analyzes one's personal preferences and/or choices of exercise and exercise tools for the benefits, risk, safety, accessibility, adherence, and enjoyment. Develops and maintains a fitness portfolio that includes. assessments, goals, activities, and a tracking system for personal improvement. 

3.2 SkillRelated Fitness and Training 
Participates and examines exercise programs that train each of the skillrelated fitness components. 
Designs or implements a training plan that incorporates one or more training principles. 

3.3 Training Principles for Fitness and Sport 
Applies training principles to healthrelated fitness exercise plans or a sport skill or sport fitness improvement plan. 
Evaluates performance data and applies training principles to revise healthrelated fitness or sport skill/fitness plan to improve performance. 

3.4 Healthrelated and/or sport fitness or training plan 
Creates, implements, monitors (log), reassess, and revises a personal healthrelated and/or sport fitness plan for home, community, and school. 
Creates, monitors (log), and revises one or more personal healthrelated and/or sport fitness plans implemented by one or more peers. 

3.5 Fitness, Sport, and Technology 
Investigates and uses available technology tools, applications, and connections on social media as tools for supporting a healthy, active lifestyle and/or to selfmonitor exercise and/or physical activity. 
Investigates and uses available technology tools, applications, and connections on social media as tools for supporting a healthy, active lifestyle and/or to selfmonitor exercise and/or physical activity. 

3.6 Physical Activity, Community 
Evaluates one or more recreation or sport activities that can be pursued in the local community and evaluates the activity and/or activities based on benefits, social support networks, and participation requirements. 
Evaluates one or more recreation or sport activities that can be pursued in the local community and evaluates the activity and/or activities based on benefits, social support networks, and participation requirements 
Standard 4 
Responsible Personal and Social Behavior: Physically literate students exhibit responsible personal and social behavior that respects self and others. 

Childhood 

Performance Expectation 
Kindergarten 
Grade 1 
Grade 2 
4.1 Personal Responsibility 
Uses basic strategies, concepts, and communication skills for working cooperatively in group settings. Acknowledges responsibility for behavior when prompted. 
Uses basic strategies, concepts, and communication skills for working cooperatively in group settings. Accepts personal responsibility for behavior. 
Explains the value of working cooperatively in group settings. Accepts personal responsibility for behavior. 
4.2 Working with Others 
Demonstrates cooperative skills. Understands how social interaction can make activities more enjoyable. 
Demonstrates cooperative skills. Understands how social interaction can make activities more enjoyable. 
Demonstrates cooperative skills. Summarizes the benefits of positive social interaction to make activities more enjoyable. 
4.3 Rules, Etiquette, and Safety 
Uses safe practices when engaging in physical education activities. 
Uses safe practices when engaging in physical education activities. 
Uses safe practices when engaging in physical education activities with little or no prompting. 
Childhood 

Performance Expectation 
Grade 3 
Grade 4 
Grade 5 
4.1 Personal Responsibility 
Uses selfcontrol to demonstrate personal responsibility and respect for self and others. 
Uses selfcontrol through structure, expectations, and engagement to demonstrate personal responsibility and respect for self and others. 
Uses selfcontrol to work independently in developing responsibility and respect for self and others. 
4.2 Working with others 
Demonstrates cooperation and communication skills to achieve common goals. Explains the importance of working productively with others. 
Demonstrates cooperation and communication skills to achieve common goals. Understands the importance of culture and ethnicity in developing selfawareness and working productively with others. 
Demonstrates cooperation and communication skills to achieve common goals. Understands the importance of culture and ethnicity in developing selfawareness and working productively with others. 
4.3 Rules, Etiquette, and Safety 
Uses safe practices when engaging in physical education activities with little or no prompting. 
Uses safe practices when engaging in physical education activities without prompting. 
Uses safe practices when engaging in physical education activities without prompting. 
Early Adolescence 

Grades 6  8 

Performance Expectation 
Emerging 
Maturing 
Applying 
4.1 Personal Responsibility 
Exhibits personal responsibility by using appropriate strategies to seek greater independence from adults, and reinforce positive behaviors, when completing assigned tasks. 
Demonstrates personal responsibility by using a variety of appropriate strategies to seek greater independence from adults, and reinforce positive behaviors, when completing assigned tasks. 
Demonstrates personal responsibility by working independently from adults. Consistently applies strategies to reinforce positive behaviors when completing assigned tasks. 
4.2 Cooperative Skills 
Uses welldeveloped cooperation skills to accomplish group goals in both cooperative and competitive situations. Analyzes conflicts that arise in competitive activities to determine the most appropriate ways of resolving the conflicts. 
Contrasts between appropriate and inappropriate strategies for communicating ideas and feelings. Understands the role of diversity in physical activity, respecting limitations and strengths of members of a variety of groups. 
Exemplifies welldeveloped cooperation skills to accomplish group goals in both cooperative and competitive situations. Compares factors in different cultures and/or social settings that influence the choice of physical activity. 
4.3 Rules, Etiquette, and Safety 
Uses safe practices when engaging in physical education activities without prompting. 
Uses safe practices when engaging in physical education activities without prompting. 
Uses safe practices when engaging in physical education activities without prompting. 
Adolescence 

Grades 9  Diploma 

Performance Expectations 
Level 1 
Level 2 

4.1 Personal Responsibility 
Demonstrates personal responsibility in all physical education activities. 
Implements leadership skills to promote responsibility in self and others. 

4.2 Cooperative Skills 
Apply appropriate communication and cooperative skills including problem solving and resolving conflict in a variety of physical activities and team or group situations. Compares factors in different cultures and/or social settings that influence the choice of physical activity. 
Selects the most appropriate ways of responding and mediation to settle conflicts. Explains the influence of physical activity on cultural competence and the development of selfawareness 

4.3 Rules, Etiquette, and Safety 
Uses safe practices when engaging in physical education activities. 
Uses safe practices when engaging in physical education activities. 
Standard 5 
Recognition of the Value of Physical Activity: Physically literate students recognize the value of physical activity for health, enjoyment, challenge, selfexpression, and /or social interaction. 

Childhood 

Performance Expectations 
Kindergarten 
Grade 1 
Grade 2 
5.1 Health 
Recognizes that physical activity is important to good health. 
Identifies that physical activity is a component of good health. 
Recognizes the value of physical activity for good health. 
5.2 Challenge 
Understands that some physical activities are challenging. 
Recognizes challenges when learning a new physical activity. 
Recognizes that perseverance in physical activities can lead to improvement 
5.3 Selfexpression and Enjoyment 
Identifies positive feelings that result from participating in physical activity. 
Describes physical activities that are enjoyable. 
Describes reasons for enjoying physical activity. 
5.4 Social Interaction 
Recognizes that physical activity can help develop friendships. 
Identifies that physical activity promotes opportunity for social interaction 
Understands that physical activities can foster cooperation 
Childhood 

Performance Expectations 
Grade 3 
Grade 4 
Grade 5 
5.1 Health 
Discusses the relationship between physical activity and health. 
Examines the health benefits of participating in physical activity. 
Compares the health benefits of participating in selected physical activities. 
5.2 Challenge 
Describes how practice develops confidence in challenging physical activities 
Understands that improving performance in challenging physical activities requires consistent practice 
Explains how to overcome challenges essential for improvement 
5.3 Selfexpression and Enjoyment 
Identifies physical activities that provide opportunities for selfexpression. 
Identifies physical activities for the purpose of selfexpression and enjoyment. 
Analyzes how various physical activities promote selfexpression and enjoyment. 
5.4 Social Interaction 
Describes how physical activities can promote positive social interactions 
Describes social benefits gained from participating in physical activity. Describe physical activities that promote camaraderie. 
Describes social benefits of engaging in partner, small group, and large group physical activities. 
Early Adolescence 

Grades 6  8 

Performance Expectations 
Emerging 
Maturing 
Applying 
5.1 Health 
Identifies and compare health benefits and physical activities 
Describes how different types of physical activity exert a positive impact on health and improve the quality of life. 
Explains the connections between healthrelated fitness and overall physical and mental health, and the positive impacts on the quality of life. 
5.2 Challenge 
Applies strategies for overcoming individual challenges in a physical activity setting. 
Uses positive strategies when faced with a group challenge. 
Applies strategies to overcome challenges in a physical activity. 
5.3 Selfexpression and Enjoyment 
Describes how moving competently in a physical activity setting creates enjoyment. Identify how selfexpression and physical activity are related. 
Identifies why selfselected physical activities create enjoyment Explain the relationship between selfexpression and lifelong enjoyment through physical activity. 
Discusses how enjoyment can be increased in selfselected physical activities. Identify and participate in an enjoyable activity that prompts individual selfexpressions. 
5.4 Social Interaction 
Demonstrates the importance of social interaction by following rules and encouraging others in various physical activities and games. 
Demonstrates the importance of social interaction by avoiding trash talk and playing in the spirit of activities and games. 
Demonstrates importance of social interaction by asking for help and helping others in various physical activities and games 
Adolescence 

Grade 9  Diploma 

Performance Expectations 
Level 1 
Level 2 

5.1 Health 
Analyzes the health benefits of physical activity. 
Analyzes the health benefits of a selfselected physical activity. 

5.2 Challenge 
Chooses an appropriate level of challenge to experience success in a physical activity 
Chooses an appropriate level of challenge to experience success in a selfselected physical activity 

5.3 Selfexpression and Enjoyment 
Participates in a selfselected physical activity for selfexpression and enjoyment 
Participates in a selfselected physical activity for selfexpression and enjoyment 

5.4 Social Interaction 
Identifies opportunities for social interaction in a selfselected physical activity 
Evaluates opportunities for social interaction and social support in a selfselected physical activity. 
Mathematics
A strong mathematics education depends upon a clear understanding of its interrelated concepts, skills and practices to ensure students are on the pathway to success in their academic careers. The knowledge and skills students need to be prepared for mathematics in college, career, and life are woven throughout the K12 mathematics performance expectations.
Outline of Mathematics Strands and Standards
These mathematical performance expectations are building blocks to standards. The standards are grouped into four strands:
Quantitative Reasoning (Blue): Counting and Cardinality, Number and Operations in Base Ten, Number and Operations Fractions, Ratio and Proportional Relations, The Number System, and Number and Quantity. Algebraic Reasoning (Green): Operations and Algebraic Thinking, Expressions and Equations, Functions, and Algebra Geometric Reasoning (Red): Geometry Statistical Reasoning (Purple): Measurement and Data, Statistics and ProbabilityThese mathematical performance expectations are broken into three grade spans: Childhood (K 5), Early Adolescence (68), and Adolescence (9Diploma). The strands are colorcoded, as indicated above, for continuity throughout the grade spans. Standards do not work in isolation, they are connected through and across strands.
How to Read the Standards
Within the high school performance expectations, modeling is woven throughout the four strands and is denoted with a star (* ). The high school standards also contain some performance expectations which are denoted by a plus (+ ). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.
The Guiding Principles & Standards for Mathematical Practice
The Guiding Principles influence education in Maine and should be reflected throughout Mathematics curriculum. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. Full descriptions of the Guiding Principles and Standards for Mathematical Practice can be found in the Supplemental Material. Examples of how students can show evidence of those Guiding Principles and Standards for Mathematical Practice may include:
Guiding Principles
A. A clear and effective communicator: Students will use written, oral, symbolic, and visual forms of expression to communicate mathematically.
B. A selfdirected and lifelong learner: Students generate and persevere in solving questions while demonstrating a growth mindset.
C. A creative and practical problem solver: Students will pose and solve mathematical problems by using a variety of strategies that connect to realworld examples.
D. A responsible and involved citizen: Students make sense of the world around them through mathematics including economic literacy.
E. An integrative and informed thinker: Students connect mathematics to other learning by understanding the interrelationships of mathematical ideas and the role math plays in other disciplines and life.
Standards for Mathematical Practice
Quantitative Reasoning
Quantitative reasoning is the application of basic mathematics skills to analyze and process realworld information. In the K5 grades, students use numbers, including written numerals, to represent quantities and to solve quantitative problems. Students will work on counting and cardinality, number and operations in Base Ten and fractions. Students will develop strategies to extend their understanding of the base ten system and apply those strategies to solve realworld problems using all four operations. Students progress from working with whole numbers to fractions and decimals.
In grades 68 students use reasoning about multiplication and division to solve ratio and rate problems about quantities. They develop an understanding of proportionality to solve problems and graph relationships. Overall, students extend and develop their understanding of rational numbers and can compute in all operations. Students use these operations to solve realworld problems. Students use this understanding of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane.
In the high school grades, the foundational concepts of operations with rational numbers and numerical properties built in the K5 and 68 grade spans are applied to irrational numbers. Using a wider variety of units in modeling, (e.g. acceleration, currency conversions, and derived quantities such as personhours and heating degree days), as well as the properties of rational and irrational numbers students are guided to the solution(s) to multistep problems. Extending the properties of integer exponents to rational exponents deepens student understanding of how various but equivalent notations can facilitate their algebraic reasoning and problemsolving processes. Students are encouraged to expand these operations and properties into complex numbers, vectors, and matrices to further deepen their understanding of quantitative reasoning.
Strand 
Quantitative Reasoning Counting and Cardinality 

Standard 
QR.C.1 Know the number names and the count sequence. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
K.CC.A.1: Count to 100 by ones and by tens K.CC.A.2: Count forward beginning from a given number within the known sequence (instead of having to begin at 1) K.CC.A.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 020 (with 0 representing a count of no objects) 

Strand 
Quantitative Reasoning Counting and Cardinality 

Standard 
QR.C.2 Count to tell the number of objects. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
K.CC.B.4: Understand the relationship between numbers and quantities; connect counting to cardinality. K.CC.B.4a: When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. K.CC.B.4b: Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. K.CC.B.4c: Understand that each successive number name refers to a quantity that is one larger. Recognize the one more pattern of counting using objects. K.CC.B.5: Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 120, count out that many objects. 

Strand 
Quantitative Reasoning Counting and Cardinality 

Standard 
QR.C.3 Compare numbers. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
K.CC.C.6: Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. Include groups with up to ten objects. K.CC.C.7: Compare two numbers between 1 and 10 presented as written numerals. 

Strand 
Quantitative Reasoning  Numbers and Operations in Base Ten 

Standard 
QR.C.4 Extend the counting sequence. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
1.NBT.A.1: Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. 

Strand 
Quantitative Reasoning  Numbers and Operations in Base Ten 

Standard 
QR.C.5 Understand place value. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
K.NBT.A.1: Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8 and 10+8=18); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. 
1.NBT.B.2: Understand that the two digits of a twodigit number represent amounts of tens and ones. Understand the following as special cases: 1.NBT.B.2a: 10 can be thought of as a bundle of ten ones  called a "ten." 1.NBT.B.2b: The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. 1.NBT.B.2c: The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). 1.NBT.B.3: Compare two twodigit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. 
2.NBT.A.1: Understand that the three digits of a threedigit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 2.NBT.A.1a: 100 can be thought of as a bundle of ten tens  called a "hundred." 2.NBT.A.1b: The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). 2.NBT.A.2: Count within 1000; skipcount by 5s, 10s, and 100s. Identify patterns in skip counting at any number. (For example, 37, 47, 57 or 328, 428, 528, etc.) 2.NBT.A.3: Read and write numbers to 1000 using baseten numerals, number names, and expanded form. 2.NBT.A.4: Compare two threedigit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. 
Strand 
Quantitative Reasoning  Numbers and Operations in Base Ten 

Standard 
QR.C.6 Use place value understanding and properties of operations to add and subtract. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
1.NBT.C.4: Add within 100, including adding a twodigit number and a onedigit number, and adding a twodigit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding twodigit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 1.NBT.C.5: Given a twodigit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. 1.NBT.C.6: Subtract multiples of 10 in the range 1090 from multiples of 10 in the range 1090 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 
2.NBT.B.5: Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 2.NBT.B.7: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting threedigit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 2.NBT.B.8: Mentally add 10 or 100 to a given number 100900, and mentally subtract 10 or 100 from a given number 100900. 2.NBT.B.6: Add up to four twodigit numbers using strategies based on place value and properties of operations. 2.NBT.B.9: Explain why addition and subtraction strategies work, using place value and the properties of operations. Explanations may be supported by drawings or objects. 

Strand 
Quantitative Reasoning  Numbers and Operations in Base Ten 

Standard 
QR.C.7 Use place value understanding and properties of operations to perform multidigit arithmetic with whole numbers and decimals to hundredths. 

Childhood 

Grade 3 A range of algorithms may be used. 
Grade 4 Grade 4 expectations in this strand are limited to whole numbers less than or equal to 1,000,000 
Grade 5 

Performance Expectations 
3.NBT.A.2: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 3.NBT.A.3: Multiply onedigit whole numbers by multiples of 10 in the range 1090 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. 
4.NBT.B.4: Fluently add and subtract multidigit whole numbers using the standard algorithm. 4.NBT.B.5: Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.NBT.B.6: Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 
5.NBT.B.5: Fluently multiply multidigit whole numbers using the standard algorithm. 5.NBT.B.6: Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 5.NBT.B.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, money and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 
Strand 
Quantitative Reasoning  Numbers and Operations in Base Ten 

Standard 
QR.C.8 Understand the place value system. 

Childhood 

Grade 3 A range of algorithms may be used. 
Grade 4 Grade 4 expectations in this strand are limited to whole numbers less than or equal to 1,000,000 
Grade 5 

Performance Expectations 
3.NBT.A.1: Use place value understanding to round whole numbers to the nearest 10 or 100. 
4.NBT.A.3: Use place value understanding to round multidigit whole numbers to any place. 4.NBT.A.2: Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4.NBT.A.1: Recognize that in a multidigit whole number, a digit in any place represents ten times what it represents in the place to its right.For example, recognize that 700 / 70 = 10 by applying concepts of place value and division. 
5.NBT.A.4: Use place value understanding to round decimals to any place. 5.NBT.A.3: Read, write, and compare decimals to thousandths. 5.NBT.A.3a: Read and write decimals to thousandths using baseten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). 5.NBT.A.3b: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 5.NBT.A.1: Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 5.NBT.A.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. 
Strand 
Quantitative Reasoning  Numbers and Operations: Fractions 

Standard 
QR.C.9 Develop and extend the understanding of fractions as numbers, including equivalence and ordering. 

Childhood 

Grade 3 Grade 3 expectations in this strand are limited to fractions with denominators 2, 3, 4, 6, and 8. 
Grade 4 Grade 4 expectations in this strand are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. 
Grade 5 

Performance Expectations 
3.NF.A.1: Understand a unit fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 3.NF.A.2: Understand a fraction as a number on the number line; represent fractions on a number line diagram. 3.NF.A.2a: Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. 3.NF.A.2b: Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 3.NF.A.3: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 3.NF.A.3a: Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. 3.NF.A.3b: Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model. 3.NF.A.3c: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. 3.NF.A.3d: Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 
4.NF.A.1: Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions, including fractions greater than 1. 4.NF.A.2: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 

Strand 
Quantitative Reasoning  Numbers and Operations: Fractions 

Standard 
QR.C.10 Understand decimal notation for fractions, and compare decimal fractions. 

Childhood 

Grade 3 
Grade 4 Grade 4 expectations in this strand are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. 
Grade 5 

Performance Expectations 
4.NF.C.5: Express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. 4.NF.C.6: Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. 4.NF.C.7: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. 

Strand 
Quantitative Reasoning  Numbers and Operations: Fractions 

Standard 
QR.C.11 Use equivalent fractions as a strategy to add and subtract fractions. 

Childhood 

Grade 3 
Grade 4 Grade 4 expectations in this strand are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. 
Grade 5 

Performance Expectations 
4.NF.B.3: Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 4.NF.B.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. 4.NF.B.3b: Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model to build fractions from unit fractions. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. 4.NF.B.3c: Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 4.NF.B.3d: Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. 
5.NF.A.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 5.NF.A.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. 

Strand 
Quantitative Reasoning  Numbers and Operations: Fractions 

Standard 
QR.C.12 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 

Childhood 

Grade 3 
Grade 4 
Grade 5 Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade. 

Performance Expectations 
4.NF.B.4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. 4.NF.B.4a: Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). 4.NF.B.4b: Understand a multiple of a/b as a multiple of 1/b and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b.) 4.NF.B.4c: Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? 
5.NF.B.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.B.4a: Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q / b. For example, use a visual fraction model to show (2/3) x 4 = 8/3, and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = (ac)/(bd). 5.NF.B.4b: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles and represent fraction products as rectangular areas. 5.NF.B.3: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? 5.NF.B.5: Interpret multiplication scaling (resizing), by: 5.NF.B.5a: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. 5.NF.B.5b: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a)/(n x b) to the effect of multiplying a/b by 1. 5.NF.B.6: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 5.NF.B.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1 5.NF.B.7a: Interpret division of a unit fraction by a nonzero whole number and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3. 5.NF.B.7b: Interpret division of a whole number by a unit fraction and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4. 5.NF.B.7c: Solve real world problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3cup servings are in 2 cups of raisins? 
Strand 
Quantitative Reasoning Ratio and Proportional Relationships 
Standard 
QR.EA.1 Understand ratio and rate concepts and use ratio and rate reasoning to solve problems. 
Early Adolescence 

Grades 68 

Performance Expectations 
6.RP.A.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks of the chickadees in the pine tree was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." 6.RP.A.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b [NOT EQUALS] 0 and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 5 lobsters, which is a rate of $15 per lobster." Expectations for unit rates in this grade are limited to noncomplex fractions. 6.RP.A.3: Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 6.RP.A.3a: Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. 6.RP.A.3b: Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? 6.RP.A.3c: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 6.RP.A.3d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. 
Strand 
Quantitative Reasoning Ratio and Proportional Relationships 
Standard 
QR.EA.2 Analyze proportional relationships and use them to solve realworld and mathematical problems. 
Early Adolescence 

Grades 68 

Performance Expectations 
7.RP.A.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ½ / ¼ miles per hour, equivalently 2 miles per hour 7.RP.A.2: Recognize and represent proportional relationships between quantities. 7.RP.A.2a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.A.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 7.RP.A.2c: Represent proportional relationships by equations. For example, if the total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. 7.RP.A.2d: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. 7.RP.A.3: Use proportional relationships to solve multistep ratio, rate, and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 
Strand 
Quantitative Reasoning The Number System 
Standard 
QR.EA.3 Apply and extend previous understandings of operations with whole numbers to rational numbers. 
Early Adolescence 

Grades 68 

Performance Expectations 
6.NS.A.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and/or equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) 6.NS.B.3: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. 7.NS.A.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. 7.NS.A.1a: Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has a zero charge because its two constituents are oppositely charged. 7.NS.A.1b: Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing realworld contexts. 7.NS.A.1c: Understand subtraction of rational numbers as adding the additive inverse, p  q = p+ (q). Show that the distance between two rational numbers on the number line is the absolute value of their difference and apply this principle in realworld contexts. 7.NS.A.1d: Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.A.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 7.NS.A.2a: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (1)(1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing realworld contexts. 7.NS.A.2b: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero divisor) is a rational number. If p and q are integers, then (p/q) = (p)/q = p/(q). Interpret quotients of rational numbers by describing realworld contexts. 7.NS.A.2c: Apply properties of operations as strategies to multiply and divide rational numbers. 7.NS.A.2d: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. 7.NS.A.3: Solve realworld and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions. 
Strand 
Quantitative Reasoning The Number System 
Standard 
QR.EA.4 Compute fluently with multidigit whole numbers and find common factors and multiples. 
Early Adolescence 

Grades 68 

Performance Expectations 
6.NS.B.2: Fluently divide multidigit numbers using the standard algorithm. 6.NS.B.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. (For example: Use prime factorization to find the greatest common factor);Use the distributive property to express a sum of two whole numbers 1100 with a common factor as a multiple of a sum of two relatively prime numbers. For example, express 36 + 8 as 4 (9 + 2). 
Strand 
Quantitative Reasoning  The Number System 
Standard 
QR.EA.5 Apply and extend previous understandings of numbers to the system of rational numbers. 
Early Adolescence 

Grades 68 

Performance Expectations 
6.NS.C.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative rational numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation. 6.NS.C.6: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.C.6a: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., (3) = 3, and that 0 is its own opposite. 6.NS.C.6b: Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. 6.NS.C.6c: Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 6.NS.C.7: Understand ordering and absolute value of rational numbers. 6.NS.C.7a: Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret 3 > 7 as a statement that 3 is located to the right of 7 on a number line oriented from left to right. 6.NS.C.7b: Write, interpret, and explain statements of order for rational numbers in realworld contexts. For example, write 3° C > 7° C to express the fact that 3° C is warmer than 7° C. 6.NS.C.7c: Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a realworld situation. For example, for an account balance of 30 dollars, write 30 = 30 to describe the size of the debt in dollars. 6.NS.C.7d: Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars. 6.NS.C.8: Solve realworld and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 
Strand 
Quantitative Reasoning The Number System 
Standard 
QR.EA.6 Know that there are numbers that are not rational, and approximate them by rational numbers. 
Early Adolescence 

Grades 68 

Performance Expectations 
8.NS.A.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansions terminate in 0s or eventually repeats and convert a decimal expansion into a rational number. 8.NS.A.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., [PI]2). For example, by truncating the decimal expansion of [SQUARE ROOT RADICAL]2, show that [SQUARE ROOT RADICAL]2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. 
Strand 
Quantitative Reasoning  Number and Quantity: The Real Number System 
Standard 
QR.A.1 Extend the properties of exponents to rational exponents. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSN.RN.A.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. HSN.RN.A.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. 
Strand 
Quantitative Reasoning Number and Quantity: The Real Number System 
Standard 
QR.A.2 Use properties of rational and irrational numbers. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSN.RN.B.3: Explain when and why the sum or product of two rational and/or irrational numbers is rational or irrational. 
Strand 
Quantitative Reasoning  Number and Quantity: Quantities Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
QR.A.3 Reason quantitatively and use units to solve problems.* 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSN.Q.A.1: Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. Example: Marlena made a scale drawing of the sand volleyball court at her summer camp. The drawing of the volleyball court is 6 cm long by 3 cm wide. The actual volleyball court is 18 meters long. What scale did Marlena use for the drawing?* HSN.Q.A.2: Define appropriate quantities for the purpose of descriptive modeling. Example: If a town in Aroostook county with a population of 1254 people is projected to double in size every 105 years, what will the population be 315 years from now?* HSN.Q.A.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Example: The label on a ½  liter bottle of flavored water bottled in Maine indicates that one serving of 8 ounce contains 60 calories. The label also says that the full bottle contains 130 calories. Is this the actual amount or the estimated amount of calories in this bottle? How would you explain any discrepancy?* 
Strand 
Quantitative Reasoning  Number and Quantity: Complex Number System The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
QR.A.4 (+) Perform arithmetic operations with complex numbers. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
(+) HSN.CN.A.1: Know there is a complex number i (which is a nonreal number) such that i2 = 1, and every complex number has the form a + bi with a and b real. (+) HSN.CN.A.2: Use the relation i2 = 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. (+) HSN.CN.A.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. 
Strand 
Quantitative Reasoning  Number and Quantity: Complex Number System The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
QR.A.5 (+) Represent complex numbers and their operations on the complex plane. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
(+) HSN.CN.B.4: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. (+) HSN.CN.B.5: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (1 + [SQUARE ROOT RADICAL]3 i)3 = 8 because (1 + [SQUARE ROOT RADICAL]3 i) has modulus 2 and argument 120°. (+) HSN.CN.B.6: Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. 
Strand 
Quantitative Reasoning  Number and Quantity: Complex Number System The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
QR.A.6 (+) Use complex numbers in polynomial identities and equations. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
(+) HSN.CN.C.7: Solve quadratic equations with real coefficients that have complex solutions. (+) HSN.CN.C.8: Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x  2i). (+) HSN.CN.C.9: Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. 
Strand 
Quantitative Reasoning  Number and Quantity: Vector and Matrix Quantities The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
QR.A.7 (+) Represent and model with vector quantities. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
(+) HSN.VM.A.1: Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments and use appropriate symbols for vectors and their magnitudes (e.g., v, v , v , v). (+) HSN.VM.A.2: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. (+) HSN.VM.A.3: Solve problems involving velocity and other quantities that can be represented by vectors. 
Strand 
Quantitative Reasoning  Number and Quantity: Vector and Matrix Quantities The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
QR.A.8 (+) Perform operations on vectors. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
(+) HSN.VM.B.4: Add and subtract vectors. (+) HSN.VM.B4a: Add vectors endtoend, componentwise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. (+) HSN.VM.B4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. (+) HSN.VM.B4c: Understand vector subtraction v  w as v + (w ), where w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction componentwise. (+) HSN.VM.B.5: Multiply a vector by a scalar. (+) HSN.VM.B5a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication componentwise, e.g., as c(vx, vy) = (cvx, cvy). (+) HSN.VM.B5b: Compute the magnitude of a scalar multiple cv using cv = cv. Compute the direction of cv knowing that when cv [NOT EQUALS] 0, the direction of cv is either along v (for c > 0) or against v (for c < 0). 
Strand 
Quantitative Reasoning  Number and Quantity: Vector and Matrix Quantities The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
QR.A.9 (+) Perform operations on matrices and use matrices in applications. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
(+) HSN.VM.C.6: Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. (+) HSN.VM.C.7: Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. (+) HSN.VM.C.8: Add, subtract, and multiply matrices of appropriate dimensions. (+) HSN.VM.C.9: Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. (+) HSN.VM.C.10: Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. (+) HSN.VM.C.11: Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. (+) HSN.VM.C12: Work with 2 x 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area. 
Algebraic Reasoning
Algebraic thinking is about generalizing arithmetic operations and determining unknown quantities by recognizing and analyzing patterns along with developing generalizations about these patterns. In this K5 strand, students explore, analyze, represent, and generalize mathematical ideas and relationships. Students will develop an understanding of the fundamental properties of number and operations, understand the use of the equal sign to represent equivalence, and use quantitative reasoning to understand mathematical relationships.
Students in grades 68 progress in their understanding of variables in mathematical expressions and equations. They understand that expressions in different forms can be equivalent, use the properties of operations to rewrite expressions in equivalent forms, and describe relationships between quantities. Students begin to analyze and solve realworld and mathematical problems using equations and inequalities. They construct and interpret tables and graphs. Understanding builds from writing and solving simple equations to solving proportional situations. These skills lead to exploring slope and yintercept and relationships between variables, and eventually include multiple equations to solve systems of linear equations. Students grow to understand that the concept of a function is a rule that assigns one output to each input, and they learn to translate among different representations of functions.
In grades 912, students will continue to develop their understanding of expressions, equations, functions and function notation. They will interpret the structure of algebraic expressions and be able to write expressions in equivalent forms to reveal information and to solve problems. Students will perform arithmetic operations on polynomials and rewrite rational functions. An understanding of the relationship between zeros and factors of polynomials will transition into using polynomial identities to solve problems. Students will create equations that describe relationships and solve equations as a process of reasoning (with appropriate justification). They will represent and solve equations, inequalities, and systems of equations using a variety of mathematically sound techniques.
Students will interpret functions that arise in applications in terms of context and analyze functions using different representations. They will build functions that model relationships between two quantities, and build new functions from existing functions through transformations, combinations, compositions, and examining the inverse. Students will construct and compare linear, quadratic, and exponential models and use those models to solve problems. They will interpret expressions for functions in terms of the situation they model. Students will be encouraged to extend their understanding of algebra and functions and apply similar processes of reasoning to polynomial, logarithmic and trigonometric functions and their graphs.
Strand 
Algebraic Reasoning  Operations and Algebraic Thinking 

Standard 
AR.C.1 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.  
Childhood 

Kindergarten (Drawings need not show detail but should show the mathematics in the problem. This applies wherever drawings are mentioned in the Standards.) 
Grade 1 
Grade 2 

Performance Expectations 
K.OA.A.1: Represent addition and subtraction with objects, fingers, mental images, drawings sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. K.OA.A.2: Solve addition and subtraction word problems, and add and subtract within 10, (e.g., by using objects or drawings to represent the problem). K.OA.A.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). K.OA.A.4: For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. K.OA.A.5: Fluently add and subtract within 5 including zero. 
1.OA.A.1: Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.OA.A.2: Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.) 
2.OA.A.1: Use addition and subtraction within 100 to solve one and twostep word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 
Strand 
Algebraic Reasoning  Operations and Algebraic Thinking 

Standard 
AR.C.2 Understand and apply properties of operation and the relationship between addition and subtraction within 20.  
Childhood 

Kindergarten 
Grade 1 Students need not use formal terms for these properties. 
Grade 2 

Performance Expectations 
1.OA.B.3: Apply properties of operations as strategies to add. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) a + 0 = a (Additive identity property of 0) 1.OA.B.4: Understand subtraction as an unknownaddend problem. For example, subtract 10  8 by finding the number that makes 10 when added to 8. 1.OA.C.5: Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). 1.OA.C.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13  4 = 13  3  1 = 10  1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12  8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). 1.OA.D.7: Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8  1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. 1.OA.D.8: Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _  3, 6 + 6 = _. 
2.OA.B.2: Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two onedigit numbers. 

Strand 
Algebraic Reasoning  Operations and Algebraic Thinking 

Standard 
AR.C.3 Work with equal groups of objects to gain foundations for multiplication.  
Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
2.OA.C.3: Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. 2.OA.C.4: Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. 

Strand 
Algebraic Reasoning  Operations and Algebraic Thinking 

Standard 
AR.C.4 Understand properties of multiplication and the relationship between multiplication and division to represent and solve problems within 100.  
Childhood 

Grade 3 Students need not use formal terms for these properties. 
Grade 4 
Grade 5 

Performance Expectations 
3.OA.A.1: Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x7. 3.OA.A.2: Interpret wholenumber quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. 3.OA.A.3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 3.OA.A.4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = _ ÷ 3, 6 x 6 = ? 3.OA.B.5: Apply properties of operations as strategies to multiply. Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative property of multiplication.) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication.) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributive property.) 3.OA.B.6: Understand division as an unknownfactor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. 3.OA.C.7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two onedigit numbers. 

Strand 
Algebraic Reasoning  Operations and Algebraic Thinking 

Standard 
AR.C.5 Solve problems involving the four operations.  
Childhood 

Grade 3 This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in conventional order when there are no parentheses to specify a particular order (Order of Operations). 
Grade 4 
Grade 5 

Performance Expectations 
3.OA.D.8: Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 
4.OA.A.1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. 4.OA.A.2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 4.OA.A.3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 

Strand 
Algebraic Reasoning  Operations and Algebraic Thinking 

Standard 
AR.C.6 Gain familiarity with factors and multiples.  
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
4.OA.B.4: Find all factor pairs for a whole number in the range 1100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1100 is prime or composite. 

Strand 
Algebraic Reasoning  Operations and Algebraic Thinking 

Standard 
AR.C.7 Write and interpret numerical expressions. 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
5.OA.A.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 5.OA.A.2: Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 x (8 + 7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. 

Strand 
Algebraic Reasoning  Operations and Algebraic Thinking 

Standard 
AR.C.8 Identify, explain, generate and analyze patterns.  
Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
3.OA.D.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. 
4.OA.C.5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. 
5.OA.B.3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. 
Strand 
Algebraic Reasoning  Expressions and Equations 
Standard 
AR.EA.1 Apply and extend previous understandings of arithmetic to algebraic expressions. 
Early Adolescence 

Grades 68 

Performance Expectations 
6.EE.A.1: Write and evaluate numerical expressions involving wholenumber exponents. 6.EE.A.2: Write, read, and evaluate expressions in which letters represent numbers. 6.EE.A.2a: Write expressions that record operations with numbers and with letters representing numbers. For example, express the calculation "Subtract y from 5" as 5  y. 6.EE.A.2b: Identify parts of an expression using mathematical terms (including but not limited to: sum, term, product, factor, quotient, coefficient, variable, constant); view one or more parts of an expression as a single entity. For example, describe the expression 2 (x + 7) as a product of two factors; view (x + 7) as both a single entity and a sum of two terms. 6.EE.A.2c: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in realworld problems. Perform arithmetic operations, including those involving wholenumber exponents, using the order of operations. For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2. 6.EE.A.3: Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to factor the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. 6.EE.A.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. 
Strand 
Algebraic Reasoning  Expressions and Equations 
Standard 
AR.EA.2 Reason about and solve onevariable equations and inequalities. 
Early Adolescence 

Grades 68 

Performance Expectations 
6.EE.B.5: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.EE.B.6: Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 6.EE.B.7: Solve realworld and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. For example, Sal is paid $0.50 per pound of blueberries that she rakes. If she rakes x pounds, and earns $17.25, write and solve an equation that determines how many pounds she raked. 6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. 
Strand 
Algebraic Reasoning  Expressions and Equations 
Standard 
AR.EA.3 Represent and analyze quantitative relationships between dependent and independent variables. 
Early Adolescence 

Grades 68 

Performance Expectations 
6.EE.C.9: Use variables to represent two quantities in a realworld problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables and relate these to the equation.For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. 
Strand 
Algebraic Reasoning  Expressions and Equations 
Standard 
AR.EA.4 Use properties of operations to generate equivalent expressions. 
Early Adolescence 

Grades 68 

Performance Expectations 
7.EE.A.1: Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. For example, 4x + 2 = 2(2x+1) and 3(x5/3) = 3x +5 7.EE.A.2: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, A shirt is on sale for 20% off the regular price, p. The discount can be expressed as 0.2p. The new price for the shirt can be expressed as p  0.2p or 0.8p. 
Strand 
Algebraic Reasoning  Expressions and Equations 
Standard 
AR.EA.5 Solve reallife and mathematical problems using numerical and algebraic expressions and equations. 
Early Adolescence 

Grades 68 

Performance Expectations 
7.EE.B.3: Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. 7.EE.B.4: Use variables to represent quantities in a realworld or mathematical problem and construct simple equations and inequalities to solve problems by reasoning about the quantities. 7.EE.B.4a: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? 7.EE.B.4b: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make and describe the solutions. 
Strand 
Algebraic Reasoning  Expressions and Equations 
Standard 
AR.EA.6 Work with radicals and integer exponents. 
Early Adolescence 

Grades 68 

Performance Expectations 
8.EE.A.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 x 35 = 33 = (1/3)3 = 1/27. 8.EE.A.2: Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that &[Square Root]2 is irrational. 8.EE.A.3: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger. 8.EE.A.4: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. 
Strand 
Algebraic Reasoning  Expressions and Equations 
Standard 
AR.EA.7 Understand the connections between proportional relationships, lines, and linear equations. 
Early Adolescence 

Grades 68 

Performance Expectations 
8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distancetime graph to a distancetime equation to determine which of two moving objects has greater speed. 8.EE.B.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.For example, given the line y = 0.5x + 3 explain why the similar triangles have the same slope. 
Strand 
Algebraic Reasoning  Expressions and Equations 
Standard 
AR.EA.8 Analyze and solve linear equations and pairs of simultaneous linear equations. 
Early Adolescence 

Grades 68 

Performance Expectations 
8.EE.C.7: Solve linear equations in one variable. 8.EE.C.7a: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). 8.EE.C.7b: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.EE.C.8: Analyze and solve pairs of simultaneous linear equations. 8.EE.C.8a: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. 8.EE.C.8b: Solve systems of two linear equations in two variables algebraically (i.e. by substitution or elimination) and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. 8.EE.C.8c: Solve realworld and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. 
Strand 
Algebraic Reasoning  Functions 
Standard 
AR.EA.9 Define, evaluate, and compare functions in order to model relationships between quantities. 
Early Adolescence 

Grades 68 Function notation is not required for Grade 8. 

Performance Expectations 
8.F.A.1: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. 8.F.A.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. 8.F.A.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. 8.F.B.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. 8.F.B.5: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. 
Strand 
Algebraic Reasoning  Algebra: Seeing Structure in Expressions Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
AR.A.1 Interpret the structure of expressions. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSA.SSE.A.1: Interpret expressions that represent a quantity in terms of its context.* SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.* SSE.A.1b: Interpret multipart expressions by viewing one or more of their parts as a single entity. For example, view P(1+r)n as the product of P and a factor not depending on P and interpret the parts.* HSA.SSE.A.2: Use the structure of an expression to identify ways to rewrite it. For example, see x4  y4 as (x2)2  (y2)2, allowing for it to be recognized as a difference of squares that can be factored as (x2  y2)(x2 + y2). 
Strand 
Algebraic Reasoning  Algebra: Seeing Structure in Expressions Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
AR.A.2 Write expressions in equivalent forms to reveal information and to solve problems.* 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSA.SSE.B.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* HSA.SSE.B.3a: Rewrite a quadratic expression (such as by factoring) to reveal the zeros of the function it defines.* HSA.SSE.B.3b: Rewrite a quadratic expression (such as by completing the square) to reveal the maximum or minimum value of the function it defines.* HSA.SSE.B.3c: Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15t can be rewritten as (1.151/12)12t = 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.* HSA.SSE.B.4: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, Watermilfoil in one Maine lake triples in the number of plants each week during the summer when boat propellers are not cleared when exiting the lake. If the lake has 20 plants at the beginning of the season, how many plants will exist at the end of the 12week summer season? What is the general formula for Watermilfoil growth for this lake? * 
Strand 
Algebraic Reasoning  Algebra: Arithmetic with Polynomials & Rational Expressions 
Standard 
AR.A.3 Perform arithmetic operations on polynomials. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSA.APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations. HSA.APR.A.1a: Perform operations on polynomial expressions (addition, subtraction, multiplication, and division), and compare the system of polynomials to the system of integers. HSA.APR.A.1b: Factor and/or expand polynomial expressions, identify and combine like terms, and apply the Distributive Property. 
Strand 
Algebraic Reasoning  Algebra: Arithmetic with Polynomials & Rational Expressions The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
AR.A.4 Understand the relationship between zeros and factors of polynomials. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSA.APR.B.2: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x  a is p(a), so p(a) = 0 if and only if (x  a) is a factor of p(x). For example, consider the polynomial function P(x) = x4  2x3 + ax2 + 8x + 12, where a is an unknown real number. If (x3) is a factor of this polynomial, what is the value of a? (+) HSA.APR.B.3: Identify zeros of polynomials of degree three or higher when suitable factorizations (in factored form or easily factorable) are available, and use the zeros to construct a rough graph of the function defined by the polynomial. 
Strand 
Algebraic Reasoning  Algebra: Arithmetic with Polynomials & Rational Expressions The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
AR.A.5 (+) Use polynomial identities to solve problems. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
(+) HSA.APR.C.4: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2  y2)2 + (2xy)2 can be used to generate Pythagorean triples. (+) HSA.APR.C.5: Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle. The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument. 
Strand 
Algebraic Reasoning  Algebra: Arithmetic with Polynomials & Rational Expressions The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
AR.A.6 Rewrite rational expressions. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSA.APR.D.6: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. (+) HSA.APR.D.7: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. 
Strand 
Algebraic Reasoning Algebra: Creating Equations and/or Inequalities Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
AR.A.7 Create equations and/or inequalities that describe numbers or relationships.* 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSA.CED.A.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.* HSA.CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.* HSA.CED.A.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods such as lobsters, blueberries, and potatoes.* HSA.CED.A.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.* 
Strand 
Algebraic Reasoning  Algebra: Reasoning with Equations & Inequalities 
Standard 
AR.A.8 Understand solving equations as a process of reasoning and explain the reasoning. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSA.REI.A.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify or refute a solution method. HSA.REI.A.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. 
Strand 
Algebraic Reasoning  Algebra: Reasoning with Equations & Inequalities The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
AR.A.9 Solve equations and inequalities in one variable. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSA.REI.B.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. HSA.REI.B.4: Solve quadratic equations in one variable. HSA.REI.B.4a: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x  p)2 = q that has the same solutions. Derive the quadratic formula from this form. HSA.REI.B.4b: i) Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. (+) HSA.REI.B.4b: ii) Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. 
Strand 
Algebraic Reasoning  Algebra: Reasoning with Equations & Inequalities The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
AR.A.10 Solve systems of equations. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSA.REI.C.5: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. HSA.REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. HSA.REI.C.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the point(s) of intersection between the line y = 3x and the circle x2 + y2 = 3. (+) HSA.REI.C.8: Represent a system of linear equations as a single matrix equation in a vector variable. (+) HSA.REI.C.9: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 x 3 or greater). 
Strand 
Algebraic Reasoning  Algebra: Reasoning with Equations & Inequalities Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
AR.A.11 Represent and solve equations and inequalities graphically. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSA.REI.D.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Show that any point on the graph of an equation in two variables is a solution to the equation. HSA.REI.D.11: Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* HSA.REI.D.12: Graph the solutions of a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set of a system of linear inequalities in two variables as the intersection of the corresponding halfplanes. 
Strand 
Algebraic Reasoning  Functions: Interpreting Functions 
Standard 
AR.A.12 Understand the concept of a function and use function notation. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSF.IF.A.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. HSF.IF.A.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n1) for n >= 1. 
Strand 
Algebraic Reasoning  Functions: Interpreting Functions Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
AR.A.13 Interpret functions that arise in applications in terms of the context.* 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSF.IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features may include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative and absolute maximums and minimums; symmetries; end behavior; and periodicity.* HSF.IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. * HSF.IF.B.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* 
Strand 
Algebraic Reasoning  Functions: Interpreting Functions Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
AR.A.14 Analyze functions using different representations. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSF.IF.C.7: Graph functions expressed symbolically as well as show and describe key features of the graph, by hand in simple cases and using technology for more complicated cases.* HSF.IF.C.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima. HSF.IF.C.7b: i) Graph square root and piecewisedefined functions, (including step functions and absolute value functions), as well as show and describe key features of the graph. (+) HSF.IF.C.7b: ii) Graph cube root functions, as well as show and describe key features of the graph. (+) HSF.IF.C.7c: Graph polynomial functions of degree three or higher, identifying zeros when suitable factorizations (in factored form or easily factorable) are available, and showing end behavior. (+) HSF.IF.C.7d: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. HSF.IF.C.7e: i) Graph exponential functions, showing intercepts and end behavior, and (+) HSF.IF.C.7e: ii) Graph logarithmic functions, showing intercepts and end behavior and trigonometric functions, showing period, midline, and amplitude. HSF.IF.C.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. HSF.IF.C.8a: Use the process of factoring and completing the square in a quadratic function to show zeros, maximum and minimum values, and symmetry of the graph, and interpret these in terms of a context. HSF.IF.C.8b: Use the properties of exponents to interpret expressions for exponential functions. For example, apply the properties to financial situations such as identifying appreciation and depreciation rate for the value of a house or car sometime after its initial purchase: Vn = P(1 + r)n. HSF.IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 
Strand 
Algebraic Reasoning  Functions: Building Functions Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
AR.A.15 Build a function that models a relationship between two quantities.* 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSF.BF.A.1: Write a function that describes a relationship between two quantities.* HSF.BF.A.1a: Determine an explicit expression, a recursive process, or steps for calculation from a context. HSF.BF.A.1b: Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. (+) HSF.BF.A.1c: Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. HSF.BF.A.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* 
Strand 
Algebraic Reasoning  Functions: Building Functions The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
AR.A.16 Build new functions from existing functions. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSF.BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Okay as written. HSF.BF.B.4: Find inverse functions. HSF.BF.B.4a: Solve an equation of the form f(x) = c (where c represents the output value of the function) for a simple function f that has an inverse and write an expression for the inverse. For example, if f(x) =2 x3, then solving f(x) = c leads to x = (c/2)1/3, which is the general formula for finding an input from a specific output, c, for this function. (+) HSF.BF.B.4b: Verify by composition that one function is the inverse of another. (+) HSF.BF.B.4c: Read values of an inverse function from a graph or a table, given that the function has an inverse. (+) HSF.BF.B.4d: Produce an invertible function from a noninvertible function by restricting the domain. (+) HSF.BF.B.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. 
Strand 
Algebraic Reasoning  Functions: Linear, Quadratic, & Exponential Models Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
AR.A.17 Construct and compare linear, quadratic, and exponential models and solve problems.* 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSF.LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential functions. * HSF.LE.A.1a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. HSF.LE.A.1b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. HSF.LE.A.1c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. HSF.LE.A.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table).* HSF.LE.A.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.* (+) HSF.LE.A.4: For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.* 
Strand 
Algebraic Reasoning  Functions: Linear, Quadratic, & Exponential Models Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
AR.A.18 Interpret expressions for function in terms of the situation they model.* 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSF.LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context.* 
Strand 
Algebraic Reasoning  Functions: Trigonometric Functions The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
AR.A.19 Extend the domain of trigonometric functions using the unit circle. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSF.TF.A.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. HSF.TF.A.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. (+) HSF.TF.A.3: Use special triangles to determine geometrically the values of sine, cosine, tangent for p/3, p/4 and p/6, and use the unit circle to express the values of sine, cosine, and tangent for x, p + x, and 2p  x in terms of their values for x, where x is any real number. (+) HSF.TF.A.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. 
Strand 
Algebraic Reasoning  Functions: Trigonometric Functions Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
AR.A.20 (+) Model periodic phenomena with trigonometric functions. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
(+) HSF.TF.B.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* (+) HSF.TF.B.6: Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. (+) HSF.TF.B.7: Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. * 
Strand 
Algebraic Reasoning  Functions: Trigonometric Functions The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
AR.A.21 (+) Prove and apply trigonometric identities. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
(+) HSF.TF.C.8: Prove the Pythagorean identity sin2([CIRCLED MINUS]) + cos2([CIRCLED MINUS]) = 1 and use it to find sin([CIRCLED MINUS]), cos([CIRCLED MINUS]), or tan([CIRCLED MINUS]) given sin([CIRCLED MINUS]), cos([CIRCLED MINUS]), or tan([CIRCLED MINUS]) and the quadrant of the angle. (+) HSF.TF.C.9: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. 
Geometric Reasoning
Geometric reasoning is the use of critical thinking, logical argument and spatial reasoning to solve problems and find new relationships. Students must first have a critical understanding of any underlying assumptions and relationships. This allows them to develop coherent knowledge and apply their reasoning skills. In this K5 strand, students will develop an understanding of the attributes of two and threedimensional shapes and apply this knowledge to realworld problems. Students will also be introduced to the coordinate system.
Students in grades 68 work with two and threedimensional objects to reason about relationships among shapes. They learn to calculate area, surface area, volume, and circumference using multiple methods including decomposing shapes so that they can develop, justify, and use formulas including the Pythagorean Theorem and its converse. They use scale drawings and informal constructions to gain familiarity with the relationships between angles formed by intersecting lines and transformations.
During high school, students begin to formalize their geometry experiences from elementary and middle school, using more complex definitions and reasoning of proofs. Students make geometric constructions using a variety of technological tools and connect these explorations to reasoning and proofs. Attributes of parallel lines intersected by a transversal are further developed and extended into properties of triangles, quadrilaterals, and regular polygons as well as circles using informal and formal reasoning. Fundamental to the concepts of congruence, similarity, and symmetry are transformations which can preserve distance and angles.
The definitions of sine, cosine, and tangent for acute angles are founded on right triangles and similarity. The Pythagorean Theorem along with these ratios are fundamental in many realworld and theoretical situations. Correspondence between numerical coordinates and geometric points allows methods from algebra to be applied to geometry and vice versa. Concepts of two and threedimensional shapes are explored using algebraic formulas and modeling. Students are encouraged to extend their geometric reasoning through the exploration of trigonometric identities and properties of conic sections.
Strand 
Geometric Reasoning  Geometry 

Standard 
GR.C.1 Identify, describe, analyze, compare, create, and compose shapes based on their attributes. 

Childhood 

Kindergarten 
Grade 1 Students should apply the principle of transitivity of measurement to make indirect comparisons, but they need not use this technical term. 
Grade 2 Sizes are compared directly or visually, not compared by measuring. 

Performance Expectations 
K.G.A.1: Describe objects in the environment using names of shapes and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. K.G.A.2: Correctly name shapes regardless of their orientations or overall size. K.G.A.3: Identify shapes as twodimensional (lying in a plane, "flat") or threedimensional ("solid"). K.G.B.4: Analyze and compare two and threedimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides of equal length). K.G.B.5: Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. K.G.B.6: Compose simple shapes to form larger shapes. For example, "Can you join these two triangles with full sides touching to make a rectangle?" 
1.G.A.1: Distinguish between defining attributes (e.g., triangles are closed and threesided) versus nondefining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. 1.G.A.2: Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quartercircles) or threedimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. 1.G.A.3: Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. 
2.G.A.1: Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals (including squares, rectangles, rhombuses, and trapezoids) pentagons, hexagons, and cubes. Sizes are compared directly or visually, not compared by measuring. 2.G.A.2: Partition a rectangle into rows and columns of samesize squares and count to find the total number of them. 2.G.A.3: Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. 

Strand 
Geometric Reasoning  Geometry 

Standard 
GR.C.2 Analyze, compare, create, and compose shapes based on their attributes. 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
3.G.A.1: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. 3.G.A.2: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape. 
5.G.B.3: Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. 5.G.B.4: Classify twodimensional figures in a hierarchy based on properties. (e.g., all rectangles are parallelograms, because they are all quadrilaterals with two pairs of opposite sides parallel.) 

Strand 
Geometric Reasoning  Geometry 

Standard 
GR.C.3 Draw and identify lines and angles and classify shapes by properties of their lines and angles. 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
4.G.A.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. 4.G.A.2: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category and identify right triangles. 4.G.A.3: Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry. 

Strand 
Geometric Reasoning  Geometry 

Standard 
GR.C.4 Graph points on the coordinate plane to solve realworld and mathematical problems. 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
5.G.A.1: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). 5.G.A.2: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation. 
Strand 
Geometric Reasoning  Geometry 
Standard 
GR.EA.1 Solve realworld and mathematical problems involving angle measure, area, surface area, and volume. 
Early Adolescence 

Grades 68 

Performance Expectations 
6.G.A.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. 6.G.A.2: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h (where B stands for the area of the base) to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. 6.G.A.3: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving realworld and mathematical problems. 6.G.A.4: Represent threedimensional figures using nets made up of rectangles and triangles and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. 7.G.B.4: Know that a circle is a twodimensional shape created by connecting all the points equidistant from a fixed point called the center of the circle. Understand and describe the relationships among the radius, diameter, circumference and area of a circle. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 7.G.B.5: Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. 7.G.B.6: Solve realworld and mathematical problems involving area, volume and surface area of two and/or threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 8.G.C.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. 
Strand 
Geometric Reasoning  Geometry 
Standard 
GR.EA.2 Draw, construct, and describe geometrical figures and describe the relationships between them. 
Early Adolescence 

Grades 68 

Performance Expectations 
7.G.A.1: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. 7.G.A.2: Draw (freehand, with ruler and protractor, and with technology) twodimensional geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 7.G.A.3: Describe the shape of the crosssection twodimensional face of the figures that results from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. 
Strand 
Geometric Reasoning  Geometry 
Standard 
GR.EA.3 Understand congruence and similarity using physical models, transparencies, or geometry software, 
Early Adolescence 

Grades 68 

Performance Expectations 
8.G.A.1: Verify experimentally the properties of rotations, reflections, and translations: 8.G.A.1a: Lines are taken to lines, and line segments to line segments of the same length. 8.G.A.1b: Angles are taken to angles of the same measure. 8.G.A.1c: Parallel lines are taken to parallel lines. 8.G.A.2: Understand that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 8.G.A.3: Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. 8.G.A.4: Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. 8.G.A.5: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. 
Strand 
Geometric Reasoning  Geometry 
Standard 
GR.EA.4 Understand and apply the Pythagorean Theorem. 
Early Adolescence 

Grades 68 

Performance Expectations 
8.G.B.6: Explain a proof of the Pythagorean Theorem and its converse using pictures, diagrams, narratives or models. 8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. 8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 
Strand 
Geometric Reasoning  Geometry: Congruence 
Standard 
GR.A.1 Experiment with transformations in the plane. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSG.CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. HSG.CO.A.2: Represent transformations in the plane using, e.g., transparencies and/or geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). HSG.CO.A.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. HSG.CO.A.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. HSG.CO.A.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. 
Strand 
Geometric Reasoning  Geometry: Congruence 
Standard 
GR.A.2 Understand congruence in terms of rigid motions. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSG.CO.B.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. HSG.CO.B.7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. HSG.CO.B.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. 
Strand 
Geometric Reasoning  Geometry: Congruence 
Standard 
GR.A.3 Prove geometric theorems and when appropriate, the converse of theorems. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSG.CO.C.9: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent, and conversely prove lines are parallel; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. HSG.CO.C.10: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180° base angles of isosceles triangles are congruent, and conversely prove a triangle is isosceles; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. HSG.CO.C.11: Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. 
Strand 
Geometric Reasoning  Geometry: Congruence 
Standard 
GR.A.4 Make geometric constructions. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSG.CO.D.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. HSG.CO.D.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. 
Strand 
Geometric Reasoning  Geometry: Similarity, Right Triangles, & Trigonometry 
Standard 
GR.A.5 Understand similarity in terms of similarity transformations. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSG.SRT.A.1: Verify experimentally the properties of dilations given by a center and a scale factor: HSG.SRT.A.1a: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. HSG.SRT.A.1b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor. HSG.SRT.A.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. HSG.SRT.A.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. 
Strand 
Geometric Reasoning  Geometry: Similarity, Right Triangles, & Trigonometry 
Standard 
GR.A.6 Prove theorems involving similarity using a variety of ways of writing proofs, showing validity of underlying reasoning. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSG.SRT.B.4: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. HSG.SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. 
Strand 
Geometric Reasoning  Geometry: Similarity, Right Triangles, & Trigonometry Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
GR.A.7 Define trigonometric ratios and solve problems involving right triangles. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSG.SRT.C.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. HSG.SRT.C.7: Explain and use the relationship between the sine and cosine of complementary angles. HSG.SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. For example, find the current height of the tallest pine tree in Maine using the angle of elevation and the distance from the tree.* 
Strand 
Geometric Reasoning  Geometry: Similarity, Right Triangles, & Trigonometry The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
GR.A.8 (+) Apply trigonometry to general triangles. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
(+) HSG.SRT.D.9: Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. (+) HSG.SRT.D.10: Prove the Laws of Sines and Cosines and use them to solve problems. (+) HSG.SRT.D.11: Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces). 
Strand 
Geometric Reasoning  Geometry: Circle The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
GR.A.9 Understand and apply theorems about circles. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSG.C.A.1: Prove that all circles are similar. HSG.C.A.2: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. HSG.C.A.3: Construct the inscribed and circumscribed circles of a triangle and prove properties of angles for a quadrilateral inscribed in a circle. (+) HSG.C.A.4: Construct a tangent line from a point outside a given circle to the circle. 
Strand 
Geometric Reasoning  Geometry: Circle 
Standard 
GR.A.10 Find arc lengths and areas of sectors of circles. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSG.C.B.5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. 
Strand 
Geometric Reasoning  Geometry: Expressing Geometric Properties with Equations The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
GR.A.11 Translate between the geometric description and the equation for a conic section. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSG.GPE.A.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. HSG.GPE.A.2: Derive the equation of a parabola given a focus and directrix. (+) HSG.GPE.A.3: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. 
Strand 
Geometric Reasoning  Geometry: Expressing Geometric Properties with Equations Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
GR.A.12 Use coordinates to prove simple geometric theorems algebraically. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSG.GPE.B.4: Use coordinates to prove simple geometric theorems algebraically including the distance formula and its relationship to the Pythagorean Theorem. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, [ Square Root]3) lies on the circle centered at the origin and containing the point (0, 2). HSG.GPE.B.5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). HSG.GPE.B.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio. HSG.GPE.B.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* 
Strand 
Geometric Reasoning  Geometry: Geometric Measurements & Dimension Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
GR.A.13 Explain volume formulas and use them to solve problems. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSG.GMD.A.1: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and/or informal limit arguments. (+) HSG.GMD.A.2: Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. HSG.GMD.A.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* 
Strand 
Geometric Reasoning  Geometry: Geometric Measurements & Dimension 
Standard 
GR.A.14 Visualize relationships between twodimensional and threedimensional objects. 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSG.GMD.B.4: Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. 
Strand 
Geometric Reasoning  Geometry: Modeling with Geometry Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
GR.A.15 Apply geometric concepts in modeling situations.* 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSG.MG.A.1: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* HSG.MG.A.2: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).* HSG.MG.A.3: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).* 
Statistical Reasoning
Statistical reasoning is the way people analyze data and make sense of information. It involves generalizations that connect one concept to another. In this K5 strand, students will develop strategies to represent and interpret data, describe and compare measurable attributes, and understand concepts of measurement including perimeter, area, volume, time, and money.
Students in grades 68 continue to develop their ability to think statistically. Measures of central tendency (mean, median, and mode) as well as measures of variability (range, interquartile range, mean absolute deviation) are used to describe data. Previous work with single data distributions is expanded to compare two data distributions and address questions about differences between populations. Informal work with random sampling and learning about the importance of representative samples for drawing inferences is introduced. Students then expand their statistical understanding to include connections involving modeling with linear equations, as well as nonlinear expressions. Looking for patterns in a bivariate data system is emphasized.
In grades 912 students extend their statistical understanding of univariate and bivariate data in a realworld context. This understanding is used to make decisions or predictions based on the data. Since data can be variable, statistics provide the tools for taking this variability into account. Data can be categorical or quantitative in nature. Appropriate methods for collecting, displaying, summarizing, and analyzing data are learned and employed. Algebraic and geometric reasoning are utilized to create linear regression models in order to interpret the relationship between two quantitative variables when appropriate.
The conditions under which data are collected and the use of randomization in the design of a study are necessary for drawing valid conclusions about the population under study. Since random processes can be described mathematically by using a probability model, the role of probability in making predictions or in making decisions becomes evident. Technology makes it possible to generate plots, find regression functions, compute correlation coefficients, and run simulations to better understand data. Statistical reasoning is a deeply rich and complex process which is essential to comprehend in order to stay informed in civic matters and personal decisionmaking.
Strand 
Statistical Reasoning  Measurement & Data 

Standard 
SR.C.1 Describe and compare measurable attributes. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
K.MD.A.1: Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. K.MD.A.2: Directly compare two objects with a measurable attribute in common, to see which object has "more of" / "less of" the attribute and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. K.MD.B.3: Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.) 
1.MD.A.1: Order three objects by length; compare the lengths of two objects indirectly by using a third object. 1.MD.A.2: Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of samesize length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. 
2.MD.A.4: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. 2.MD.A.1: Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. 2.MD.A.2: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. 2.MD.A.3: Estimate lengths using units of inches, feet, centimeters, and meters. 

Strand 
Statistical Reasoning  Measurement & Data 

Standard 
SR.C.2 Represent and interpret data. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
1.MD.C.4: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. 
2.MD.D.9: Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Organize and record data on a line plot, where the horizontal scale is marked off in wholenumber units. 2.MD.D.10: Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. Solve simple puttogether, takeapart, and compare problems using information presented in a bar graph. 

Strand 
Statistical Reasoning  Measurement & Data 

Standard 
SR.C.3 Relate addition and subtraction to length. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
2.MD.B.5: Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 2.MD.B.6: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,..., and represent wholenumber sums and differences within 100 on a number line diagram. 

Strand 
Statistical Reasoning  Measurement & Data 

Standard 
SR.C.4 Work with time and money. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
1.MD.B.3: Tell and write time in hours and halfhours using analog and digital clocks. 1.MD.D.5: Identify the coins and each corresponding value. (e.g. penny, nickel, dime, and quarter) 
2.MD.C.7: Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. 2.MD.C.8: Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? 

Strand 
Statistical Reasoning  Measurement & Data 

Standard 
SR.C.5 Solve problems involving measurement, conversion of measurement and estimation of intervals of time, liquid volumes, and masses of objects. 

Childhood 

Grade 3 Excludes compound units such as cm3 and finding the geometric volume of a container Excludes multiplicative comparison problems (problems involving notions of "times as much") 
Grade 4 
Grade 5 

Performance Expectations 
3.MD.A.1: Tell and write time to the nearest minute and measure time intervals in minutes using analog and digital clocks. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. 3.MD.A.2: Measure and estimate liquid volumes and masses of objects using standard metric units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same metric units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. 
4.MD.A.1: Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),... 4.MD.A.2: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 
5.MD.A.1: Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, real world problems. 

Strand 
Statistical Reasoning  Measurement & Data 

Standard 
SR.C.6 Represent and interpret data. 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
3.MD.B.3: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. 3.MD.B.4: Generate measurement data by measuring lengths of objects using rulers marked with halves and fourths of an inch. Record and show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or fourths. 
4.MD.B.4: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. 
5.MD.B.2: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. 

Strand 
Statistical Reasoning  Measurement & Data 

Standard 
SR.C.7 Understand concepts of Geometric measurement: involving perimeter, area, and volume. 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
3.MD.C.5: Recognize area as an attribute of plane figures and understand concepts of area measurement. 3.MD.C.5a: A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area. 3.MD.C.5b: A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. 3.MD.C.6: Measure areas by counting unit squares (square cm, square m, square in, square ft, and non standard units 3.MD.C.7: Relate area to the operations of multiplication and addition. 3.MD.C.7a: Find the area of a rectangle with wholenumber side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengths. 3.MD.C.7b: Multiply side lengths to find areas of rectangles with wholenumber side lengths in the context of solving real world and mathematical problems and represent wholenumber products as rectangular areas in mathematical reasoning. 3.MD.C.7c: Use tiling to show in a concrete case that the area of a rectangle with wholenumber side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning. 3.MD.C.7d: Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real world problems. 3.MD.D.8: Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. 
4.MD.A.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. 
5.MD.C.3: Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 5.MD.C.3a: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. 5.MD.C.3b: A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. 5.MD.C.4: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and nonstandard units. 5.MD.C.5: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. When finding volumes of objects answers will be in cubic units. 5.MD.C.5a: Find the volume of a right rectangular prism with wholenumber edge lengths by packing it with unit cubes and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. 5.MD.C.5b: Apply the formulas V = l x w x h and V = B x h (where B stands for the area of the base) for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real world and mathematical problems. 5.MD.C.5c: Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problems. 

Strand 
Statistical Reasoning  Measurement & Data 

Standard 
SR.C.8 Geometric measurement: understand concept of angle and measure angles. 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
4.MD.C.5: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: 4.Md.C.5a: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "onedegree angle," and can be used to measure angles. 4.MD.C.5b: An angle that turns through n onedegree angles is said to have an angle measure of n degrees. 4.MD.C.6: Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. 4.MD.C.7: Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. 
Strand 
Statistical Reasoning  Statistics & Probability 
Standard 
SR.EA.1 Summarize distribution using measures of center, variability, and graphical displays. 
Early Adolescence 

Grades 68 

Performance Expectations 
6.SP.A.1: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages. 6.SP.A.2: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean, median and/or mode), spread (range and/or interquartile range), and overall shape. 6.SP.A.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.SP.B.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.B.5: Summarize numerical data sets in relation to their context, such as by: 6.SP.B.5a: Reporting the number of observations. 6.SP.B.5b: Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. 6.SP.B.5c: Calculating quantitative measures of center (median and/or mean) and variability (range and/or interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. 6.SP.B.5d: Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. 
Strand 
Statistical Reasoning  Statistics & Probability 
Standard 
SR.EA.2 Use random sampling, visual representations, and measures of center and variability to draw inferences about one or more populations. 
Early Adolescence 

Grades 68 

Performance Expectations 
7.SP.A.1: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.A.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean length of a largemouth bass in a lake by randomly sampling largemouth bass from the lake; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. 7.SP.B.3: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team and both distributions have similar variability (mean absolute deviation) of about 5 cm. The difference between the mean heights of the two teams (10 cm) is about twice the variability (5 cm mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. 7.SP.B.4: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventhgrade science book are generally longer than the words in a chapter of a fourthgrade science book. 
Strand 
Statistical Reasoning  Statistics & Probability 
Standard 
SR.EA.3 Investigate chance processes and develop, use, and evaluate probability models. 
Early Adolescence 

Grades 68 

Performance Expectations 
7.SP.C.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 7.SP.C.6: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. 7.SP.C.7: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. 7.SP.C.7a: Develop a uniform probability model by assigning equal probability to all outcomes and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. 7.SP.C.7b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land openend down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? 7.SP.C.8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 7.SP.C.8a: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. 7.SP.C.8b: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event. 7.SP.C.8c: Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? 
Strand 
Statistical Reasoning  Statistics & Probability 
Standard 
SR.EA.4 Investigate patterns of association in bivariate data. 
Early Adolescence 

Grades 68 

Performance Expectations 
8.SP.A.1: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 8.SP.A.2: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. 8.SP.A.3: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. 8.SP.A.4: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? 
Strand 
Statistical Reasoning  Statistics & Probability: Interpreting Categorical & Quantitative Data Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
SR.A.1 Summarize, represent, and interpret data on a single count or measurement variable.* 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HHS.ID.A.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).* HSS.ID.A.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. * HSS.ID.A.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).* HSS.ID.A.4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.* 
Strand 
Statistical Reasoning  Statistics & Probability: Interpreting Categorical & Quantitative Data Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
SR.A.2 Summarize, represent, and interpret data on two categorical variables and two quantitative variables.* 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSS.ID.B.5: Summarize categorical data for two categories in twoway frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.* HSS.ID.B.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.* HSS.ID.B.6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.* HSS.ID.B.6b: Informally assess the fit of a function by plotting and analyzing residuals.* HSS.ID.B.6c: Fit a linear function for a scatter plot that suggests a linear association.* 
Strand 
Statistical Reasoning  Statistics & Probability: Interpreting Categorical & Quantitative Data Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
SR.A.3 Interpret linear models.* 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSS.ID.C.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.* HSS.ID.C.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.* HSS.ID.C.9: Distinguish between correlation and causation.* 
Strand 
Statistical Reasoning  Statistics & Probability: Making Inferences & Justifying Conclusions Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
SR.A.4 Understand and evaluate random processes underlying statistical experiments.* 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSS.IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.* HSS.IC.A.2: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?* 
Strand 
Statistical Reasoning  Statistics & Probability: Making Inferences & Justifying Conclusions Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
SR.A.5 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. * 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSS.IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.* HSS.IC.B.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.* HSS.IC.B.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.* HSS.IC.B.6: Evaluate reports based on data. For example, use an article in the local news and interpret the validity of the information presented. Consider animal wildlife reports, medical studies, and/or manufacturer claims.* 
Strand 
Statistical Reasoning  Statistics & Probability: Conditional Probability & the Rules of Probability Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). 
Standard 
SR.A.6 Understand independence and conditional probability and use them to interpret data.* 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSS.CP.A.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").* HSS.CP.A.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.* HSS.CP.A.3: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.* HSS.CP.A.4: Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.* HSS.CP.A.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. * 
Strand 
Statistical Reasoning  Statistics & Probability: Conditional Probability & the Rules of Probability Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
SR.A.7 Use the rules of probability to compute probabilities of compound events in a uniform probability model. * 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSS.CP.B.6: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.* HSS.CP.B.7: Apply the Addition Rule, P(A or B) = P(A) + P(B)  P(A and B), and interpret the answer in terms of the model.* (+) HSS.CP.B.8: Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BA) = P(B)P(AB), and interpret the answer in terms of the model.* (+) HSS.CP.B.9: Use permutations and combinations to compute probabilities of compound events and solve problems. * 
Strand 
Statistical Reasoning  Statistics & Probability: Using Probability to Make Decisions Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
SR.A.8 (+) Calculate expected values and use them to solve problems.* 
Adolescence 

Grades 9Diploma 

Performance Expectations 
(+) HSS.MD.A.1: Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.* (+) HSS.MD.A.2: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.* (+) HSS.MD.A.3: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiplechoice test where each question has four choices, and find the expected grade under various grading schemes. * (+) HSS.MD.A.4: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?* 
Strand 
Statistical Reasoning  Statistics & Probability: Using Probability to Make Decisions Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*). The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected. 
Standard 
SR.A.9 (+) Use probability to evaluate outcomes of decisions.* 
Adolescence 

Grades 9Diploma 

Performance Expectations 
(+) HSS.MD.B.5: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.* (+) HSS.MD.B.5a: Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fastfood restaurant.* (+) HSS.MD.B.5b: Evaluate and compare strategies on the basis of expected values. For example, compare a highdeductible versus a lowdeductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.* (+) HSS.MD.B.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). * (+) HSS.MD.B.7: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game and replacing the goalie with an extra skater).* 
Definitions:
Strand: A body of knowledge in a content area identified by a simple title.
Standard: Enduring understandings and skills that students can apply and transfer to contexts that are new to the student.
Performance Expectation: Building blocks to the standard and measurable articulations of what the student understands and can do.
Science, Technology, and Engineering Standards
Science and engineering provide people with knowledge and tools to understand and address many of the challenges of a rapidly changing world, thus enabling them to be creative and practical problem solvers (Maine Guiding Principle C). Science is a way of knowing about the world that enables people to both engage in the construction of new knowledge and to use information to achieve desired ends (NIH). Engineering enables people to systematically solve problems using scientific knowledge, to design and test solutions and evaluate them using agreedupon and measurable criteria.
Science and Engineering Literacy
In the last few decades, much has been written about the critical role of science literacy in an equitable and just society. For example, the Board on Science Education within the National Academies of Science argue that
"Science literacy is desirable not only for individuals, but also for the health and wellbeing of communities and society. More than just basic knowledge of science facts, contemporary definitions of science literacy have expanded to include understandings of scientific processes and practices, familiarity with how science and scientists work, a capacity to weigh and evaluate the products of science, and an ability to engage in civic decisions about the value of science."
Here we recognize that, in addition to understanding and evaluating science knowledge and critiquing the development of that knowledge, learners must also develop literacy related to science and engineering practices and design. In other words, they should know about and be able to critique the processes by which engineers develop and test products in response to consumer, industrial, and/or civic needs. The Maine Science and Engineering Standards provide a framework for supporting K12 students' development as selfdirected lifelong learners (Maine Guiding Principle B) who are able to apply knowledge from the domains of science and engineering to set goals and make decisions.
Understanding Controversy in Science
Individuals have ready access to abundant information in our
modern global society. Consequently, they will encounter myriad arguments
related to various scientific topics. Moreover, arguments will change over
time, as new evidence becomes available and as people draw on scientific
evidence to formulate arguments in shifting social contexts. It is therefore
imperative that individuals understand that controversy within the scientific
community is normal and has been historically productive. "True scientific
controversy involves competing scientific ideas that are evaluated according to
the standards of science  i.e., fitting the evidence, generating accurate
expectations, offering satisfying explanations, inspiring research, etc...few
theories fit our observations of the world perfectly. There is usually some
anomalous observation that doesn't seem to fit with our current understanding.
Scientists assume that by working at such anomalies, they'll either disentangle
them to see how they fit with the current theory or contribute to a new theory"
("Even Theories Change." Understanding Science. University of California Museum
of Paleontology. 23 July 2018
Becoming Critical and Engaged Consumers of Science and Engineering
As learners encounter diverse perspectives related to scientific issues, it is crucial that they become integrative and informed thinkers (Maine Guiding Principle E) able to discern reliable and valid information. Such information is generated through accepted scientific and engineering practices (e.g., analyzing and interpreting data, engaging in argument from evidence, etc.). Armed with knowledge and these skills, learners will be able to function as responsible and involved citizens (Maine Guiding Principle D) who utilize clear and effective communication strategies (Maine Guiding Principle A) to participate productively in decision making that impacts the broader community.
References:
National Research Council. 2012. A Framework for K12 Science Education: Practices, Crosscutting Concepts, and Core Ideas. Washington, DC: The National Academies Press.
From NAEP (https://nces.ed.gov/nationsreportcard/tel/)
NGSS Lead States. (2013). Next Generation Science Standards: For states, by states. Washington, DC: The National Academies Press.
https://www.ncbi.nlm.nih.gov/books/NBK396081/
Committee on Science Literacy and Public Perception of Science; Board on Science Education; Division of Behavioral and Social Sciences and Education; National Academies of Sciences, Engineering, and Medicine; Snow CE, Dibner KA, editors.
Washington (DC): National Academies Press (US); 2016 Oct 14.
OUTLINE OF SCIENCE, TECHNOLOGY AND ENGINEERING STRANDS AND STANDARDS
Physical Sciences
PS1 Matter and Its Interactions
PS2 Motion and Stability: Forces and Interactions
PS3 Energy
PS4 Waves and Their Applications in Technologies
Life Sciences
LS1 From Molecules to Organisms: Structures and Processes
LS2 Ecosystems: Interactions, Energy, and Dynamics
LS3 Heredity: Inheritance and Variation of Traits
LS4 Biological Evolution: Unity and Diversity
Earth and Space Sciences
ESS1 Earth's Place in the Universe
ESS2 Earth's Systems
ESS3 Earth and Human Activity Engineering, Technology, and Applications of Science
ETS1 Engineering Design
HOW TO READ THE STANDARDS 
COLOR SCHEME 
Science & Engineering Practices (blue) Disciplinary Core Ideas (orange) Crosscutting Concepts (green) 
Strand 
Physical Science (PS) 

Standard 
PS1: Matter and Its Interactions 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
2PS11 Plan and conduct an investigation to describe and classify different kinds of materials by their observable properties. Further explanation: Observations could include color, texture, hardness, and flexibility. Patterns could include the similar properties that different materials share. Planning and Carrying out Investigations, Structure and Properties of Matter, Patterns 2PS12 Analyze data obtained from testing different materials to determine which materials have the properties that are best suited for an intended purpose. Further explanation: Examples of properties could include strength, flexibility, hardness, texture, and absorbency. Potential Maine connections include snow tires vs. regular tires and mittens made of varying materials (e.g. wool, cotton, Gortex, etc.) Analyzing and Interpreting Data, Structure and Properties of Matter, Cause and Effect 2PS13 Make observations to construct an evidencebased account of how an object made of a small set of pieces can be disassembled and made into a new object. Further explanation: Examples of pieces could include blocks, building bricks, or other assorted small objects. Constructing Explanations and Designing Solutions, Structure and Properties of Matter, Energy and Matter 2PS14 Construct an argument with evidence that some changes caused by heating or cooling can be reversed and some cannot. Further explanation: Examples of reversible changes could include materials such as water and butter at different temperatures. Potential Maine examples include snow and ice having reversible properties (e.g. water freezes and thaws which allows for ice fishing and skating in colder months). Examples of irreversible changes could include cooking an egg, freezing a plant leaf, heating paper and burning wood in a campfire or woodstove. Engaging in Argument from Evidence, Chemical Reactions, Cause and Effect 
Strand 
Physical Science (PS) 

Standard 
PS1: Matter and Its Interactions 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
5PS11 Develop a model to describe that matter is made of particles too small to be seen. Further Explanation: Examples of evidence could include adding air to expand a basketball, compressing air in a syringe, dissolving sugar in water, and evaporating salt water. Investigate the science behind creating Maine maple sugar. Developing and Using Models, Structure and Properties of Matter, Scale, Proportion, and Quantity 5PS12 Measure and graph quantities to provide evidence that regardless of the type of change that occurs when heating, cooling, or mixing substances, the total weight of matter is conserved. Further Explanation: Examples of reactions or changes could include phase changes, dissolving, and mixing that form new substances. Investigate the conservation of mass when making fake snow and how the crystals form. Using Mathematics and Computational Thinking, Structure and Properties of Matter, Chemical Reactions, Cause and Effect 5PS13 Make observations and measurements to identify materials based on their properties. Further Explanation: Examples of materials to be identified could include baking soda and other powders, metals, minerals, and liquids. Examples of properties could include color, hardness, reflectivity, electrical conductivity, thermal conductivity, response to magnetic forces, and solubility; density is not intended as an identifiable property. Possibly examine Maine minerals. Planning and Carrying out Investigations, Structure and Properties of Matter, Scale, Proportion and Quantity 5PS14 Conduct an investigation to determine whether the mixing of two or more substances results in new substances. Planning and Carrying out Investigations, Chemical Reactions, Cause and Effect 
Strand 
Physical Science (PS) 
Standard 
PS1: Matter and Its Interactions 
Early Adolescence 

Grades 68 

Performance Expectations 
MSPS11 Develop models to describe the atomic composition of simple molecules and extended structures. Further explanation: Emphasis is on developing models of molecules that vary in complexity. Examples of simple molecules could include ammonia and methanol. Examples of extended structures could include sodium chloride or diamonds. Examples of molecularlevel models could include drawings, threedimensional ball and stick structures, or computer representations showing different molecules with different types of atoms. Developing and using models; Obtaining, evaluating, and communicating information; structure and properties of matter; scale, proportion, and quantity MSPS12 Analyze and interpret data on the properties of substances before and after the substances interact to determine if a chemical reaction has occurred. Further explanation: Examples of reactions could include burning sugar or steel wool, fat reacting with sodium hydroxide, and mixing zinc with hydrogen chloride. Examine electrical conductivity differences between fresh water and sea water. Obtaining, evaluating, and communicating information; Analyzing and interpreting data; structure and properties of matter; chemical reactions; patterns 
MSPS13 Gather and make sense of information to describe that synthetic materials come from natural resources and impact society. Further explanation: Emphasis is on natural resources that undergo a chemical process to form synthetic material. Examples of new materials could include new medicines, foods, and alternative fuels (alternative plastics derived from potatoes and jet fuel made from trees). Other possible areas of study might include plastics from organics, advanced composites and wood products under development at UMO. Obtaining, evaluating, and communicating information; chemical reactions; structure and properties of matter; structure and function 

MSPS14 Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed. Further explanation: Emphasis is on qualitative molecularlevel models of solids, liquids, and gases to show that adding or removing thermal energy increases or decreases kinetic energy of the particles until a change of state occurs. Examples of models could include drawings and diagrams. Examples of particles could include molecules or inert atoms. Examples of pure substances could include water, carbon dioxide, and helium. Developing and using models; structure and properties of matter; definitions of energy; cause and effect 

MSPS15 Develop and use a model to describe how the total number of atoms does not change in a chemical reaction and thus mass is conserved. Further explanation: Emphasis is on the law of conservation of matter and on physical models or drawings, including digital forms that represent atoms. Developing and using models; chemical reactions; energy and matter 

MSPS16 Undertake a design project to construct, test, and modify a device that either releases or absorbs thermal energy by chemical processes. Further explanation: Emphasis is on design, controlling the transfer of energy to the environment, and modification of a device using factors such as type and concentration of a substance. Examples of designs could involve chemical reactions such as dissolving ammonium chloride or calcium chloride for road treatments in Maine winters. Constructing explanations and designing solutions; chemical reactions; developing possible solutions; optimizing the design solution; structure and function 
Strand 
Physical Science (PS) 
Standard 
PS1: Matter and Its Interactions 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSPS11 Use the periodic table as a model to predict the relative properties of elements based on the patterns of electrons in the outermost energy level of atoms. Further explanation: Examples of properties that could be predicted from patterns could include reactivity of metals, types of bonds formed, numbers of bonds formed, and reactions with oxygen. Examples include the properties and bonding of water and the rusting of metals as found in guardrails, ship parts, etc. Consider the metal compounds found in fireworks. Developing and Using Models, structure and properties of matter, types of interactions, patterns 
HSPS12 Construct and revise an explanation for the outcome of a simple chemical reaction based on the outermost electron states of atoms, trends in the periodic table, and knowledge of the patterns of chemical properties. Further explanation: Examples of chemical reactions could include the reaction of sodium and chlorine, carbon and oxygen, or carbon and hydrogen. Examples could include ocean salt formation, combustion (as found in the burning of fuels in Maine homes, cars and the trucking industry) or the detection of carbon monoxide in a home (complete vs incomplete combustion). Constructing Explanations and Designing Solutions, structure and properties of matter, chemical reaction, patterns 

HSPS13 Plan and conduct an investigation to gather evidence to compare the structure of substances at the bulk scale to infer the strength of electrical forces between particles. Further explanation: Emphasis is on understanding the strengths of forces between particles, not on naming specific intermolecular forces (such as dipoledipole). Examples of particles could include ions, atoms, molecules, and networked materials (such as graphite). Examples of bulk properties of substances could include the melting point and boiling point, vapor pressure, and surface tension. Examples could consider why we salt roads in the winter, differences in melting points of water vs saltwater, the production of maple syrup or the strength of Maine minerals. Planning and Carrying out Investigations, structure and properties of matter, types of interactions, patterns 

HSPS14 Develop a model to illustrate that the release or absorption of energy from a chemical reaction system depends on the changes in total bond energy. Further explanation: Emphasis is on the idea that a chemical reaction is a system that affects the energy change. Examples of models could include molecularlevel drawings and diagrams of reactions, graphs showing the relative energies of reactants and products, and representations showing energy is conserved. Developing and Using Models, structure and properties of matter, Energy and Matter 

HSPS15 Apply scientific principles and evidence to provide an explanation about the effects of changing the temperature or concentration of the reacting particles on the rate at which a reaction occurs. Further explanation: Emphasis is on student reasoning that focuses on the number and energy of collisions between molecules. Examples could include the varied rates of oxidation of metals in winter vs in summer or the rate of dissolution of calcium shells in the ocean due to an increase in carbon dioxide an increase in temperature from climate change. Constructing Explanations and Designing Solutions, Chemical Reactions, patterns 

HSPS16 Refine the design of a chemical system by specifying a change in conditions that would produce increased amounts of products at equilibrium. Further explanation: Emphasis is on the application of Le Chatelier's Principle and on refining designs of chemical reaction systems, including descriptions of the connection between changes made at the macroscopic level and what happens at the molecular level. Examples of designs could include different ways to increase product formation including adding reactants or removing products. Other examples to consider include the Kraft paper making process, soap making or rock candy formation. Constructing Explanations and Designing Solutions, structure and properties of matter, Chemical Reactions, Types of Interactions, Optimizing Design Solution patterns, cause and effect, scale, proportion, and quantity 

HSPS17 Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction. Further explanation: Emphasis is on using mathematical ideas to communicate the proportional relationships between masses of atoms in the reactants and the products, and the translation of these relationships to the macroscopic scale using the mole as the conversion from the atomic to the macroscopic scale. Emphasis is on assessing students' use of mathematical thinking and not on memorization and rote application of problemsolving techniques. Examples could include the proportion of ingredients combined in baked goods or the combustion of fuels. Using Mathematics and Computational Thinking, Chemical Reactions, Energy and Matter 

HSPS18 Develop models to illustrate the changes in the composition of the nucleus of the atom and the energy released during the processes of fission, fusion, and radioactive decay. Further explanation: Emphasis is on simple qualitative models, such as pictures or diagrams and on the scale of energy released in nuclear processes relative to other kinds of transformations. Examples could include radon gas in basements, thorium in white gas mantles or, historically, Wiscasset's Maine Yankee nuclear power plant and Fukushima in Japan. Developing and engineering practices, Nuclear Processes, patterns, cause and effect, scale, proportion, and quantity 
Strand 
Physical Science (PS) 

Standard 
PS2: Motion and Stability: Forces and Interactions 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
KPS21 Plan and conduct an investigation to compare the effects of different strengths or different directions of pushes and pulls on the motion of an object. Further explanation: Examples of pushes or pulls could include a string attached to an object being pulled, a person pushing an object, a person stopping a rolling ball, and two objects colliding and pushing on each other. Planning and Carrying out Investigations, Forces and Motion, Types of Interactions, Relationship between Energy and Forces, Cause and Effect KPS22 Analyze data to determine if a design solution works as intended to change the speed or direction of an object with a push or a pull. Further explanation: Examples of problems requiring a solution could include having a marble or other object move a certain distance, follow a particular path, and knock down other objects. Examples of solutions could include tools such as a ramp to increase the speed of the object and a structure that would cause an object such as a marble or ball to turn. Analyzing and Interpreting Data, Forces and Motion, Defining Engineering Problems, Cause and Effect 
Strand 
Physical Science (PS) 

Standard 
PS2: Motion and Stability: Forces and Interactions 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
3PS21 Plan and conduct an investigation to provide evidence of the effects of balanced and unbalanced forces on the motion of an object. Further Explanation: Examples could include an unbalanced force on one side of a ball can make it start moving and balanced forces pushing on a box from both sides will not produce any motion at all. Other examples can be found in a variety of Maine sports from ice skating, curling, skiing to sledding. Planning and Carrying Out Investigations, Forces and Motion, Types of Interactions, Cause and Effect 3PS22 Make observations and/or measurements of an object's motion to provide evidence that a pattern can be used to predict future motion. Further Explanation: Examples of motion with a predictable pattern could include a child swinging in a swing, a ball rolling back and forth in a bowl, and two children on a seesaw. Other examples include dropping down in a skate park, snowboarding pipes and telemark skiing (slowing down, turns, etc.). Planning and Carrying out Investigations, Forces and Motion, Patterns 3PS23 Ask questions to determine cause and effect relationships of electrical or magnetic interactions between two objects not in contact with each other. Further Explanation: Examples of an electric force could include the force on hair from an electrically charged balloon and the electrical forces between a charged rod and pieces of paper; examples of a magnetic force could include the force between two permanent magnets, the force between an electromagnet and steel paperclips, and the force exerted by one magnet versus the force exerted by two magnets. Examples of cause and effect relationships could include how the distance between objects affects strength of the force and how the orientation of magnets affects the direction of the magnetic force. Asking Questions and Defining Problems, Types of Interactions, Cause and Effect 3PS24 Define a simple design problem that can be solved by applying scientific ideas about magnets. Further Explanation: Examples of problems could include constructing a latch to keep a door shut and creating a device to keep two moving objects from touching each other. Other examples include a magnetic latch for a container or device (Apple and magnetic plug for charger). Asking Questions and Defining Problems, Types of Interactions 
5PS21 Support an argument that the gravitational force exerted by Earth on objects is directed down. Further Explanation: "Down" is a local description of the direction that points toward the center of the spherical Earth. Engaging in Argument from Evidence, Types of Interactions, Cause and Effect 
Strand 
Physical Science (PS) 
Standard 
PS2: Motion and Stability: Forces and Interactions 
Early Adolescence 

Grades 68 

Performance Expectations 
MSPS21 Apply Newton's Third Law to design a solution to a problem involving the motion of two colliding objects. Further explanation: Examples of practical problems could include the impact of collisions between two cars, between a car and stationary objects, and between a meteor and a space vehicle. Constructing explanations and designing solutions; forces and motion; system and system models; 
MSPS22 Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object. Further explanation: Emphasis is on balanced (Newton's First Law) and unbalanced forces in a system, qualitative comparisons of forces, mass and changes in motion (Newton's Second Law), frame of reference, and specification of units. Plan and carry out investigations; forces and motion; stability and change; 

MSPS23 Ask questions about data to determine the factors that affect the strength of electrical and magnetic forces. Further explanation: Examples of devices that use electrical and magnetic forces could include electromagnets, electric motors, or generators. Examples of data could include the effect of the number of turns of wire on the strength of an electromagnet, or the effect of increasing the number or strength of magnets on the speed of an electric motor. Possible explorations include the effects of living near high tension power lines, the similarities found in hydroelectric generators and wind turbines or the growing electric car market in Maine. Asking questions and defining problems; types of interactions; cause and effect; 

MSPS24 Construct and present arguments using evidence to support the claim that gravitational interactions are attractive and depend on the masses of interacting objects. Further explanation: Examples of evidence for arguments could include data generated from simulations or digital tools and charts displaying mass, strength of interaction, distance from the Sun, and orbital periods of objects within the solar system. Examples include the gravitational effects of the moon on Maine tides. Engaging in argument from evidence; types of interactions; system and system models; 

MSPS25 Conduct an investigation and evaluate the experimental design to provide evidence that fields exist between objects exerting forces on each other even though the objects are not in contact. Further explanation: Examples of this phenomenon could include the interactions of magnets, electricallycharged strips of tape, electricallycharged pith balls, and maglev trains. Examples of investigations could include firsthand experiences or simulations. Plan and carry out investigations; types of interactions; cause and effect; 
Strand 
Physical Science (PS) 
Standard 
PS2: Motion and Stability: Forces and Interactions 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSPS21 Analyze data to support the claim that Newton's second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration. Further explanation: Examples of data could include tables or graphs of position or velocity as a function of time for objects subject to a net unbalanced force, such as a falling object, an object rolling down a ramp, or moving object being pulled by a constant force. Examples could include the acceleration of a snowmobile in different gears (same mass with different forces creating different accelerations) or the comparison of gas mileage between a truck vs a truck hauling a boat (same acceleration with different masses). Analyzing and Interpreting Data, Types of Interactions, Forces and Motion, Cause and Effect 
HSPS22 Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system. Further explanation: Emphasis is on the quantitative conservation of momentum in interactions and the qualitative meaning of this principle. Examples could include jumping off a boat or canoe and the total momenta of all the various pieces exploding from fireworks. Using Mathematics and Computational Thinking, Forces and Motion, Systems and System Models 

HSPS23 Apply scientific and engineering ideas to design, evaluate, and refine a device that minimizes the force on a macroscopic object during a collision. Further explanation: Examples of evaluation and refinement could include determining the success of a device at protecting an object from damage and modifying the design to improve it. Examples of a device could include a football helmet or a parachute. Examples could also include the barriers on the sides of NASCAR tracks, truck safety hills on the sides of highways, bike helmets or car bumpers. Constructing Explanations and Designing Solutions, structure and properties of matter, Forces and Motion, Defining and Delimiting Engineering Problems, Optimizing the Design Solution, types of interactions, Cause and Effects 

HSPS24 Use mathematical representations of Newton's Law of Gravitation and Coulomb's Law to describe and predict the gravitational and electrostatic forces between objects. Further explanation: Emphasis is on both quantitative and conceptual descriptions of gravitational and electrical fields. Using Mathematics and Computational Thinking, Types of Interactions, Patterns 

HSPS25 Plan and conduct an investigation to provide evidence that an electric current can produce a magnetic field and that a changing magnetic field can produce an electric current. Further explanation: Examples could include wind turbines or generators along with any DC motorized toy. Planning and Carrying out an Investigation, Types of Interactions, Definitions of Energy, Cause and Effect 

HSPS26 Communicate scientific and technical information about why the molecularlevel structure is important in the functioning of designed materials. Further explanation: Emphasis is on the attractive and repulsive forces that determine the functioning of the material. Examples could include why electrically conductive materials are often made of metal, flexible but durable materials are made up of long chained molecules, and pharmaceuticals are designed to interact with specific receptors. Examples could also include composite material substitutes for wood and the structure of solar cells along with how they work. Obtaining, Evaluating, and Communicating Information, Structure and Property of Matter, Types of Interactions, Structure and Function 
Strand 
Physical Science (PS) 

Standard 
PS3: Energy 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
KPS31 Make observations to determine the effect of sunlight on Earth's surface. Further explanation: Examples of Earth's surface could include sand, soil, rocks, and water. Potential Maine connections could also include beach sand in the sun vs. beach sand in the shade. Planning and Carrying out Investigations, Conservation of Energy and Energy Transfer, Cause and Effect KPS32 Use tools and materials to design and build a structure that will reduce the warming effect of sunlight on an area. Further explanation: Examples of structures could include umbrellas, canopies, and tents that minimize the warming effect of the sun. Constructing Explanations and Designing Solutions, Conservation of Energy and Energy Transfer, Cause and Effect 
Strand 
Physical Science (PS) 

Standard 
PS3: Energy 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
4PS31 Use evidence to construct an explanation relating the speed of an object to the energy of that object. Further Explanation: Examples include coasting on a bike down a hill or how bumping into someone or something when walking or running changes speed. Other examples include dropping into a skateboard bowl or off of a ramp. Constructing Explanations and Designing Solutions, Definitions of Energy, Cause and Effect 4PS32 Make observations to provide evidence that energy can be transferred from place to place by sound, light, heat, and electric currents. Planning and Carrying out Investigations, Definitions of Energy, Conservation of Energy and Energy Transfer, Cause and Effect 4PS33 Ask questions and predict outcomes about the changes in energy that occur when objects collide. Further Explanation: Emphasis is on the changes in the energy due to the changes in speed, not on the forces, as objects interact. These changes can be observed in playing pool or marbles. Asking Questions and Defining Problems, Definitions of Energy, Conservation of Energy and Energy Transfer, Relationship between Energy and Forces, Cause and Effect 4PS34 Apply scientific ideas to design, test, and refine a device that converts energy from one form to another. Further Explanation: Examples of devices could include electric circuits that convert electrical energy into motion energy of a vehicle, light, or sound and a passive solar heater that converts light into heat. Such devices can be used to make s'mores or to turn on a small light when camping in the Maine woods. Examples of constraints could include the materials, cost, or time to design the device. Constructing Explanations and Designing Solutions, Natural Hazards, Conservation of Energy and Energy Transfer, Energy in Chemical Processes, Defining Engineering Problems, Cause and Effect 
5PS31 Use models to describe that energy in animals' food (used for body repair, growth, and motion, and to maintain body warmth) was once energy from the sun. Further Explanation: Examples of models could include diagrams, and flow charts. Developing and Using Models, Energy in Chemical Processes and Everyday Life, Organization for Matter and Energy Flow in Organisms, Energy and Matter 
Strand 
Physical Science (PS) 
Standard 
PS3: Energy 
Early Adolescence 

Grades 68 

Performance Expectations 
MSPS31 Construct and interpret graphical displays of data to describe the relationships of kinetic energy to the mass of an object and to the speed of an object. Further explanation: Emphasis is on descriptive relationships between kinetic energy and mass separately from kinetic energy and speed. Examples could include riding a bicycle at different speeds, rolling different sizes of rocks downhill, and getting hit by a whiffle ball versus a tennis ball. Consider different sized skiers or different vehicles from pulp trucks to personal cars. Analyzing and interpreting data; definitions of energy; scale, proportion, and quantity 
MSPS32 Develop a model to describe that when the arrangement of objects interacting at a distance changes, different amounts of potential energy are stored in the system. Further explanation: Emphasis is on relative amounts of potential energy, not on calculations of potential energy. Examples of objects within systems interacting at varying distances could include the Earth and either a roller coaster cart at varying positions on a hill or objects at varying heights on shelves, changing the direction/orientation of a magnet, and a balloon with static electrical charge being brought closer to a classmate's hair. Examples of models could include representations, diagrams, pictures, and written descriptions of systems. Developing and using models; definitions of energy; relationship between energy and forces; system and system models 

MSPS33 Apply scientific principles to design, construct, and test a device that either minimizes or maximizes thermal energy transfer. Further explanation: Examples of devices could include an insulated box, a solar cooker, and a Styrofoam cup. Possible explorations could include insulating outerwear and clothing for winter sports or emergency shelters designed for Maine winters. Constructing explanations and designing solutions; definitions of energy; conservation of energy and energy transfer; defining and delimiting an engineering problem; developing possible solutions; energy and matter 

MSPS34 Plan an investigation to determine the relationships among the energy transferred, the type of matter, the mass, and the change in the average kinetic energy of the particles as measured by the temperature of the sample. Further explanation: Examples of experiments could include comparing final water temperatures after different masses of ice melted in the same volume of water with the same initial temperature, the temperature change of samples of different materials with the same mass as they cool or heat in the environment, or the same material with different masses when a specific amount of energy is added. Planning and carrying out investigations, Definitions of energy; conservation of energy and energy transfer; scale, proportion, and quantity 

MSPS35 Construct, use, and present arguments to support the claim that when the kinetic energy of an object changes, energy is transferred to or from the object. Further explanation: Examples of empirical evidence used in arguments could include an inventory or other representation of the energy before and after the transfer in the form of temperature changes or motion of an object. Engaging in argument from evidence; conservation of energy and energy transfer; energy and matter 
Strand 
Physical Science (PS) 
Standard 
PS3: Energy 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSPS31 Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known. Further explanation: Emphasis is on explaining the meaning of mathematical expressions used in the model. Examples could include wind turbines, hydroelectric or tidal power. Further examples could be found in FunTown USA roller coasters or any sport (e.g. why a hockey puck changes motion, a baseball being hit, etc.). Using Mathematics and Computational Thinking, Definitions of Energy, Conservation of Energy and Energy Transfer, Systems and System Models 
HSPS32 Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects). Further explanation: Examples of phenomena at the macroscopic scale could include the conversion of kinetic energy to thermal energy, the energy stored due to position of an object above the earth, and the energy stored between two electricallycharged plates. Examples of models could include diagrams, drawings, descriptions, and computer simulations. Developing and Using Models, Definitions of Energy, Energy and Matter 

HSPS33 Design, build, and refine a device that works within given constraints to convert one form of energy into another form of energy. Further explanation: Emphasis is on both qualitative and quantitative evaluations of devices. Examples of devices could include Rube Goldberg devices, wind turbines, solar cells, solar ovens, and generators. Examples of constraints could include use of renewable energy forms and efficiency. Consider the Wind Blade Challenge or use of a solar oven when camping. Constructing Explanations and Designing Solutions, Definitions of Energy, Defining and Delimiting Engineering Problems, Energy and Matter 

HSPS34 Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics). Further explanation: Emphasis is on analyzing data from student investigations and using mathematical thinking to describe the energy changes both quantitatively and conceptually. Examples of investigations could include mixing liquids at different initial temperatures or adding objects at different temperatures to water. Other examples can be found in heat pumps for radiant heat systems, insulation (to prevent heat transfer) or the use of hot rocks to warm a tent when camping. Planning and Carrying out an Investigation, Conservation of Energy and Energy Transfer, Energy in Chemical Processes, Systems and System Models 

HSPS35 Develop and use a model of two objects interacting through electrical or magnetic fields to illustrate the forces between objects and the changes in energy of the objects due to the interaction. Further explanation: Examples of models could include drawings, diagrams, and texts, such as drawings of what happens when two charges of opposite polarity are near each other. Developing and Using Models, Relationship between Energy and Forces, Cause and Effect 
Strand 
Physical Science (PS) 

Standard 
PS4: Waves and Their Applications in Technologies for Information Transfer 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
1PS41 Plan and conduct investigations to provide evidence that vibrating materials can make sound and that sound can make materials vibrate. Further explanation: Examples of vibrating materials that make sound could include tuning forks and plucking a stretched string. Examples of how sound can make matter vibrate could include holding a piece of paper near a speaker making sound and holding an object near a vibrating tuning fork. Planning and Carrying Out Investigations, Wave Properties, Cause and Effect 1PS42 Make observations to construct an evidencebased account that objects can be seen only when illuminated. Further explanation: Examples of observations could include those made in a completely dark room, a pinhole box, and a video of a cave explorer (in Acadia National Park) with a flashlight. Illumination could be from an external light source or by an object giving off its own light. Constructing Explanations and Designing Solutions, Electromagnetic Radiation, Cause and Effect 1PS43 Plan and conduct an investigation to determine the effect of placing objects made with different materials in the path of a beam of light. Further explanation: Examples of materials could include those that are transparent (such as clear plastic), translucent (such as wax paper), opaque (such as cardboard), and reflective (such as a mirror). Planning and Carrying out Investigations, Electromagnetic Radiation, Cause and Effect 1PS44 Use tools and materials to design and build a device that uses light or sound to solve the problem of communicating over a distance. Further explanation: Examples of devices could include a light source to send signals, paper cup and string "telephones," and a pattern of drum beats. Constructing Explanations and Designing Solutions, Information Technologies and Instrumentation 
Strand 
Physical Science (PS) 

Standard 
PS4: Waves and Their Applications in Technologies for Information Transfer 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
4PS41 Develop a model of waves to describe patterns in terms of amplitude and wavelength and that waves can cause objects to move. Further Explanation: Examples of models could include diagrams, analogies, and physical models using wire to illustrate wavelength and amplitude of waves. Use an oscilloscope app to illustrate the patterns in an animal call or musical instrument and engineer a pattern to mimic the call. Developing and Using Models, Wave Properties, Patterns 4PS42 Develop a model to describe that light reflecting from objects and entering the eye allows objects to be seen. Further Explanation: Examples of Maine animal eyes at night such as coyotes, deer and foxes reflecting light from their retinas. Developing and Using Models, Electromagnetic Radiation, Patterns 4PS43 Generate and compare multiple solutions that use patterns to transfer information. Further Explanation: Examples of solutions could include drums sending coded information through sound waves, using a grid of 1's and 0's representing black and white to send information about a picture, and using Morse code to send text or introduce basic computer code. Constructing Explanations and Designing Solutions, Information Technologies and Instrumentation, Optimizing the Design Solution, Patterns 
Strand 
Physical Science (PS) 
Standard 
PS4: Waves and Their Applications in Technologies for Information Transfer 
Early Adolescence 

Grades 68 

Performance Expectations 
MSPS41 Use mathematical representations to describe a simple model for waves that includes how the amplitude of a wave is related to the energy in a wave. Further explanation: Emphasis is on describing waves with both qualitative and quantitative thinking. Possibilities for exploration might include coastal wave erosion, effects of the wind turbines/farms on the air flow patterns and harmonics. Using mathematics and computational thinking; Obtaining, evaluating, and communicating information; wave properties; patterns 
MSPS42 Develop and use a model to describe that waves are reflected, absorbed, or transmitted through various materials. Further explanation: Emphasis is on both light and mechanical waves. Examples of models could include drawings, simulations, and written descriptions. Possibilities for explorations might include Maine's geographic location for utilizing solar power, power generation from ocean waves, possibility for extended farming seasons with artificial lighting. Developing and using models; wave properties; electromagnetic radiation; structure and function 

MSPS43 Integrate qualitative scientific and technical information to support the claim that digitized signals are a more reliable way to encode and transmit information than analog signals. Further explanation: Emphasis is on a basic understanding that waves can be used for communication purposes. Examples could include using fiber optic cable to transmit light pulses, radio wave pulses in WiFi devices, and conversion of stored binary patterns to make sound or text on a computer screen. Obtaining, evaluating, and communicating information; information technologies and instrumentation; structure and function 
Strand 
Physical Science (PS) 
Standard 
PS4: Waves and Their Applications in Technologies for Information Transfer 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSPS41 Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media. Further explanation: Examples of data could include electromagnetic radiation traveling in a vacuum and glass, sound waves traveling through air and water, and seismic waves traveling through the Earth. Examples include rainbows and how to aim when spearfishing. Using Mathematics and Computational Thinking, Wave Properties, Cause and Effect 
HSPS42 Evaluate questions about the advantages of using a digital transmission and storage of information. Further explanation: Examples of advantages could include that digital information is stable because it can be stored reliably in computer memory, transferred easily, and copied and shared rapidly. Disadvantages could include issues of easy deletion, security, and theft. Asking Questions and Defining Problems, Wave Properties, Stability and Change 

HSPS43 Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described either by a wave model or a particle model, and that for some situations one model is more useful than the other. Further explanation: Emphasis is on how the experimental evidence supports the claim and how a theory is generally modified in light of new evidence. Examples of a phenomenon could include resonance, interference, diffraction, and photoelectric effect. Engaging in Argument from Evidence, Wave Properties, Systems and System Models 

HSPS44 Evaluate the validity and reliability of claims in published materials of the effects that different frequencies of electromagnetic radiation have when absorbed by matter. Further explanation: Emphasis is on the idea that photons associated with different frequencies of light have different energies, and the damage to living tissue from electromagnetic radiation depends on the energy of the radiation. Examples of published materials could include trade books, magazines, web resources, videos, and other passages that may reflect bias. Arguments around evidence could be made for dangers of cell phone usage or living near high voltage power lines. Obtaining, Evaluating, and Communicating Information, Electromagnetic Radiation, Cause and Effect 

HSPS45 Communicate technical information about how some technological devices use the principles of wave behavior and wave interactions with matter to transmit and capture information and energy. Further explanation: Examples could include solar cells capturing light and converting it to electricity; medical imaging; and communications technology. Obtaining, Evaluating, and Communicating Information, Wave Properties, Electromagnetic Radiation, Information Technologies and Instrumentation, Cause and Effect 
Strand 
Life Sciences (LS) 

Standard 
LS1: From Molecules to Organisms: Structures and Processes 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
KLS11 Use observations to describe patterns of what plants and animals (including humans) need to survive. Further explanation: Examples of patterns could include that animals need to take in food but plants do not, the different kinds of food needed by different types of animals, the requirement of plants to have light, and that all living things need water. Examples could include the pattern a bear makes when preparing to hibernate for winter, the seasonal patterns of trees losing and/or keeping their leaves. Analyzing and Interpreting Data, Organization for Matter and Energy Flow in Organisms, Patterns 
1LS11 Use materials to design a solution to a human problem by mimicking how plants and/or animals use their external parts to help them survive, grow, and meet their needs. Further explanation: Examples of human problems that can be solved by mimicking plant or animal solutions could include designing clothing or equipment to protect bicyclists by mimicking turtle shells, acorn shells, and animal scales; stabilizing structures by mimicking animal tails and roots on plants; keeping out intruders by mimicking thorns on branches and animal quills; waterproofing boots, jackets, gloves thereby mimicking animal feathers and, detecting intruders by mimicking eyes and ears. Constructing Explanations and Designing Solutions, Structure and Function, Information Processing, Structure and Function 1LS12 Read texts and use media to determine patterns in behavior of parents and offspring that help offspring survive. Further explanation: Examples of patterns of behaviors could include the signals that offspring make (such as crying, cheeping, and other vocalizations) and the responses of the parents (such as feeding, comforting, and protecting the offspring). Potential Maine connections include Maine animal sounds to signal their offspring (e.g. loons, moose, deer, coyotes, etc.) and how animals, especially birds, bring back food for their young. Obtaining, Evaluating, and Communicating Information, Growth and Development of Organisms, Patterns 
Strand 
Life Sciences (LS) 

Standard 
LS1: From Molecules to Organisms: Structures and Processes 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
3LS11 Develop models to describe that organisms have unique and diverse life cycles but all have in common birth, growth, reproduction, and death. Further Explanation: Changes organisms go through during their life form a pattern. Potential Maine connections include frogs in vernal pools, Atlantic salmon life cycle and gestation vs. metamorphosis. Developing and Using Models, Growth and Development of Organisms, Patterns 
4LS11 Construct an argument that plants and animals have internal and external structures that function to support survival, growth, behavior, and reproduction. Further Explanation: Examples of structures could include thorns, stems, roots, colored petals, heart, stomach, lung, brain, and skin found in Maine plants and animals. Engaging in Argument from Evidence, Structure and Function, Systems and System Models 4LS12 Use a model to describe that animals receive different types of information through their senses, process the information in their brain, and respond to the information in different ways. Further Explanation: Emphasis is on systems of information transfer. Engaging in Argument from Evidence, Information Processing, Systems and System Models 
5LS11 Support an argument that plants get the materials they need for growth chiefly from air and water. Further Explanation: Emphasis is on the idea that plant matter comes mostly from air and water, not from the soil. Investigate Maine plants. Engaging in Argument from Evidence, Organization for Matter and Energy Flow in Organisms, Energy and Matter 
Strand 
Life Sciences (LS) 
Standard 
LS1: From Molecules to Organisms: Structures and Processes 
Early Adolescence 

Grades 68 

Performance Expectations 
MSLS11 Conduct an investigation to provide evidence that living things are made of cells; either one cell or many different numbers and types of cells. Further explanation: Emphasis is on developing evidence that living things are made of cells, distinguishing between living and nonliving things, and understanding that living things may be made of one cell or many and varied cells. Planning and carrying out investigations; structure and function; scale, proportion, and quantity 
MSLS12 Develop and use a model to describe the function of a cell as a whole and ways the parts of cells contribute to the function. Further explanation: Emphasis is on the cell functioning as a whole system and the primary role of identified parts of the cell, specifically the nucleus, chloroplasts, mitochondria, cell membrane, and cell wall. Developing and using models; structure and function; structure and function 

MSLS13 Use argument supported by evidence for how the body is a system of interacting subsystems composed of groups of cells. Further explanation: Emphasis is on conceptual understanding that cells form tissues and tissues form organs specialized for particular body functions. Examples could include the interaction of subsystems within a system and the normal functioning of those systems. Engaging in argument from evidence; structure and function; system and system models 

MSLS14 Use argument based on empirical evidence and scientific reasoning to support an explanation for how characteristic animal behaviors and specialized plant structures affect the probability of successful reproduction of animals and plants, respectively. Further explanation: Examples of behaviors that affect the probability of animal reproduction could include nest building to protect young from cold, herding of animals to protect young from predators, and vocalization of animals and colorful plumage to attract mates for breeding. Examples of animal behaviors that affect the probability of plant reproduction could include transferring pollen or seeds and creating conditions for seed germination and growth. Examples of plant structures could include bright flowers attracting butterflies that transfer pollen, flower nectar and odors that attract insects that transfer pollen, and hard shells on nuts that squirrels bury. Potential Maine connections could include herding of whitetail deer and caribou, vocalizations of moose and cardinals, and keystone species such as those on the coast (e.g. harbor seals and sea stars). 

MSLS15 Construct a scientific explanation based on evidence for how environmental and genetic factors influence the growth of organisms. Further explanation: Examples of local environmental conditions could include availability of food, light, space, and water. Examples of genetic factors could include large breed cattle and species of grass affecting the growth of organisms. Examples of evidence could include drought decreasing plant growth, fertilizer increasing plant growth, different varieties of plant seeds growing at different rates in different conditions, and fish growing larger in large ponds than in small ponds. Examples could include winter and cold temperatures, hibernation (e.g. black bear), and the migration of hummingbirds and Canada geese. Constructing explanations and designing solutions; growth and development of organisms; cause and effect 

MSLS16 Construct a scientific explanation based on evidence for the role of photosynthesis in the cycling of matter and flow of energy into and out of organisms. Further explanation: Emphasis is on tracing movement of matter and flow of energy. Constructing explanations and designing solutions; organization for matter and energy flow in organisms; energy in chemical processes and everyday life; energy and matter 

MSLS17 Develop a model to describe how food is rearranged through chemical reactions forming new molecules that support growth and/or release energy as this matter moves through an organism. Further explanation: Emphasis is on describing that molecules are broken apart and put back together and that in this process energy is released. Developing and using models; organization for matter and energy flow in organisms; energy in chemical processes and everyday life; energy and matter 

MSLS18 Gather and synthesize information that sensory receptors respond to stimuli by sending messages to the brain for immediate behavior or storage as memories. Obtaining, evaluating, and communicating information; information processing; cause and effect 
Strand 
Life Sciences (LS) 
Standard 
LS1: From Molecules to Organisms: Structures and Processes 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSLS11 Construct an explanation based on evidence for how the structure of DNA determines the structure of proteins which carry out the essential functions of life through systems of specialized cells. Further explanation: Emphasis is on protein synthesis from DNA to codon to amino acid sequence. Constructing Explanations and Designing Solutions, Structure and Function, Structure and Function 
HSLS12 Develop and use a model to illustrate the hierarchical organization of interacting systems that provide specific functions within multicellular organisms. Further explanation: Emphasis is on functions at the organism system level such as nutrient uptake, water delivery, and organism movement in response to neural stimuli. An example of an interacting system could be an artery depending on the proper function of elastic tissue and smooth muscle to regulate and deliver the proper amount of blood within the circulatory system. Another example could be the water and nutrient intake in soft shell clams. Developing and Using Models, Structure and Function, Systems and System Models 

HSLS13 Plan and conduct an investigation to provide evidence that feedback mechanisms maintain homeostasis. Further explanation: Examples of investigations could include heart rate response to exercise, stomate response to moisture and temperature, and root development in response to water levels. Another example is commonly observed in the daphnia heart rate response to changes in temperature, caffeine, alcohol, or nicotine. Planning and Carrying out Investigations, Structure and Function, Stability and Change 

HSLS14 Use a model to illustrate the role of cellular division (mitosis) and differentiation in producing and maintaining complex organisms. Developing and Using Models, Growth and Development of Organisms, Systems and System Models 

HSLS15 Use a model to illustrate how photosynthesis transforms light energy into stored chemical energy. Further explanation: Emphasis is on illustrating inputs and outputs of matter and the transfer and transformation of energy in photosynthesis by plants and other photosynthesizing organisms. Examples of models could include diagrams, chemical equations, and conceptual models. Models may focus on Maine based economy of photosynthetic organisms such as seaweeds, potatoes and pine trees. Developing and Using Models, Organization for Matter and Energy flow in Organisms, Energy and Matter 

HSLS16 Construct and revise an explanation based on evidence for how carbon, hydrogen, and oxygen from sugar molecules may combine with other elements to form amino acids and/or other large carbonbased molecules. Further explanation: Emphasis is on using evidence from models and simulations to support explanations. Constructing Explanations and Designing Solutions, Organization for Matter and energy Flow in Organisms, Energy and Matter 

HSLS17 Use a model to illustrate that cellular respiration is a chemical process whereby the bonds of food molecules and oxygen molecules are broken and the bonds in new compounds are formed, resulting in a net transfer of energy. Further explanation: Emphasis is on the conceptual understanding of the inputs and outputs of the process of cellular respiration. An example could be a moose eating a lily pad, the lily pad producing energy for the moose and the breathing of oxygen by the moose to enable the process of cellular respiration. Developing and Using Models, Organization for Matter and Energy Flow in Organisms, Energy and Matter 
Strand 
Life Sciences (LS) 

Standard 
LS2: Ecosystems: Interactions, Energy, and Dynamics 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
2LS21 Plan and conduct an investigation to determine if plants need sunlight and water to grow. Planning and Carrying out Investigations, Interdependent Relationships in Ecosystems, Cause and Effect 2LS22 Develop a simple model that mimics the function of an animal in dispersing seeds or pollinating plants. Further explanation: Examples of animals or insects that pollinate plants or disperse seeds could include bees, hummingbirds or bats. An example of a model could be using Velcro to show how seeds of burdocks are spread. Developing and Using Models, Interdependent Relationships in Ecosystems, Developing Possible Solutions, Structure and Function 
Strand 
Life Sciences (LS) 

Standard 
LS2: Ecosystems: Interactions, Energy, and Dynamics 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
3LS21 Construct an argument that some animals form groups that help members survive. Further explanation: Maine animals that form groups such as coyotes, deer herds, turkeys, bees, moose, salmon and alewives migration. Engaging in Argument from Evidence, Social Interactions and Group Behaviors, Cause and Effect 
5LS21 Develop a model to describe the movement of matter among plants, animals, decomposers, and the environment. Further Explanation: Emphasis is on the idea that matter that is not food (air, water, decomposed materials in soil) is changed by plants into matter that is food. Examples of systems could include organisms, ecosystems, and the Earth. Utilize Maine or Atlantic plants and animals to develop a model of a food chain or web. Developing and Using Models, Interdependent Relationships in Ecosystems, Cycles of Matter and Energy Transfer, Systems and System Models 
Strand 
Life Sciences (LS) 
Standard 
LS2: Ecosystems: Interactions, Energy, and Dynamics 
Early Adolescence 

Grades 68 

Performance Expectations 
MSLS21 Analyze and interpret data to provide evidence for the effects of resource availability on organisms and populations of organisms in an ecosystem. Further explanation: Emphasis is on cause and effect relationships between resources and the growth of individual organisms and the numbers of organisms in ecosystems during periods of abundant and scarce resources. Analyzing and interpreting data; interdependent relationships in ecosystems; cause and effect 
MSLS22 Construct an explanation that predicts patterns of interactions among organisms across multiple ecosystems. Further explanation: Emphasis is on predicting consistent patterns of interactions in different ecosystems in terms of the relationships among and between organisms and abiotic components of ecosystems. Examples of types of interactions could include competitive, predatory, and mutually beneficial. Potential Maine connections include predation: coyotes and house cats with smaller prey or white tail deer and wolves; mutualism in the union of algae and fungus to form lichen; parasitism in deer ticks on dogs; and commensalism when barnacles attach to minke whales or a grey squirrel makes a nest in a red oak tree. Constructing explanations and designing solutions; interdependent relationships in ecosystems; patterns 

MSLS23 Develop a model to describe the cycling of matter and flow of energy among living and nonliving parts of an ecosystem. Further explanation: Emphasis is on describing the conservation of matter and flow of energy into and out of various ecosystems and on defining the boundaries of the system. Explore the reason behind burning blueberry fields biennially and the cycling of matter. Developing and using models; cycle of matter and energy transfer in ecosystems; energy and matter 

MSLS24 Construct an argument supported by empirical evidence that changes to physical or biological components of an ecosystem affect populations. Further explanation: Emphasis is on recognizing patterns in data and making warranted inferences about changes in populations and on evaluating empirical evidence supporting arguments about changes to ecosystems. Examples include the introduction of invasive species like the green crab or knotweed and their impact on native species. Explore the impacts of farming, urban sprawl and pollution. Engaging in argument from evidence; ecosystem dynamics, functioning, and resilience; stability and change 

MSLS25 Evaluate competing design solutions for maintaining biodiversity and ecosystem services. Further explanation: Examples of ecosystem services could include water purification, nutrient recycling, and prevention of soil erosion. Examples of design solution constraints could include scientific, economic, and social considerations. Consider the balance of conservation with the logging of forests or with the lobster and blueberry industries. Engaging in argument from evidence; ecosystem dynamics, functioning, and resilience; biodiversity and humans; developing possible solutions; stability and change 
Strand 
Life Sciences (LS) 
Standard 
LS2: Ecosystems: Interactions, Energy, and Dynamics 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSLS21 Use mathematical and/or computational representations to support explanations of factors that affect carrying capacity of ecosystems at different scales. Further Explanation: Emphasis is on quantitative analysis and comparison of the relationships among interdependent factors including boundaries, resources, climate, and competition. Examples of mathematical comparisons could include graphs, charts, histograms, and population changes gathered from simulations or historical data sets. Examples could include a look at historical data of the population of a species that has moved north into Maine, such as opossum, and how it has changed as the climate in Maine has changed. Observe data of the populations of harbor seals and the effect that a hunting ban has had on their population and the resulting increase in the number of large predatory sharks in the Gulf of Maine. Using Mathematics and Computational Thinking, Interdependent Relationships in Ecosystems, Scale, Proportion, and Quantity 
HSLS22 Use mathematical representations to support and revise explanations based on evidence about factors affecting biodiversity and populations in ecosystems of different scales. Further explanation: Examples of mathematical representations include finding the average, determining trends, and using graphical comparisons of multiple sets of data. Examples could include a graphical analysis of historical data on the population of trout and/or landlocked salmon before and after the introduction of bass into Moosehead Lake. Or data on a variety of populations (biodiversity) affected by dredging for sea scallops. Using Mathematics and Computational Thinking, Interdependent Relationships in Ecosystems, Scale, Proportion, and Quantity 

HSLS23 Construct and revise an explanation based on evidence for the cycling of matter and flow of energy in aerobic and anaerobic conditions. Further explanation: Emphasis is on conceptual understanding of the role of aerobic and anaerobic respiration in different environments. An example could include a classroom lab activity around a Winogradsky Column with groups changing a variable such as temperature or light. Additional examples could look at the fermentation processes when bluegreen algae is grown in aerobic and anaerobic environments. Constructing Explanations and Designing Solutions, Cycles of Matter and Energy Transfer in Ecosystems, Energy and Matter 

HSLS24 Use mathematical representations to support claims for the cycling of matter and flow of energy among organisms in an ecosystem. Further Explanation: Emphasis is on using a mathematical model of stored energy in biomass to describe the transfer of energy from one trophic level to another and that matter and energy are conserved as matter cycles and energy flows through ecosystems. Emphasis is on atoms and molecules such as carbon, oxygen, hydrogen and nitrogen being conserved as they move through an ecosystem. An example could include an illustration of a food pyramid students may find in Maine (e.g. seaweed >snail >fish >shark, or grass >insects >turkeys >foxes). Using Mathematics and Computational Thinking, Cycles of Matter and Energy Transfer in Ecosystems, Energy and Matter 

HSLS25 Develop a model to illustrate the role of photosynthesis and cellular respiration in the cycling of carbon among the biosphere, atmosphere, hydrosphere, and geosphere. Further explanation: Examples of models could include simulations and mathematical models. Models may include multimedia illustration of the carbon cycle to include a Maine ecosystem they are familiar with such as pond, seaside, farm, forest, etc. Developing and Using Models, Cycles of Matter and Energy Transfer, Energy in Chemical Processes, Systems and System Models 

HSLS26 Evaluate the claims, evidence, and reasoning that the complex interactions in ecosystems maintain relatively consistent numbers and types of organisms in stable conditions, but changing conditions may result in a new ecosystem. Further explanation: Examples of changes in ecosystem conditions could include modest biological or physical changes, such as moderate hunting or a seasonal flood; and extreme changes, such as volcanic eruption or sea level rise. Examples could include how the number of moose hunting licenses impacts other populations or how fishing limits or shortened seasons decreases the catch of many fish species and the effects on ground fish or smaller fish. Engaging in Argument from Evidence, Ecosystem Dynamics, Functioning, and Resilience, Stability and Change 

HSLS27 Design, evaluate, and refine a solution for reducing the impacts of human activities on the environment and biodiversity. Further explanation: Examples of human activities can include urbanization, building dams, and dissemination of invasive species. Potential Maine connections include the effects of: salting the roads in winter, introducing green crabs into coastal waters, introducing invasive species into Maine lakes, or examining historical data on water pollution in the Androscoggin during the height of mill activity, closing of mills and legislation on water quality. Constructing Explanations and Designing Solutions, Ecosystem Dynamics, Functioning, and Resilience, Biodiversity and Humans, Developing Possible Solutions, Stability and Change 

HSLS28 Evaluate the evidence for the role of group behavior on individual and species' chances to survive and reproduce. Further explanation: Emphasis is on: (1) distinguishing between group and individual behavior, (2) identifying evidence supporting the outcomes of group behavior, and (3) developing logical and reasonable arguments based on evidence. Examples of group behaviors could include flocking, schooling, herding, and cooperative behaviors such as hunting, migrating, and swarming. Examples could include turkeys flocking to evade hunters or Canada geese migrating to and through Maine for breeding purposes. Engaging in Argument from Evidence, Social Interactions and Group Behavior, Cause and Effect 
Strand 
Life Sciences (LS) 

Standard 
LS3 Heredity: Inheritance and Variation of Traits 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
1LS31 Make observations to construct an evidencebased account that young plants and animals are like, but not exactly like, their parents. Further explanation: Examples of patterns could include features that plants or animals share. Examples of observations could include that leaves from the same kind of plant are the same shape but can differ in size and that a particular breed of dog looks like its parents but is not exactly the same. Constructing Explanations and Designing Solutions, Inheritance of Traits, Variation of Traits, Patterns 
Strand 
Life Sciences (LS) 

Standard 
LS3 Heredity: Inheritance and Variation of Traits 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
3LS31 Analyze and interpret data to provide evidence that plants and animals have traits inherited from parents and that variation of these traits exists in a group of similar organisms. Further Explanation: Patterns are the similarities and differences in traits shared between offspring and their parents, or among siblings. Emphasis is on organisms other than humans, such as lupins, apples or garden plants. Analyzing and Interpreting Data, Inheritance of Traits, Variation of Traits, Patterns 3LS32 Use evidence to support the explanation that traits can be influenced by the environment. Further Explanation: Examples of the environment affecting a trait could include normally tall plants grown with insufficient water are stunted; and, a pet dog that is given too much food and little exercise may become overweight. In addition, hydrangea grown under higher acidic conditions will cause the petals to turn blue. Constructing Explanations an Designing Solutions, Inheritance of Traits, Variation of Traits, Cause and Effect 
Strand 
Life Sciences (LS) 
Standard 
LS3 Heredity: Inheritance and Variation of Traits 
Early Adolescence 

Grades 68 

Performance Expectations 
MSLS31 Develop and use a model to describe why structural changes to genes (mutations) located on chromosomes may affect proteins and may result in harmful, beneficial, or neutral effects to the structure and function of an organism. Further explanation: Emphasis is on conceptual understanding that changes in genetic material may result in making different proteins. Developing and using models; inheritance of traits; variation of traits; structure and function 
MSLS32 Develop and use a model to describe why asexual reproduction results in offspring with identical genetic information and sexual reproduction results in offspring with genetic variation. Further explanation: Emphasis is on using models such as Punnett squares, diagrams, and simulations to describe the cause and effect relationship of gene transmission from parent(s) to offspring and the resulting genetic variation. Connections can be made to Maine agricultural crops, i.e. strawberries, blueberries, and potatoes. Developing and using models; growth and development of organisms; inheritance of traits; variation of traits; cause and effect 
Strand 
Life Sciences (LS) 
Standard 
LS3 Heredity: Inheritance and Variation of Traits 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSLS31 Ask questions to clarify relationships about the role of DNA and chromosomes in coding the instructions for characteristic traits passed from parents to offspring Further explanation: Emphasis is on the asking of clarifying questions about the general principles of genetics. An example is how cystic fibrosis (one of the most common autosomal recessive inherited diseases in Maine) is passed from parents to child. Asking Questions and Defining Problems, Structure and Function, Inheritance of Traits, Cause and Effect 
HSLS32 Make and defend a claim based on evidence that inheritable genetic variations may result from: (1) new genetic combinations through meiosis, (2) viable errors occurring during replication, and/or (3) mutations caused by environmental factors. Further explanation: Emphasis is on using data to support arguments for the way variation occurs. Provide data on specific mutations caused by environmental factors. Engaging in Argument from Evidence, Variation of Traits, Cause and Effect 

HSLS33 Apply concepts of statistics and probability to explain the variation and distribution of expressed traits in a population. Further explanation: Emphasis is on the use of mathematics to describe the probability of traits as it relates to genetic and environmental factors in the expression of traits. An example would be the population of red fox in Maine and the incidences of the red allele vs. the sable allele. Analyzing and Interpreting Data, Variation of Traits, Scale, Proportion, and Quantity 
Strand 
Life Sciences (LS) 

Standard 
LS4 Biological Evolution: Unity and Diversity 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
2LS41 Make observations of plants and animals to compare the diversity of life in different habitats. Further Explanation: Emphasis is on the diversity of living things in each of a variety of different habitats. Potential Maine connections include Maine habitats (e.g. ocean, lake/pond, mountains, forests, cities, etc.) Planning and Carrying out Investigations, Biodiversity in Humans 
Strand 
Life Sciences (LS) 

Standard 
LS4 Biological Evolution: Unity and Diversity 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
3LS41 Analyze and interpret data from fossils to provide evidence of the organisms and environments in which they lived long ago. Further Explanation: Examples of data could include type, size, and distributions of fossil organisms. Examples of fossils and environments could include marine fossils found on dry land, tropical plant fossils found in Arctic areas, and fossils of extinct organisms. Analyzing and Interpreting Data, Evidence of Common Ancestry and Diversity, Scale, Proportion, and Quantity 3LS42 Use evidence to construct an explanation for how the variations in characteristics among individuals of the same species may provide advantages in surviving, finding mates, and reproducing. Further Explanation: Examples of cause and effect relationships could be plants that have larger thorns than other plants may be less likely to be eaten by predators and animals that have better camouflage coloration than other animals may be more likely to survive and therefore more likely to leave offspring such as yellow spotted salamanders and newts. Constructing Explanations an Designing Solutions, Natural Selection, Cause and Effect 3LS43 Construct an argument with evidence that in a particular habitat some organisms can survive well, some survive less well, and some cannot survive at all. Further Explanation: Examples of evidence could include needs and characteristics of the organisms (such as loons) and habitats involved. The organisms and their habitats make up a system in which the parts depend on each other. Potential Maine connections include the introduction of Pike and Bass into areas that are nonnative to the species and their impact on native trout and other native species. Engaging in Argument from Evidence, Inheritance of Traits, Variation of Traits, Scale, Proportion, and Quantity, Cause and Effect 3LS44 Make a claim about the merit of a solution to a problem caused when the environment changes and the types of plants and animals that live there may change. Further Explanation: Examples of environmental changes could include changes in land characteristics, water distribution, temperature, food, and other organisms. Lobster migrate as a result of water temperature, Cod follow prey fish (Mackerel), Atlantic Salmon start life in streams and migrate to saltwater. Engaging in Argument from Evidence, Biodiversity and Humans, Ecosystem Dynamics, Functioning, and Resilience, Systems and System Models 
Strand 
Life Sciences (LS) 
Standard 
LS4 Biological Evolution: Unity and Diversity 
Early Adolescence 

Grades 68 

Performance Expectations 
MSLS41 Analyze and interpret data for patterns in the fossil record that document the existence, diversity, extinction, and change of life forms throughout the history of life on Earth under the assumption that natural laws operate today as in the past. Further explanation: Emphasis is on finding patterns of changes in the level of complexity of anatomical structures in organisms and the chronological order of fossil appearance in rock layers. Analyzing and interpreting data; evidence of common ancestry and diversity; patterns 
MSLS42 Apply scientific ideas to construct an explanation for the anatomical similarities and differences among modern organisms and between modern and fossil organisms to infer evolutionary relationships. Further explanation: Emphasis is on explanations of the evolutionary relationships among organisms in terms of similarities or differences of the gross appearance of anatomical structures. Constructing explanations and designing solutions; evidence of common ancestry and diversity; patterns 

MSLS43 Analyze displays of pictorial data to compare patterns of similarities in the embryological development across multiple species to identify relationships not evident in the fully formed anatomy. Further explanation: Emphasis is on inferring general patterns of relatedness among embryos of different organisms by comparing the macroscopic appearance of diagrams or pictures. Analyzing and interpreting data; evidence of common ancestry and diversity; patterns 

MSLS44 Construct an explanation based on evidence that describes how genetic variations of traits in a population increase some individuals' probability of surviving and reproducing in a specific environment. Further explanation: Emphasis is on using simple probability statements and proportional reasoning to construct explanations. Constructing explanations and designing solutions; natural selection; cause and effect 

MSLS45 Gather and synthesize information about the technologies that have changed the way humans influence the inheritance of desired traits in organisms. Further explanation: Emphasis is on synthesizing information from reliable sources about the influence of humans on genetic outcomes in artificial selection (such as genetic modification, animal husbandry, and gene therapy) and on the impacts these technologies have on society as well as the technologies leading to these scientific discoveries. Obtaining, evaluating, and communicating information; natural selection; cause and effect 

MSLS46 Use mathematical representations to support explanations of how natural selection may lead to increases and decreases of specific traits in populations over time. Further explanation: Emphasis is on using mathematical models, probability statements, and proportional reasoning to support explanations of trends in changes to populations over time. Using mathematics and computational thinking; adaptation; cause and effect 
Strand 
Life Sciences (LS) 
Standard 
LS4 Biological Evolution: Unity and Diversity 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSLS41 Communicate scientific information that common ancestry and biological evolution are supported by multiple lines of empirical evidence. Further explanation: Emphasis is on a conceptual understanding of the role each line of evidence has relating to common ancestry and biological evolution. Examples of evidence could include similarities in DNA sequences, anatomical structures, and order of appearance of structures in embryological development. Obtaining, Evaluating, and Communicating Information, Evidence of Common Ancestry and Diversity, Patterns 
HSLS42 Construct an explanation based on evidence that the process of evolution primarily results from four factors: (1) the potential for a species to increase in number, (2) the heritable genetic variation of individuals in a species due to mutation and sexual reproduction, (3) competition for limited resources, and (4) the proliferation of those organisms that are better able to survive and reproduce in the environment. Further explanation: Emphasis is on using evidence to explain the influence each of the four factors has on number of organisms, behaviors, morphology, or physiology in terms of ability to compete for limited resources and subsequent survival of individuals and adaptation of species. Examples of evidence could include mathematical models such as simple distribution graphs and proportional reasoning. Constructing Explanations and Designing Solutions, Adaptation, Cause and Effect 

HSLS43 Apply concepts of statistics and probability to support explanations that organisms with an advantageous heritable trait tend to increase in proportion to organisms lacking this trait. Further explanation: Emphasis is on analyzing shifts in numerical distribution of traits and using these shifts as evidence to support explanations. Observe historical data for the distribution of humpback whales in the Gulf of Maine looking specifically at skin pigmentation. Analyzing and Interpreting Data, Natural Selection, Adaptation, Patterns 

HSLS44 Construct an explanation based on evidence for how natural selection leads to adaptation of populations. Further explanation: Emphasis is on using data to provide evidence for how specific biotic and abiotic differences in ecosystems (such as ranges of seasonal temperature, longterm climate change, acidity, light, geographic barriers, or evolution of other organisms) contribute to a change in gene frequency over time, leading to adaptation of populations. Constructing Explanations and Designing Solutions, Adaptation, Cause and Effect 

HSLS45 Evaluate the evidence supporting claims that changes in environmental conditions may result in: (1) increases in the number of individuals of some species, (2) the emergence of new species over time, and (3) the extinction of other species. Further explanation: Emphasis is on determining cause and effect relationships for how changes to the environment such as deforestation, fishing, application of fertilizers, drought, flood, and the rate of change of the environment affect distribution or disappearance of traits in species. Engaging in Argument from Evidence, Adaptation, Cause and Effect 

HSLS46 Create or revise a simulation to test a solution to mitigate adverse impacts of human activity on biodiversity. Further explanation: Emphasis is on designing solutions for a proposed problem related to threatened or endangered species, or to genetic variation of organisms for multiple species. Using Mathematics and Computational Thinking, Biodiversity and Humans, Developing Possible Solutions, Cause and Effect 
Strand 
Earth and Space Sciences (ESS) 

Standard 
ESS1 Earth's Place in the Universe 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
1ESS11 Use observations of the sun, moon, and stars to describe patterns that can be predicted. Further explanation: Examples of patterns could include that the sun and moon appear to rise in one part of the sky, move across the sky, and set and that stars other than our sun are visible at night but not during the day. Analyzing and Interpreting Data, The Universe and Its Stars, Patterns 1ESS12 Make observations at different times of the year to relate the amount of daylight to the time of year. Further explanation: Emphasis is on relative comparisons of the amount of daylight in the winter or summer to the amount in the spring or fall. Planning and Carrying out Investigations, Earth and the Solar System, Patterns 
2ESS11 Use information from several sources to provide evidence that Earth events can occur quickly or slowly. Further Explanation: Examples of events and timescales could include volcanic explosions and earthquakes, which happen quickly, and erosion of rocks, which occurs slowly. Examples of Maine phenomena (e.g. flash floods, erosion and tides). Constructing Explanations and Designing Solutions, The History of Planet Earth, Stability and Change 
Strand 
Earth and Space Sciences (ESS) 

Standard 
ESS1 Earth's Place in the Universe 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
4ESS11 Identify evidence from patterns in rock formations and fossils in rock layers to support an explanation for changes in a landscape over time. Further Explanation: Examples of evidence from patterns could include rock layers with marine shell fossils above rock layers with plant fossils and no shells, indicating a change from land to water over time and a canyon with different rock layers in the walls and a river in the bottom, indicating that over time a river cut through the rock. Constructing Explanations and Designing Solutions, The History of Planet Earth, Patterns 
5ESS11 Support an argument that differences in the apparent brightness of the sun compared to other stars is due to their relative distances from Earth. Engaging in Argument from Evidence, The Universe and its Stars, Scale Proportion and Quantity 5ESS12 Represent data in graphical displays to reveal patterns of daily changes in length and direction of shadows, day and night, and the seasonal appearance of some stars in the night sky. Further Explanation: Examples of patterns could include the position and motion of Earth with respect to the sun and selected stars that are visible only in particular months. Analyzing and Interpreting Data, Earth and the Solar System, Patterns 
Strand 
Earth and Space Sciences (ESS) 
Standard 
ESS1 Earth's Place in the Universe 
Early Adolescence 

Grades 68 

Performance Expectations 
MSESS11 Develop and use a model of the Earthsunmoon system to describe the cyclic patterns of lunar phases, eclipses of the sun and moon, and seasons. Further explanation: Examples of models can be physical, graphical, or conceptual. Examples could incorporate latitude and season connections, why Lubec is the first town in the continental U.S. to see the sunrise, and tides (king, neap, spring). Developing and using models; the universe and its stars; earth and the solar system; patterns 
MSESS12 Develop and use a model to describe the role of gravity in the motions within galaxies and the solar system. Further explanation: Emphasis for the model is on gravity as the force that holds together the solar system and Milky Way galaxy and controls orbital motions within them. Examples of models can be physical (such as the analogy of distance along a football field or computer visualizations of elliptical orbits) or conceptual (such as mathematical proportions relative to the size of familiar objects such as students' school or state). Developing and using models; the universe and its stars; earth and the solar system; systems and system models 

MSESS13 Analyze and interpret data to determine scale properties of objects in the solar system. Further explanation: Emphasis is on the analysis of data from Earthbased instruments, spacebased telescopes, and spacecraft to determine similarities and differences among solar system objects. Examples of scale properties include the sizes of an object's layers (such as crust and atmosphere), surface features (such as volcanoes), and orbital radius. Examples of data include statistical information, drawings and photographs, and models. Analyzing and interpreting data; earth and the solar system; scale, proportion, and quantity 

MSESS14 Construct a scientific explanation based on evidence from rock strata for how the geologic time scale is used to organize Earth's 4.6billionyearold history. Further explanation: Emphasis is on how analysis of rock formations and the fossils they contain are used to establish relative ages of major events in Earth's history. Examples of Earth's major events could range from being very recent (such as the last Ice Age or the earliest fossils of homo sapiens) to very old (such as the formation of Earth or the earliest evidence of life). Examples can include the formation of mountain chains and ocean basins, the evolution or extinction of particular living organisms, or significant volcanic eruptions. Constructing explanations and designing solutions; the history of planet earth; scale, proportion, and quantity 
Strand 
Earth and Space Sciences (ESS) 
Standard 
ESS1 Earth's Place in the Universe 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSESS11 Develop a model based on evidence to illustrate the life span of the sun and the role of nuclear fusion in the sun's core to release energy that eventually reaches Earth in the form of radiation. Further explanation: Emphasis is on the energy transfer mechanisms that allow energy from nuclear fusion in the sun's core to reach Earth. Examples of evidence for the model include observations of the masses and lifetimes of other stars, as well as the ways that the sun's radiation varies due to sudden solar flares ("space weather"), the 11 year sunspot cycle, and noncyclic variations over centuries. Developing and Using Models, The Universe and its Stars, Energy in Chemical Processes and Everyday Life, Scale, Proportion and Quantity 
HSESS12 Construct an explanation of the Big Bang theory based on astronomical evidence of light spectra, motion of distant galaxies, and composition of matter in the universe. Further explanation: Emphasis is on the astronomical evidence of the red shift of light from galaxies as an indication that the universe is currently expanding, the cosmic microwave background as the remnant radiation from the Big Bang, and the observed composition of ordinary matter of the universe, primarily found in stars and interstellar gases (from the spectra of electromagnetic radiation from stars), which matches that predicted by the Big Bang theory (3/4 hydrogen and 1/4 helium). Constructing Explanations and Designing Solutions, The Universe and its Stars, Electromagnetic Radiation, Energy and Matter 

HSESS13 Communicate scientific ideas about the way stars, over their life cycle, produce elements. Further explanation: Emphasis is on the way nucleosynthesis, and therefore the different elements created, varies as a function of the mass of a star and the stage of its lifetime. Obtaining, Evaluating, and Communicating Information, The Universe and its Stars, Energy and Matter 

HSESS14 Use mathematical or computational representations to predict the motion of orbiting objects in the solar system. Further explanation: Emphasis is on Newtonian gravitational laws governing orbital motions, which apply to humanmade satellites as well as planets and moons. Using Mathematical and Computational Thinking, Earth and the Solar System, Scale, Proportion, and Quantity 

HSESS15 Evaluate evidence of the past and current movements of continental and oceanic crust and the theory of plate tectonics to explain the ages of crustal rocks. Further explanation: Emphasis is on the ability of plate tectonics to explain the ages of crustal rocks. Examples include evidence of the ages oceanic crust increasing with distance from midocean ridges (a result of plate spreading) and the ages of North American continental crust increasing with distance away from a central ancient core (a result of past plate interactions). Examples could also be found from looking at differences between coastal Maine and interior Maine rock types and their ages as evidence to explain the formation of land structures and plate boundaries that cause them. Engaging in Argument from Evidence, The History of Planet Earth, Plate Tectonics and LargeScale System Interactions, Nuclear Processes, Patterns 

HSESS16 Apply scientific reasoning and evidence from ancient Earth materials, meteorites, and other planetary surfaces to construct an account of Earth's formation and early history. Further explanation: Emphasis is on using available evidence within the solar system to reconstruct the early history of Earth, which formed along with the rest of the solar system 4.6 billion years ago. Examples of evidence include the absolute ages of ancient materials (obtained by radiometric dating of meteorites, moon rocks, and Earth's oldest minerals), the sizes and compositions of solar system objects, and the impact cratering record of planetary surfaces. Constructing Explanations and Designing Solutions, The History of Planet Earth, Stability and Change 
Strand 
Earth and Space Sciences (ESS) 

Standard 
ESS2 Earth's Systems 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
KESS21 Use and share observations of local weather conditions to describe patterns over time. Further explanation: Examples of qualitative observations could include descriptions of the weather (such as sunny, cloudy, rainy, and warm); examples of quantitative observations could include graphing the number of sunny, windy, and rainy or snowy days in a month. Examples of patterns could include that it is usually cooler in the morning than in the afternoon and the number of sunny days versus cloudy days in different months. Analyzing and Interpreting Data, Weather and Climate, Patterns KESS22 Construct an argument supported by evidence for how plants and animals (including humans) can change the environment to meet their needs. Further explanation: Examples of plants and animals changing their environment could include a squirrel digging in the ground to hide its food and tree roots can break concrete. Examples could include ways that humans change their environment to meet their needs (cutting down trees to provide heat, farming to provide food, and the process of snow removal, e.g. sanding/salting the roads, snowplowing, etc.). Engaging in Argument from Evidence, Biogeology, Human Impacts on Earth Systems, Systems and System Models 
2ESS21 Compare multiple solutions designed to slow or prevent wind or water from changing the shape of the land. Further Explanation: Examples of solutions could include different designs of dikes and windbreaks to hold back wind and water and different designs for using shrubs, grass, and trees to hold back land. Constructing Explanations and Designing Solutions, Earth Materials and Systems, Optimizing the Design Solution, Stability and Change 2ESS22 Develop a model to represent the shapes and kinds of land and bodies of water in an area. Developing and Using Models, Plate Tectonics and the LargeScale System Interactions, Patterns 2ESS23 Obtain information to identify where water is found on Earth and that it can be solid or liquid. Obtaining, Evaluating, and Communicating Information, The Roles of Water in Earth's Surface Processes, Patterns 
Strand 
Earth and Space Sciences (ESS) 

Standard 
ESS2 Earth's Systems 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
3ESS21 Represent data in tables and graphical displays to describe typical weather conditions expected during a particular season. Further Explanation: Examples of data could include average temperature, precipitation, and wind direction Analyzing and Interpreting Data, Weather and Climate, Patterns 3ESS22 Obtain and combine information to describe climates in different regions of the world. Obtaining, Evaluating, and Communicating Information, Weather and Climate, Patterns 
4ESS21 Make observations and/or measurements to provide evidence of the effects of weathering or the rate of erosion by water, ice, wind, or vegetation. Further Explanation: Examples of variables to test could include angle of slope in the downhill movement of water, amount of vegetation, speed of wind, relative rate of deposition, cycles of freezing and thawing of water, cycles of heating and cooling, and volume of water flow. Maine pot holes and frost heaves are evidence of the effects of weathering and explain why roads in Maine are repaved more frequently than roads in Florida. Planning and Carrying out Investigations, Earth Materials and Systems, Biogeology, Cause and Effect 4ESS22 Analyze and interpret data from maps to describe patterns of Earth's features. Further Explanation: Maps can include topographic maps of Earth's land and ocean floor, as well as maps of the locations of mountains, continental boundaries, volcanoes, and earthquakes. Investigate the formation of the Appalachian Mountains and compare them to the formation of the Rocky or Cascade Mountain Ranges. Analyzing and Interpreting Data, Plate Tectonics and LargeScale System Interactions, Patterns 
5ESS21 Develop a model using an example to describe ways the geosphere, biosphere, hydrosphere, and/or atmosphere interact. Further Explanation: Examples could include the influence of the ocean on ecosystems, landform shape, and climate; the influence of the atmosphere on landforms and ecosystems through weather and climate; and the influence of mountain ranges on winds and clouds in the atmosphere. The geosphere, hydrosphere, atmosphere, and biosphere are each a system. Developing and Using Models, Earth's Materials and Systems, Systems and System Models 5ESS22 Describe and graph the amounts and percentages of water and fresh water in various reservoirs to provide evidence about the distribution of water on Earth. Using Mathematics and Computational Thinking, The Roles of Water in Earth's Surface Processes, Scale, Proportion, and Quantity 
Strand 
Earth and Space Sciences (ESS) 
Standard 
ESS2 Earth's Systems 
Early Adolescence 

Grades 68 

Performance Expectations 
MSESS21 Develop a model to describe the cycling of Earth's materials and the flow of energy that drives this process Further explanation: Emphasis is on the processes of melting, crystallization, weathering, deformation, and sedimentation, which act together to form minerals and rocks through the cycling of Earth's materials. Potential Maine connections include Deer Isle granite, Rockland limestone, Maine tourmaline, Acadia National Park pink granite, along with Maine mining history at Bald Mountain or Katahdin Iron Works. Developing and using models, earth's materials and systems, stability and change 
MSESS22 Construct an explanation based on evidence for how geoscience processes have changed Earth's surface at varying time and spatial scales. Further explanation: Emphasis is on how processes change Earth's surface at time and spatial scales that can be large (such as slow plate motions or the uplift of large mountain ranges) or small (such as rapid landslides or microscopic geochemical reactions), and how many geoscience processes (such as earthquakes, volcanoes, and meteor impacts) usually behave gradually but are punctuated by catastrophic events. Examples of geoscience processes include surface weathering and deposition by the movements of water, ice, and wind. Emphasis is on geoscience processes that shape local geographic features, where appropriate. Potential Maine connections include the Desert of Maine, glacial erratics, alluvial fans, Appalachian Trail and Baxter State Park, and the fjord on Mount Desert Island. Constructing explanations and designing solutions, earth's materials and systems, the roles of water in earth's surface processes, scale proportion and quantity 

MSESS23 Analyze and interpret data on the distribution of fossils and rocks, continental shapes, and seafloor structures to provide evidence of the past plate motions. Further explanation: Examples of data include similarities of rock and fossil types on different continents, the shapes of the continents (including continental shelves), and the locations of ocean structures (such as ridges, fracture zones, and trenches). Potential Maine connections can be found in the Gulf of Maine, Georges Bank and the inner continental shelf. Analyzing and interpreting data, the history of planet earth, plate tectonics and largescale system interactions, patterns 

MSESS24 Develop a model to describe the cycling of water through Earth's systems driven by energy from the sun and the force of gravity. Further explanation: Emphasis is on the ways in which water changes its state as it moves through the multiple pathways of the hydrologic cycle. Examples of models can be conceptual or physical. Developing and using models, the roles of water in earth's surface processes, energy and matter 

MSESS25 Collect data to provide evidence for how the motions and complex interactions of air masses result in changes in weather conditions. Further explanation: Emphasis is on how air masses flow from regions of high pressure to low pressure, causing weather (defined by temperature, pressure, humidity, precipitation, and wind) at a fixed location to change over time and how sudden changes in weather can result when different air masses collide. Emphasis is on how weather can be predicted within probabilistic ranges. Examples of data can be provided to students (such as weather maps, diagrams, and visualizations) or obtained through laboratory experiments (such as with condensation). Potential Maine connections include "Bombogenesis" snow storms, coastal fog, Nor'easters, sea smoke and valley fog. Planning and carrying out investigations, the roles of water in earth's surface processes, weather and climate, cause and effect 

MSESS26 Develop and use a model to describe how unequal heating and rotation of the Earth cause patterns of atmospheric and oceanic circulation that determine regional climates. Further explanation: Emphasis is on how patterns vary by latitude, altitude, and geographic land distribution. Emphasis of atmospheric circulation is on the sunlightdriven latitudinal banding, the Coriolis effect, and resulting prevailing winds; emphasis of ocean circulation is on the transfer of heat by the global ocean convection cycle, which is constrained by the Coriolis effect and the outlines of continents. Examples of models can be diagrams, maps and globes, or digital representations. Developing and using models, the roles of water in earth's surface processes, weather and climate, systems and system models 
Strand 
Earth and Space Sciences (ESS) 
Standard 
ESS2 Earth's Systems 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSESS21 Develop a model to illustrate how Earth's internal and surface processes operate at different spatial and temporal scales to form continental and oceanfloor features. Further explanation: Emphasis is on how the appearance of land features (such as mountains, valleys, and plateaus) and sea floor features (such as trenches, ridges, and seamounts) are a result of both constructive forces (such as volcanism, tectonic uplift, and orogeny) and destructive mechanisms (such as weathering, mass wasting, and coastal erosion). An example could be to utilize Maine Geologic maps, including tectonic maps, as data to create a model to illustrate how Maine's land features or oceanic features were formed. Consider looking to Maine's glacial history, features formed and materials deposited by glaciers. Developing and Using Models, Plate Tectonics and LargeScale System Interactions, Earth Materials and Systems, Stability and Change 
HSESS22 Analyze geoscience data to make the claim that one change to Earth's surface can create feedbacks that cause changes to other Earth systems. Further explanation: Examples should include climate feedbacks, such as how an increase in greenhouse gases causes a rise in global temperatures that melts glacial ice, which reduces the amount of sunlight reflected from Earth's surface, increasing surface temperatures and further reducing the amount of ice. Examples could also be taken from other system interactions, such as how the loss of ground vegetation causes an increase in water runoff and soil erosion; how dammed rivers increase groundwater recharge, decrease sediment transport, and increase coastal erosion; and how the loss of wetlands causes a decrease in local humidity that further reduces the wetlands' extent. An example could consider timber harvesting practices related to erosion and water runoff issues, river damming, or coastal erosion of Maine's beaches and dunes. Analyzing and Interpreting Data, Earth Materials and Systems, Stability and Change 

HSESS23 Develop a model based on evidence of Earth's interior to describe the cycling of matter by thermal convection. Further explanation: Emphasis is on both a onedimensional model of Earth, with radial layers determined by density, and a threedimensional model, which is controlled by mantle convection and the resulting plate tectonics. Examples of evidence include maps of Earth's threedimensional structure obtained from seismic waves, records of the rate of change of Earth's magnetic field (as constraints on convection in the outer core), and identification of the composition of Earth's layers from highpressure laboratory experiments. Developing and Using Models, Earth Materials and Systems, Plate Tectonics and LargeScale System Interactions, Wave Properties, Energy and Matter 

HSESS24 Use a model to describe how variations in the flow of energy into and out of Earth's systems result in changes in climate. Further explanation: Examples of the causes of climate change differ by timescale, over 110 years; large volcanic eruptions, ocean circulation; 10s to 100s of years: changes in human activity, ocean circulation, solar output; 10s a100s of thousands of years: changes to Earth's orbit and the orientation of its axis; and 10s100s of millions of years: longterm changes in atmospheric composition. Consider the climatic impacts of the Gulf stream and the Labrador currents on the Gulf of Maine, e.g. water temperature changes and fishing industry disruptions. Developing and Using Models, Earth and the Solar System, Earth Materials and Systems, Weather and Climate, Scale, Proportion, and Quantity 

HSESS25 Plan and conduct an investigation of the properties of water and its effects on Earth materials and surface processes. Further explanation: Emphasis is on mechanical and chemical investigations with water and a variety of solid materials to provide evidence for the connections between the hydrologic cycle and system interactions commonly known as the rock cycle. Examples of mechanical investigations include stream transportation and deposition using a stream table, erosion using variations in soil moisture content, and frost wedging by the expansion of water as it freezes. Examples of chemical investigations include chemical weathering and recrystallization (by testing the solubility of different materials) or melt generation (by examining how water lowers the melting temperature of most solids). Draw connections to Maine phenomena such as ice jams, frost heaves and potholes. Planning and Carrying Out Investigations, The Role of Water in Earth's Surface Processes, Structure and Function 

HSESS26 Develop a quantitative model to describe the cycling of carbon among the hydrosphere, atmosphere, geosphere, and biosphere. Further explanation: Emphasis is on modeling biogeochemical cycles that include the cycling of carbon through the ocean, atmosphere, soil, and biosphere (including humans), providing the foundation for living organisms. Developing and Using Models, Weather and Climate, Energy and Matter 

HSESS27 Construct an argument based on evidence about the simultaneous coevolution of Earth's systems and life on Earth. Further explanation: Emphasis is on the dynamic causes, effects, and feedbacks between the biosphere and Earth's other systems, whereby geoscience factors control the evolution of life, which in turn continuously alters Earth's surface. Examples include how photosynthetic life altered the atmosphere through the production of oxygen, which in turn increased weathering rates and allowed for the evolution of animal life; how microbial life on land increased the formation of soil, which in turn allowed for the evolution of land plants; and how the evolution of corals created reefs that altered patterns of erosion and deposition along coastlines and provided habitats for the evolution of new life forms. Engaging in Argument from Evidence, Weather and Climate, Biogeology, Stability and Change 
Strand 
Earth and Space Sciences (ESS) 

Standard 
ESS3 Earth and Human Activity 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
KESS31 Use a model to represent the relationship between the needs of different plants or animals (including humans) and the places they live. Further explanation: Examples of relationships could include that deer eat buds and leaves and therefore usually live in forested areas and that grasses need sunlight so they often grow in meadows. Plants, animals, and their surroundings make up a system. Examples could include coastal tidepools, humans in Maine live in insulated buildings for protection during cold months, or uninsulated structures during warm months (e.g. camping in a tent). Examples of animals that migrate include monarch butterflies, ducks, Canada geese, etc. Developing and Using Models, Natural Resources, Systems and System Models KESS32 Ask questions to obtain information about the purpose of weather forecasting to prepare for, and respond to, severe weather. Further explanation: Emphasis is on local forms of severe weather. Examples could include local forms of severe weather (flooding, ice, blizzards, heat, etc.) and checking the weather forecast to determine proper clothing to wear. Asking Questions and Defining Problems, Obtaining, Evaluating, and Communicating Information, Natural Hazards, Defining and Delimiting an Engineering Problem, Cause and Effect KESS33 Communicate solutions that will reduce the impact of humans on the land, water, air, and/or other living things in the local environment. Further explanation: Examples of human impact on land could include cutting trees to produce paper and using resources to produce bottles. Examples of solutions could include reusing paper and recycling cans and bottles. Examples could also include what we can do to clean public areas (e.g. beaches, parks, lakes, trails, etc.). Obtaining, Evaluating, and Communicating Information, Developing Possible Solutions, Human Impacts on Earth Systems, Cause and Effect 
Strand 
Earth and Space Sciences (ESS) 

Standard 
ESS3 Earth and Human Activity 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
3ESS31 Make a claim about the merit of a design solution that reduces the impacts of a weatherrelated hazard. Further Explanation: Examples of design solutions to weatherrelated hazards could include barriers to prevent flooding, wind resistant roofs, and lightning rods. Potential Maine connections include the construction of seawalls in southern Maine to prevent damage to homes from strong ocean storms. Engaging in Argument from Evidence, Natural Hazards, Cause and Effect 
4ESS31 Obtain and combine information to describe that energy and fuels are derived from natural resources and their uses affect the environment. Further Explanation: Examples of renewable energy resources could include wind energy, water behind dams, and sunlight; nonrenewable energy resources are fossil fuels and fissile materials. Examples of environmental effects could include loss of habitat due to dams, loss of habitat due to surface mining, and air pollution from burning of fossil fuels. Investigate the pros and cons of heating homes with wood, fossil fuels, and solar energy. Investigate what a wind or solar farm is and why they are controversial in Maine. Obtaining, Evaluating, and Communicating Information, Natural Resources, Cause and Effect 4ESS32 Generate and compare multiple solutions to reduce the impacts of natural Earth processes on humans. Further Explanation: Examples of solutions could include designing an earthquake resistant building and improving monitoring of volcanic activity. Design a microburst resistant building or design a telephone/electric pole that could sustain less damage in an ice storm. Constructing Explanations and Designing Solutions, Natural Hazards, Designing Solutions to Engineering Problems, Cause and Effect 
5ESS31 Obtain and combine information about ways individual communities use science ideas to protect the Earth's resources and environment. Obtaining, Evaluating and Communicating Information, Human Impacts on Earth systems, Systems and System Models 
Strand 
Earth and Space Sciences (ESS) 
Standard 
ESS3 Earth and Human Activity 
Early Adolescence 

Grades 68 

Performance Expectations 
MSESS31 Construct a scientific explanation based on evidence for how the uneven distributions of Earth's mineral, energy, and groundwater resources are the result of past and current geoscience processes. Further explanation: Emphasis is on how these resources are limited and typically nonrenewable and on how their distributions are significantly changing as a result of removal by humans. Examples of uneven distributions of resources as a result of past processes include but are not limited to petroleum (locations of the burial of organic marine sediments and subsequent geologic traps), metal ores (locations of past volcanic and hydrothermal activity associated with subduction zones), and soil (locations of active weathering and/or deposition of rock). Constructing explanations and designing solutions, natural resources, cause and effect 
MSESS32 Analyze and interpret data on natural hazards to forecast future catastrophic events and inform the development of technologies to mitigate their effects. Further explanation: Emphasis is on how some natural hazards, such as volcanic eruptions, and severe weather, are preceded by phenomena that allow for reliable predictions, but others, such as earthquakes, occur suddenly and with no notice and thus are not yet predictable. Examples of natural hazards can be taken from interior processes (such as earthquakes and volcanic eruptions), surface processes (such as mass wasting and tsunamis), or severe weather events (such as hurricanes, tornadoes, and floods). Examples of data can include the locations, magnitudes, and frequencies of the natural hazards. Examples of technologies can be global (such as satellite systems to monitor hurricanes or forest fires) or local (such as building basements in tornadoprone regions or reservoirs to mitigate droughts). Analyzing and interpreting data, natural hazards, patterns 

MSESS33 Apply scientific principles to design a method for monitoring and minimizing a human impact on the environment. Further explanation: Examples of the design process include examining human environmental impacts, assessing the kinds of solutions that are feasible, and designing and evaluating solutions that could reduce that impact. Examples of human impacts can include water usage (such as the withdrawal of water from streams and aquifers or the construction of dams and levees), land usage (such as urban development, agriculture, or the removal of wetlands), and pollution (such as of the air, water, or land). Constructing explanations and designing solutions, human impacts on earth systems, cause and effect 

MSESS34 Construct an argument supported by evidence for how increases in human population and percapita consumption of natural resources impact Earth's systems. Further explanation: Examples of evidence include gradeappropriate databases on human populations and the rates of consumption of food and natural resources (such as freshwater, mineral, and energy). Examples of impacts can include changes to the appearance, composition, and structure of Earth's systems as well as the rates at which they change. The consequences of increases in human populations and consumption of natural resources are described by science, but science does not make the decisions for the actions society takes. Engaging in argument from evidence, human impacts on earth systems, cause and effect MSESS35 Ask questions to clarify evidence of the factors that have caused the rise in global temperatures over the past century. Further explanation: Examples of factors include human activities (such as fossil fuel combustion, cement production, and agricultural activity) and natural processes (such as changes in incoming solar radiation or volcanic activity). Examples of evidence can include tables, graphs, and maps of global and regional temperatures, atmospheric levels of gases such as carbon dioxide and methane, and the rates of human activities. Emphasis is on the major role that human activities play in causing the rise in global temperatures. Asking questions and defining problems, global climate change, stability and change 
Strand 
Earth and Space Sciences (ESS) 
Standard 
ESS3 Earth and Human Activity 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSESS31 Construct an explanation based on evidence for how the availability of natural resources, occurrence of natural hazards, and changes in climate have influenced human activity. Further explanation: Examples of key natural resources include access to fresh water (such as rivers, lakes, and groundwater), regions of fertile soils such as river deltas, and high concentrations of minerals and fossil fuels. Examples of natural hazards can be from interior processes (such as volcanic eruptions and earthquakes), surface processes (such as tsunamis, mass wasting and soil erosion), and severe weather (such as hurricanes, floods, and droughts). Examples of the results of changes in climate that can affect populations or drive mass migrations include changes to sea level, regional patterns of temperature and precipitation, and the types of crops and livestock that can be raised. Other examples include the impacts of climate change on Maine's ski industry, fishing industry, maple sugar industry and on sea levels or droughts. Constructing Explanations and Designing Solutions, Natural Resources, Natural Hazards, Cause and Effect 
HSESS32 Evaluate competing design solutions for developing, managing, and utilizing energy and mineral resources based on costbenefit ratios. Further explanation: Emphasis is on the conservation, recycling, and reuse of resources (such as minerals and metals) where possible, and on minimizing impacts where it is not. Examples include developing best practices for agricultural soil use (for farming, timber industry, blueberry and potato crops), mining (for coal, tar sands, and oil shales), and pumping (for petroleum and natural gas). Science knowledge indicates what can happen in natural systemsnot what should happen. Engaging in Argument from Evidence, Natural Resources, Developing Possible Solutions 

HSESS33 Create a computational simulation to illustrate the relationships among management of natural resources, the sustainability of human populations, and biodiversity. Further explanation: Examples of factors that affect the management of natural resources include costs of resource extraction and waste management, percapita consumption, and the development of new technologies. Examples of factors that affect human sustainability include agricultural efficiency, levels of conservation, and urban planning. Consider the effects of urban sprawl and the loss of farmland. Using Mathematics and Computational Thinking, Human Impacts on Earth Systems, Stability and Change 

HSESS34 Evaluate or refine a technological solution that reduces impacts of human activities on natural systems. Further explanation: Examples of data on the impacts of human activities could include the quantities and types of pollutants released, changes to biomass and species diversity, or areal changes in land surface use (such as for urban development, agriculture and livestock, or surface mining). Examples for limiting future impacts could range from local efforts (such as reducing, reusing, and recycling resources) to largescale geoengineering design solutions (such as altering global temperatures by making large changes to the atmosphere or ocean). Other examples include the use of propanepowered buses in Acadia (evaluate pros and cons). Constructing Explanations and Designing Solutions, Developing Possible Solutions, Stability and Change 

HSESS35 Analyze geoscience data and the results from global climate models to make an evidencebased forecast of the current rate of global or regional climate change and associated future impacts to Earth's systems. Further explanation: Examples of evidence, for both data and climate model outputs, are for climate changes (such as precipitation and temperature) and their associated impacts (such as on sea level, glacial ice volumes, or atmosphere and ocean composition). Analyzing and Interpreting Data, Global Climate Change, Stability and Change 

HSESS36 Use a computational representation to illustrate the relationships among Earth systems and how those relationships are being modified due to human activity. Further explanation: Examples of Earth systems to be considered are the hydrosphere, atmosphere, cryosphere, geosphere, and/or biosphere. An example of the farreaching impacts from a human activity is how an increase in atmospheric carbon dioxide results in an increase in photosynthetic biomass on land and an increase in ocean acidification, with resulting impacts on sea organism health and marine populations. Use and interpret graphs and data of carbon dioxide levels in the Gulf of Maine for oysters and sea scallops. Consider the impacts of ocean acidification on shellfish. Using Mathematics and Computational Thinking, Weather and Climate, Global Climate Change, Systems and System Models 
Strand 
Engineering, Technology, and Applications of Science (ETS) 

Standard 
ETS1 Engineering Design 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
K2ETS11 Ask questions, make observations, and gather information about a situation people want to change to define a simple problem that can be solved through the development of a new or improved object or tool. Asking Questions and Defining Problems, Defining and Delimiting Engineering Problems 
K2ETS12 Develop a simple sketch, drawing, or physical model to illustrate how the shape of an object helps it function as needed to solve a given problem. Developing and Using Models, Developing Possible Solutions, Structure and Function 
K2ETS13 Analyze data from tests of two objects designed to solve the same problem to compare the strengths and weaknesses of how each performs. Analyzing and Interpreting Data, Optimizing the Design Solution 
Strand 
Engineering, Technology, and Applications of Science (ETS) 

Standard 
ETS1 Engineering Design 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
35ETS11 Define a simple design problem reflecting a need or a want that includes specified criteria for success and constraints on materials, time, or cost. Asking Questions and Defining Problems, Defining and Delimiting Engineering Problems, Influence of Engineering, Technology, and Science on Society and the Natural World 
35ETS12 Generate and compare multiple possible solutions to a problem based on how well each is likely to meet the criteria and constraints of the problem. Constructing Explanations and Designing Solutions, Developing Possible Solutions, Influence of Engineering, Technology, and Science on Society and the Natural World 
35ETS13 Plan and carry out fair tests in which variables are controlled and failure points are considered to identify aspects of a model or prototype that can be improved. Planning and Carrying out Explanations, Developing Possible Solutions, Optimizing the Design Solution 
Strand 
Engineering, Technology, and Applications of Science (ETS) 
Standard 
ETS1 Engineering Design 
Early Adolescence 

Grades 68 

Performance Expectations 
MSETS11 Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions. Further explanation: To solve a problem it needs to have clearly defined set goals and limits. The more limitations applied to a problem, the more elegant and successful the solution is likely to be. Limitations would take into account potential impacts on the environment, social/cultural norms, and allowable interactions. The application of science principles is to be used as a tool to verify solutions. Examples could include hydroelectric dams as a viable, cost effective and ecologically friendly way to generate electrical power. However, the dam holds fish populations from traveling freely through the environment. There is a need to provide a safe way for aquatic life to pass by the hydroelectric turbine in a way that does not impact the electrical generation, the original water flow of the river dammed, is cost effective to existing dam models, and has no negative impact on human populations. Asking questions and defining problems, defining and delimiting engineering problems, influence of science, engineering, and technology on society and the natural world 
MSETS12 Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem. Further explanation: When designing a solution to a problem, there need to be many possible solutions explored, tested, verified, and compared, and the use of some tool to determine the validity of competing designs in meeting the design criteria. These tools would be used to make testing data understandable, comparable, and accessible. Engaging in argument from evidence, developing possible solutions 

MSETS13 Analyze data from tests to determine similarities and differences among several design solutions to identify the best characteristics of each that can be combined into a new solution to better meet the criteria for success. Further explanation: Testing and data is used to evaluate the solutions or part of the solutions that best solve the given problem. The data needs to be assessed and then used to modify, combine, and deny solutions and then retested to arrive at the best possible solution within the constraints of the problem. Examples could include tables, graphs, matrices, check lists, spreadsheets, public polls, Venn diagrams, mathematical models, etc. Analyzing and interpreting data, developing possible solutions, optimizing design solution 

MSETS14 Develop a model to generate data for iterative testing and modification of a proposed object, tool, or process such that an optimal design can be achieved. Further explanation: Developing the proper test to verify which solutions meet and which excel when applied against the constraints. That test is then applied to a prototype or model to allow faults to be identified and then corrected, frequently the combination of two or more solutions can produce a better solution and then retest it to see if it is the best solution. Examples could include materials science testing (shear strength, compression testing, tension testing, etc.), weather testing (temperature, rain, snow, wind, sun exposure), wind tunnel, failure or destructive testing, mathematical models, etc. Developing and using models, developing possible solutions, optimizing design solution 
Strand 
Engineering, Technology, and Applications of Science (ETS) 
Standard 
ETS1 Engineering Design 
Adolescence 

Grades 9Diploma 

Performance Expectations 
HSETS11 Analyze a major global challenge to specify qualitative and quantitative criteria and constraints for solutions that account for societal needs and wants. Further explanation: Examples of challenges include local and global climate change issues, biodiversity loss or United Nations sustainable development goals. Asking Questions and Defining Problems, Defining and Delimiting Engineering Problems 
HSETS12 Design a solution to a complex realworld problem by breaking it down into smaller, more manageable problems that can be solved through engineering. Further explanation: Examples could include transportation issues, dams, green energy and wind power in Maine. Constructing Explanations and Designing Solutions, Optimizing the Design Solution 

HSETS13 Evaluate a solution to a complex realworld problem based on prioritized criteria and tradeoffs that account for a range of constraints, including cost, safety, reliability, and aesthetics, as well as possible social, cultural, and environmental impacts. Further explanation: Examples could include lobstering and exports of lobster, dry wells and water conservation in Maine, or saltwater intrusion in coastal Maine wells. Constructing Explanations and Designing Solutions, Developing Possible Solutions 

HSETS14 Use a computer simulation to model the impact of proposed solutions to a complex realworld problem with numerous criteria and constraints on interactions within and between systems relevant to the problem. Using Mathematics and Computational Thinking, Developing Possible Solutions, Systems and System Models 
SOCIAL STUDIES
Introduction
The great architects of American public education, such as Thomas Jefferson, Horace Mann, and John Dewey, believed that every student must be well versed in our nation's history, the principles and practices which support and sustain citizenship, and the institutions that define our government. Understandings of commerce and geography were critical to their thinking as well. In essence, Jefferson, Mann, and Dewey viewed the study of social studies as critical to the mission of public schools. According to the National Council for the Social Studies: advocates of citizenship education cross the political spectrum, but they are bound by a common belief that our democratic republic will not sustain unless students are aware of their changing cultural and physical environments; know the past; read, write, and think deeply; and act in ways that promote the common good. (C3 Framework for Social Studies, 2013).
A strong Social Studies education depends upon a clear understanding of its interrelated disciplines and inclusion of Maine's Guiding Principles. Without knowledge of the geography and economics of earlier times, history offers only lists of people, events, and dates. Without knowledge of history, the institutions of American government and the dynamics of today's global economy are difficult to understand. Although social studies curricula vary in their breadth and depth, the Social Studies Standards reflect a focus on government, history, geography, personal finance and economics as the pillars of the content, with other disciplines within the social sciences deemed important, but not essential.
Guiding Principles
The Guiding Principles guide education in Maine and should be reflected throughout Social Studies curriculum. Examples of how students can show evidence of those guiding principles in Social Studies may include:
A. Clear and Effective Communicator: Students research and use background knowledge to give audiovisual presentations about current and historical issues.
B. SelfDirected and Lifelong Learner: Students generate questions and explore primary and secondary sources to answer those questions while demonstrating a growth mindset.
C. Creative and Practical Problem Solver: Students draw conclusions about current and historical problems using valid research and critical thinking.
D. Responsible and Involved Citizen: Students practice and apply the duties of citizenship through the exercise of constitutional rights.
E. Integrative and Informed Thinker: Students compare and contrast to analyze point of view and differentiate between reliable and unreliable primary and secondary sources.
Performance Expectations that include the application of the Guiding Principles through Social Studies knowledge and skills are denoted in the standards with an asterisk (*).
Skills in Social Studies:
The application of skills in Social Studies is crucial to any curriculum. Best practices in Social Studies reflect curriculum, instruction, and assessment that give students opportunities to demonstrate research and develop positions on current Social Studies issues. Students will be asked to identify key words and concepts related to research questions and locate and access information by using text features. Additionally, students will demonstrate facility with notetaking, organizing information, and creating bibliographies. Students will distinguish between primary and secondary sources as well as evaluate and verify the credibility of the information found in print and nonprint sources. Equally important is that students use additional sources to resolve contradictory information.
Key Ideas in the Social Studies Standards:
Growth mindset  Our mindset includes beliefs about our abilities and qualities that include intelligence, creativity or musicality. Having a growth mindset means that students know that their abilities and strengths can change or develop, and that those changes are within their control.
Understand  The word "understand" appears in performance expectations throughout the Social Studies Standards. It refers to a variety of different levels of thinking and was used intentionally to serve as an umbrella term for the cognitive demand that is described by the descriptors beneath the performance expectations. Look to the grade level expectation for grades K5 or to the grade span expectations in spans 68 and 912 (Foundational or Developmental as noted by "F" or "D") to define the level of cognitive demand for student performance.
Various The Social Studies Standards refer to "various" peoples, nations, regions of the world, historical eras, and enduring themes. School administrative units should develop a local curriculum that assists students in gaining a coherent, broad perspective on a variety of peoples, nations, regions, historical eras, and enduring themes.
Major Enduring Themes  The term "major enduring themes" is used in several places in the Social Studies Standards. This term refers to general topics or issues that have been relevant over a long period of time. Using a consistent set of themes can serve as a framework within which other concepts, topics, and facts can be organized. It can also help students make connections between events within and across historical eras, and use history to help make informed decisions. The Civics and Government, Personal Finance and Economics, Geography, and History Standards all include performance expectations that address individual, cultural, international, and global connections. It will be up to the School Administrative Units to determine whether they use these performance expectations as an opportunity to integrate across the disciplines of the social studies or address them separately. The "enduring themes," some of which overlap, include:
Freedom and Justice Conflict and Compromise Technology and Innovation Unity and Diversity Continuity and Change Over Time Supply and DemandEras  School Administrative Units (SAU) should develop a coherent curriculum that provides students with a balanced exposure to the major eras of United States and World History. The term "various eras" in this document refers to those eras that are selected by an SAU to build a cohesive, balanced understanding. The "eras," some of which overlap, include:
Eras in United States History* 
Eras in World History* 
1. Beginnings to 1607: Migration, contact, and exchange between Native Americans, Africans, and Europeans. 2. 1607 to 1754: Conflict and competition  Europeans and Native Americans; emergence of distinctive Colonial and Native societies. 3. 1754 to 1800: Social, political, and economic tensions  Revolution and the Early National Period. 4. 1800 to 1848: Defining and extending democratic ideals during rapid economic, territorial, and demographic changes. 5. 1844 to 1877: Regional tensions and civil war. 6. 1865 to 1898: Move from agricultural to industrialized society. 7. 1890 to 1945: Domestic and global challenges; debate over Government's role and the role of the US in the world. 8. 1945 to 1980: Challenges with prosperity, living up to ideals, and unfamiliar international responsibilities. 9. 1980 to present: Cultural debates, adaptation to economic globalization and revolutionary changes in science and technology. *All eras are circa. 
1. Beginnings to 600 BCE: Technological and environmental transformations. 2. 600 BCE to 600 CE: Organization and reorganization of human societies. 3. 600 to 1450: Regional and interregional interactions. 4. 1450 to 1750: Political, social, economic and global interactions led to revolutions. 5. 1750 to 1900: Industrialization and global integration. 6. 1900 to present: Accelerating global change and realignments. 
Spiraling K12  A course of study in which students will see the same topics throughout their school career, with each encounter increasing in complexity and reinforcing previous learning. The Social Studies Standards and performance expectations have been created in order to reflect a progression of increasing complexity from K5 and between the 68, and 9diploma grade spans.
Maine Statutes Related to Social Studies
Title 20A: Education § 4722. High school diploma standards.
Title 20A MRSA § 4706, as amended by PL 1991, c. 655, § 4, is further amended to read:
§ 4706. Instruction in American history, Maine studies and Maine Native American history.
The following subjects are required:.... Maine Studies... American History... Maine Native American history (including Maine tribal governments, Maine Native American culture, Maine Native American territories, and Maine Native American economic systems). Maine Native American history and culture must be taught in all elementary and secondary schools, both public and private.
Maine Native Americans  The phrase "Maine Native Americans" refers to the four Maine Native American tribes  the Penobscot, the Passamaquoddy, the Micmac, and the Maliseet.
Strand 
Civics & Government 

Standard 
Students draw on concepts from civics and government to understand political systems, power, authority, governance, civic ideals and practices, and the role of citizens in the community, Maine, the United States, and the world. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Civics & Government 1: Students understand key ideas and processes that characterize democratic government in the community and the United States by identifying community workers and volunteers and the roles they play in promoting the common good. Civics & Government 2: Students understand key ideas and processes that characterize democratic government in the community and the United States by recognizing symbols, monuments, celebrations, and leaders of local government. Civics & Government 3: Students understand the concepts of rights, duties, responsibilities, and participation by explaining the purpose of school/classroom rules and local laws encountered in daily experiences to promote the common good and the peaceful resolution of conflict. Civics & Government 4: Students understand the concepts of rights, duties, responsibilities, and participation by describing classroom rights, duties, and responsibilities including how students participate in some classroom decisions and are obliged to follow classroom rules. Civics & Government 5: Students understand civic aspects of classroom traditions and decisions by identifying and comparing diverse interests and opinions related to classroom traditions and decisions. 
Civics & Government 1: Students understand key ideas and processes that characterize democratic government in the community and the United States by recognizing symbols, monuments, celebrations, and leaders of State government. Civics & Government 2: Students understand the concepts of rights, duties, responsibilities, and participation by explaining the purpose of school/classroom rules and state laws encountered in daily experiences to promote the common good and the peaceful resolution of conflict. Civics & Government 3: Students understand Maine Native Americans by explaining their traditions and customs. 
Civics & Government 1: Students understand key ideas and processes that characterize democratic government in the community and the United States by describing and providing examples of democratic ideals Civics & Government 2: Students understand key ideas and processes that characterize democratic government in the community and the United States by recognizing symbols, monuments, celebrations, and leaders of national government. Civics & Government 3: Students understand the concepts of rights, duties, responsibilities, and participation by explaining the purpose of school/classroom rules and national laws encountered in daily experiences to promote the common good and the peaceful resolution of conflict through selecting, planning, and participating in a civic action or servicelearning project based on a classroom or school asset or need, and describing the project's potential civic contribution.* Civics & Government 4: Students understand the traditions of Maine Native Americans and various cultures by comparing national traditions and customs. 
Strand 
Civics & Government 

Standard 
Students draw on concepts from civics and government to understand political systems, power, authority, governance, civic ideals and practices, and the role of citizens in the community, Maine, the United States, and the world. 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Civics & Government 1: Students understand the basic ideals, purposes, principles, structures, and processes of democratic government in Maine and the United States by explaining that the study of government includes how governments are organized and how citizens participate. Civics & Government 2: Students understand the basic ideals, purposes, principles, structures, and processes of democratic government in Maine and the United States by explaining how leaders are elected and how laws are made and implemented. Civics & Government 3: Students understand the basic rights, duties, responsibilities, and roles of citizens in a democratic republic by identifying the rights, duties, and responsibilities of citizens within the class, school, or community. Civics & Government 4: Students understand the basic rights, duties, responsibilities, and roles of citizens in a democratic republic by providing examples of how people influence government and work for the common good including voting and writing to legislators. Civics & Government 5: Students understand civic aspects of unity and diversity in the daily life of various cultures in Maine and the United States by identifying examples of unity (sameness) and diversity (variety). Civics & Government 6: Students understand civic aspects of unity and diversity in the daily life of Maine Native Americans and other various cultures in Maine by describing civic beliefs and activities in the daily life of diverse cultures of Maine. 
Civics & Government 1: Students understand the basic ideals, purposes, principles, structures, and processes of democratic government in Maine and the United States by explaining and providing examples of democratic ideals and constitutional principles to include the rule of law, legitimate power, and common good. Civics & Government 2: Students understand the basic ideals, purposes, principles, structures, and processes of democratic government in Maine by explaining and giving examples of governmental structures including the legislative, executive, and judicial branches and the local and State levels of government. Civics & Government 3: Students understand the basic ideals, purposes, principles, structures, and processes of democratic government in Maine by explaining that the structures and processes of government are described in documents, including the Constitution of Maine. Civics & Government 4: Students understand the basic rights, duties, responsibilities, and roles of citizens in a democratic republic by providing examples of how people influence government and work for the common good, including selecting, planning, and participating in a civic action or servicelearning project based on a classroom, school, or local community asset or need, and describe evidence of the project's effectiveness and civic contribution.* Civics & Government 5: Students understand civic aspects of unity and diversity in the daily life of various cultures in Maine and the United States, by identifying examples of unity and diversity in the United States that relate to how laws protect individuals or groups to support the common good. Civics & Government 6: Students understand civic aspects of unity and diversity in the daily life of various cultures in the United States by describing civic beliefs and activities in the daily life of diverse cultures. 
Civics & Government 1: Students understand the basic ideals, purposes, principles, structures, and processes of democratic government in Maine and the United States by explaining that the structures and processes of government are described in documents, including the Constitution of the United States. Civics & Government 2: Students understand the basic ideals, purposes, principles, structures, and processes of democratic government in Maine and the United States by explaining and giving examples of governmental structures including the legislative, executive, and judicial branches at national levels of government. Civics & Government 3: Students understand the basic rights, duties, responsibilities, and roles of citizens in a democratic republic by identifying and describing the United States Constitution and Bill of Rights as documents that establish government and protect the rights of the individual United States citizen. Civics & Government 4: Students understand the basic rights, duties, responsibilities, and roles of citizens in a democratic republic by providing examples of how people influence government and work for the common good, including engaging in civil disobedience. Civics & Government 5: Students understand civic aspects of unity and diversity in the daily life of various cultures in the world, by identifying examples of unity and diversity in the United States that relate to how laws protect individuals or groups to support the common good. Civics & Government 6: Students understand civic aspects of unity and diversity in the daily life of various cultures of the world by describing civic beliefs and activities in the daily life of diverse cultures. 
Strand 
Civics & Government 

Standard 
Students draw on concepts from civics and government to understand political systems, power, authority, governance, civic ideals and practices, and the role of citizens in the community, Maine, the United States, and the world. 

Early Adolescence 

Grades 68 

Performance Expectations 
Civics & Government 1: Students understand the basic ideals, purposes, principles, structures, and processes of constitutional government in Maine and the United States as well as examples of other forms of government in the world by: 

(F1) Explaining that the study of government includes the structures and functions of government and the political and civic activity of citizens. (F2) Describing the structures and processes of United States government and government of the State of Maine and how these are framed by the United States Constitution, the Maine Constitution, and other primary sources. (F3) Explaining the concepts of federalism and checks and balances and the role these concepts play in the governments of the United States and Maine as framed by the United States Constitution, the Maine Constitution and other primary sources. 
(D1) Comparing the structures and processes of United States government with examples of other forms of government. (D2) Comparing how laws are made in Maine and at the federal level in the United States. (D3) Analyze examples of democratic ideals and constitutional principles that include the rule of law, legitimate power, and common good. 

Civics & Government 2: Students understand constitutional and legal rights, civic duties and responsibilities, and roles of citizens in a constitutional democracy by: 

(F1) Explaining the constitutional and legal status of "citizen" and provide examples of rights, duties, and responsibilities of citizens. (F2) Describing how the powers of government are limited to protect individual rights and minority rights as described in the United States Constitution and the Bill of Rights. 
(D1) Analyzing examples of the protection of rights in court cases or from current events. (D2) Analyzing how people influence government and work for the common good including voting, writing to legislators, performing community service, and engaging in civil disobedience through selecting, planning, and implementing a civic action or servicelearning project based on a school, community, or state asset or need, and analyze the project's effectiveness and civic contribution.* 

Civics & Government 3: Students understand political and civic aspects of cultural diversity by: 

(F1) Explaining basic civic aspects of historical and/or current issues that involve unity and diversity in Maine, the United States, and other nations. (F2) Describing the political structures and civic responsibilities of the diverse historic and current cultures of Maine, including Maine Native Americans. 
(D1) Explaining constitutional and political aspects of historical and/or current issues that involve unity and diversity in Maine, the United States, and other nations. (D2) Describing the political structures and civic responsibilities of the diverse historic and current cultures of the United States and the world. 
Strand 
Civics & Government 

Standard 
Students draw on concepts from civics and government to understand political systems, power, authority, governance, civic ideals and practices, and the role of citizens in the community, Maine, the United States, and the world. 

Adolescence 

Grades 9Diploma 

Performance Expectations 
Civics & Government 1: Students understand the ideals, purposes, principles, structures, and processes of constitutional government in the United States and in the American political system, as well as examples of other forms of government and political systems in the world by: 

(F1) Explaining that the study of government includes the structures, functions, institutions, and forms of government. (F2) Explaining how and why democratic institutions and interpretations of democratic ideals and constitutional principles change over time. (F3) Describing the purpose, structures, and processes of the American political system. 
(D1) Evaluating and comparing the relationship of citizens with government in the United States and other regions of the world. (D2) Evaluating current issues by applying democratic ideals and constitutional principles of government in the United States, including checks and balances, federalism, and consent of the governed as put forth in founding documents. (D3) Comparing the American political system with examples of political systems from other parts of the world. 

Civics & Government 2: Students understand the constitutional and legal rights, the civic duties and responsibilities, and roles of citizens in a constitutional democracy and the role of citizens living under other forms of government in the world by: 

(F1) Explaining the relationship between constitutional and legal rights, and civic duties and responsibilities in a constitutional democracy. (F2) Evaluating the relationship between the government and the individual as evident in the United States Constitution, the Bill of Rights, and landmark court cases. (F3) Evaluating how people influence government and work for the common good, including voting, writing to legislators, performing community service, and engaging in civil disobedience. 
(D1) Comparing the rights, duties, and responsibilities of United States citizens with those of citizens from other nations. (D2) Analyzing the constitutional principles and the roles of the citizen and the government in major laws or cases. 

Civics & Government 3: Students understand political and civic aspects of cultural diversity by: 

(F1) Explaining basic civic aspects of historical and/or current issues that involve unity and diversity in Maine, the United States, and other nations. (F2) Describing the political structures and civic responsibilities of the diverse historic and current cultures of Maine, including Maine Native Americans. 
(D1) Analyzing constitutional and political aspects of historical and/or current issues that involve unity and diversity in Maine, the United States, and other nations through selecting, planning, and implementing a civic action or servicelearning project based on a community, school, state, national, or international asset or need, and evaluate the project's effectiveness and civic contribution.* (D2) Analyzing the political structures, political power, and political perspectives of the diverse historic and current cultures of the United States and the world. 
Strand 
Personal Finance & Economics 

Standard 
Students draw from concepts and processes in personal finance to understand issues of money management, saving, investing, credit, and debt; students draw from concepts and processes in economics to understand issues of production, distribution, consumption in the community, Maine, the United States, and the world. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Personal Finance: Students understand the nature of personal finance as well as key foundational ideas by describing how money has value and can be traded for goods and services. Economics: Students understand the nature of economics as well as key foundational ideas by describing how people make choices to meet their needs and wants. Global Connections: Students understand the influence of economics on individuals and groups in the United States and the World, including Maine Native Americans, by identifying how individuals, families, and communities are part of an economy. 
Personal Finance: Students understand the nature of personal finance as well as key foundational ideas by describing how spending, saving, and sharing are ways to use money. Economics: Students understand the nature of economics as well as key foundational ideas by explaining and making decisions about how to use scarce resources to meet their needs and wants.* Global Connections: Students understand the influence of economics on individuals and groups in the United States and the World, including Maine Native Americans by identifying how individuals, families, and communities are influenced by economic factors. 
Personal Finance: Students understand the nature of personal finance as well as key foundational ideas by describing how planning for the future is important to managing money. Economics: Students understand the nature of economics as well as key foundational ideas by explaining how people make choices about how to use scarce resources and make individual and collaborative plans to meet their own needs and wants.* Global Connections: Students understand the influence of economics on individuals and groups in the United States and the World, including Maine Native Americans by describing the work and contributions of various groups to the economics of the local community in the past and present. 
Strand 
Personal Finance & Economics 

Standard 
Students draw from concepts and processes in personal finance to understand issues of money management, saving, investing, credit, and debt; students draw from concepts and processes in economics to understand issues of production, distribution, consumption in the community, Maine, the United States, and the world. 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Personal Finance: Students understand the nature of personal finance as well as key foundational ideas by describing situations in which personal choices are related to the use of money. Economics: Students understand economics and the basis of the economies of the community, Maine, the United States, and various regions of the world by explaining how scarcity leads to choices about what goods and services are produced and for whom they are produced. Global Connections: Students understand economic aspects of unity and diversity in the community, Maine, and regions of the United States and the world, including Maine Native American communities by describing economic similarities and differences within the community, Maine, and the United States. 
Personal Finance: Students understand the principles and process of personal finance by describing situations in which financial institutions can be used to manage money. Economics: Students understand economics and the basis of the economies of the community, Maine, the United States, and various regions of the world by explaining how scarcity leads to choices about how goods and services are consumed and distributed, and by making a real or simulated decision related to scarcity.* Global Connections: Students understand economic aspects of unity and diversity in the community, Maine, and regions of the United States and the world, including Maine Native American communities by identifying economic processes, economic institutions, and economic influences related to Maine Native Americans and various cultures in the United States and the world. 
Personal Finance: Students understand the principles and process of personal finance by describing situations in which choices are related to the use of financial resources and financial institutions. Economics: Students understand the basis of the economies of the community, Maine, the United States, and various regions of the world by examining different ways producers of goods and services help satisfy the wants and needs of consumers in a market economy by using entrepreneurship, natural, human and capital resources, as well as collaborating to make a decision.* Global Connections: Students understand economic aspects of unity and diversity in the community, Maine, and regions of the United States and the world, including Maine Native American communities, by explaining economic processes, economic institutions, and economic influences related to Maine Native Americans and various cultures in the United States and the world. 
Strand 
Personal Finance & Economics 

Standard 
Students draw from concepts and processes in personal finance to understand issues of money management, saving, investing, credit, and debt; students draw from concepts and processes in economics to understand issues of production, distribution, consumption in the community, Maine, the United States, and the world. 

Early Adolescence 

Grades 68 

Performance Expectations 
Personal Finance: Students understand the principles and processes of personal finance by: 

(F1) Explaining how scarcity influences choices and relates to the market economy. (F2) Identifying factors that contribute to spending and savings decisions. 
(D1) Using a process for making spending and savings decisions based on work, wages, income, expenses, and budgets as they relate to the study of individual financial choices.* 

Economics: Students understand the principles and processes of personal economics, the influence of economics on personal life and business, and the economic systems of Maine, the United States, and various regions of the world by: 

(F1) Describing the functions of financial institutions. (F2) Describing the function and process of taxation. 
(D1) Explaining how scarcity requires choices and relates to the market economy, entrepreneurship, supply and demand. 

Global Connections: Students understand economic aspects of unity and diversity in Maine, the United States, and various world cultures, including Maine Native Americans, by: 

(F1) Researching the pros and cons of economic processes, economic institutions, and economic influences of diverse cultures, including Maine Native Americans, various historical and recent immigrant groups in the United States, and various cultures in the world to propose a solution to an economic problem.* 
(D1) Describing factors in economic development, and how states, regions, and nations have worked together to promote economic unity and interdependence. 
Strand 
Personal Finance & Economics 

Standard 
Students draw from concepts and processes in personal finance to understand issues of money management, saving, investing, credit, and debt; students draw from concepts and processes in economics to understand issues of production, distribution, consumption in the community, Maine, the United States, and the world. 

Adolescence 

Grades 9Diploma 

Performance Expectations 
Personal Finance: Students understand the principles and process of personal finance by: 

(F1) Explaining how personal finance involves the use of economics as the basis for saving, investing and managing money. (F2) Identifying factors that impact consumer credit. 
(D1) Evaluating ways credit can be used. (D2) Evaluating different strategies for money and risk management. 

Economics: Students understand the principles and processes of personal economics, the role of markets, the economic system of the United States, other economic systems in the world, and how economics serves to inform decisions in the present and future by: 

(F1) Analyzing the role of financial institutions, the financial markets, and government including fiscal, monetary, and trade policies. (F2) Identifying and explaining various economic indicators and how they represent and influence economic activity. 
(D1) Analyzing economic activities and policies in relationship to freedom, efficiency, equity, security, growth, and sustainability. (D2) Explaining and applying the concepts of specialization, economic interdependence, and comparative advantage. (D3) Proposing a solution to a problem using the theory of supply and demand.* 

Global Connections: Students understand economic aspects of unity and diversity in Maine, the United States, and the world, including Maine Native American communities, by: 

(F1) Comparing a variety of economic systems and strategies of economic development. (F1) Analyzing how resource distribution effects wealth, poverty, and other economic factors. 
(D2) Analyzing multiple views on how resource distribution has affected wealth, poverty, and other economics factors and present an argument as to the role of regional, international, and global organizations that are engaged in economic development.* 
Strand 
Geography 

Standard 
Students draw on concepts and processes from geography to understand issues involving people, places, and environments in the community, Maine, the United States, and the world. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Geography 1: Students understand the nature and basic ideas of geography byidentifying questions about their world and explaining that geography is the study of the Earth's surface and peoples. * Geography 2:Students understand the influence of geography on individuals and their immediate surroundings by identifying the impacts of geographic features on individuals and families. 
Geography 1: Students understand the nature and basic ideas of geography by gathering information about their immediate neighborhood and community, including maps, photographs, charts and graphs, and then create visual representations of their findings.* Geography 2: Students understand the influence of geography on communities by identifying the impacts of geographic features on communities. 
Geography 1: Students understand the nature and basic ideas of geography by using basic maps and globes to identify local and distant places and locations, directions (including N, S, E, and W), and basic physical, environmental, and cultural features. Geography 2: Students understand the influence of geography on individuals and groups in Maine, including Maine Native Americans, the United States and the worldby identifying the impacts of geographic features on individuals and groups in those communities. 
Strand 
Geography 

Standard 
Students draw on concepts and processes from geography to understand issues involving people, places, and environments in the community, Maine, the United States, and the world. 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Geography 1: Students understand the geography of the community, Maine, the United States, and various regions of the world by explaining that geography includes the study of Earth's physical features including climate and the distribution of plant, animal, and human life. Geography 2: Students understand geographic aspects of unity and diversity in the community and in Maine, including Maine Native American communities by collecting, evaluating, and organizing information about the impacts of geographic features on the daily life of various cultures, including Maine Native Americans and other cultures and communities.* 
Geography 1: Students understand the geography of the community, Maine, the United States, and various regions of the world by communicating their findings by creating visual representations of the world, showing a basic understanding of the geographic grid, including the equator and prime meridian.* Geography 2: Students understand geographic aspects of unity and diversity in various regions of the United States and the world by describing impacts of geographic features on the daily life of various cultures in the United States and the world. 
Geography 1: Students understand the geography of the community, Maine, the United States, and various regions of the world by identifying the Earth's major geographic features such as continents, oceans, major mountains, and rivers using a variety of geographic tools including digital mapping tools; and by explaining examples of changes in the Earth's physical features and their impact on communities and regions. Geography 2: Students understand geographic aspects of unity and diversity in the community, Maine, and regions of the United States and the world, including Maine Native American communities, by identifying examples through inquiry of how geographic features unify communities and regions as well as support diversity using print and nonprint sources.* 
Strand 
Geography 

Standard 
Students draw on concepts and processes from geography to understand issues involving people, places, and environments in the community, Maine, the United States, and the world. 

Early Adolescence 

Grades 68 

Performance Expectations 
Geography 1: Students understand the geography of the community, Maine, the United States, and various regions of the world and the geographic influences on life in the past, present, and future by: 

(F1) Using the geographic grid and a variety of types of maps, including digital sources, to locate and access relevant geographic information that reflects multiple perspectives. * (F2) Identifying the major regions of the Earth and their major physical features and political boundaries using a variety of geographic tools including digital tools and resources. * (F3) Evaluating a geographic issue of physical, environmental, or cultural importance.* 
(D1) Identifying consequences of geographic influences through inquiry and formulating predictions. (D2) Describing the impact of change on the physical and cultural environment. 

Geography 2: Students understand geographic aspects of unity and diversity in Maine, the United States, and various world cultures, including Maine Native Americans by: 

(F1) Explaining how geographic features have impacted unity and diversity in Maine, the United States, and other nations.* 
(D1) Summarizing and interpreting the relationship between geographic features and cultures of Maine Native Americans, and historical and recent immigrant groups in Maine, United States, and the world. * 
Strand 
Geography 

Standard 
Students draw on concepts and processes from geography to understand issues involving people, places, and environments in the community, Maine, the United States, and the world. 

Adolescence 

Grades 9Diploma 

Performance Expectations 
Geography 1: Students understand the geography of the United States and various regions of the world and the effect of geographic influences on decisions about the present and future by: 

(F1)Analyzing local, national, and global geographic data on physical, environmental, and cultural processes that shape and change places and regions.* (F2) Evaluating and developing a wellsupported position about the impact of change on the physical and cultural environment. * 
(D1) Proposing a solution to a geographic issue that reflects physical, environmental, and cultural features at local, state, national, and global levels.* (D2) Using inquiry to predict and evaluate consequences of geographic influences. (D3) Describing the major regions of the Earth and their major physical, environmental, and cultural features using a variety of geographic tools including digital tools and resources. * 

Geography 2: Students understand geographic aspects of unity and diversity in Maine, the United States, and the world, including Maine Native American communities by: 

(F1) Analyzing geographic features that have impacted unity and diversity in the United States and other nations.* 
(D1) Summarizing and interpreting the relationship between geographic features and cultures of Maine Native Americans, and historical and recent immigrant groups in Maine, United States, and the world. * 
Strand 
History 

Standard 
Students draw on concepts and processes using primary and secondary sources from history to develop historical perspective and understand issues of continuity and change in the community, Maine, the United States, and the world. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
History 1: Students understand the nature of history by describing history as stories of the past and identifying questions related to social studies.* History 2: Students understand the nature of history as well as the key foundation of ideas by applying terms such as "before" and "after" in sequencing events. History 3: Students understand historical aspects of the uniqueness and commonality of individuals and groups, including Maine Native Americans, by explaining how individuals and families share both common and unique aspects of culture, values, and beliefs through stories, traditions, religion, celebrations, or the arts. 
History 1: Students understand the nature of history as well as the key foundation of ideas by identifying past, present, and future in stories, pictures, poems, songs, and video. History 2: Students understand historical aspects of the uniqueness and commonality of individuals and groups, including Maine Native Americans by explaining how individuals and families share both common and unique aspects of culture, values, and beliefs through stories, traditions, religion, celebrations, or the arts. Students organize findings at a developmentally appropriate manner and share gathered information using oral and visual examples* History 3: Students understand historical aspects of the uniqueness and commonality of individuals and groups, including Maine Native Americans, by describing traditions of Maine Native Americans and various historical and recent immigrant groups and traditions common to all. 
History 1: Students understand the nature of history as well as the key foundation of ideas by following an established procedure to locate sources appropriate to reading level* and identifying a few key figures and events from personal history and the history of the community, the state, and the United States, especially those associated with historicallybased traditions. History 2: Students understand the nature of history as well as the key foundation of ideas by creating a brief historical account about family, the local community, or the nation by locating and collecting information from sources including maps, charts, graphs, artifacts, photographs*, or stories of the past. History 3: Students understand historical aspects of the uniqueness and commonality of individuals and groups, including Maine Native Americans, by describing traditions of Maine Native Americans and various historical and recent immigrant groups and traditions common to all. 
Strand 
History 

Standard 
Students draw on concepts and processes using primary and secondary sources from history to develop historical perspective and understand issues of continuity and change in the community, Maine, the United States, and the world. 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
History 1: Students understand various major eras in the history of the community, Maine, and the United States by explaining that history includes the study of past human experience based on available evidence from a variety of primary and secondary sources.* Students make real or simulated decisions related to the local community or civic organizations by applying appropriate and relevant social studies knowledge and skills, including research skills, and other relevant information.* History 2: Students understand historical aspects of unity and diversity in the community, the state, Maine Native American communities, and the United States by identifying research questions, seeking multiple perspectives from varied sources*, and describing examples in the history of the United States of diverse and shared values and traditions. 
History 1: Students understand various major eras in the history of the community, Maine, and the United States by identifying major historical eras, major enduring themes, turning points, events, consequences, persons, and timeframes, in the history of the community, the state, and the United States. Students make real or simulated decisions related to the state of Maine or civic organizations by applying appropriate and relevant social studies knowledge and skills, including research skills, and other relevant information.* Students distinguish between facts and opinions/interpretations in sources.* History 2: Students understand historical aspects of unity and diversity in the community, the state, Maine Native American communities, and the United States by describing various cultural traditions and contributions of Maine Native Americans and various historical and recent immigrant groups in the community and the state. 
History 1: Students understand various major eras in the history of the community, Maine, and the United States by tracing and explaining how the history of democratic principles is preserved in historic symbols, monuments, and traditions important in the community, Maine and the United States. Students make real or simulated decisions related to the United States, world, or civic organizations by applying appropriate and relevant social studies knowledge and skills, including research skills, and other relevant information.* Students communicate findings from a variety of print and nonprint sources, describe plagiarism and demonstrate appropriate citation.* History 2: Students understand historical aspects of unity and diversity in the community, the state, including Maine Native American communities, by describing various cultural traditions and contributions of Maine Native Americans and other cultural groups within the United States. 
Strand 
History 

Standard 
Students draw on concepts and processes using primary and secondary sources from history to develop historical perspective and understand issues of continuity and change in the community, Maine, the United States, and the world. 

Early Adolescence 

Grades 68 

Performance Expectations 
History 1: Students understand major eras, major enduring themes, and historic influences in the history of Maine, the United States, and various regions of the world by: 

(F1) Explaining that history includes the study of past human experience based on available evidence from a variety of primary and secondary sources; and explaining how history can help one better understand and make informed decisions about the present and future.* (F2) Identifying major historical eras, major enduring themes, turning points, events, consequences, and people in the history of Maine, the United States and various regions of the world.* (F3) Tracing the history of democratic ideals and constitutional principles and their importance in the history of the United States and the world.* (F4) Proposing and revising research questions related to a current social studies issue.* 
(D1) Analyzing interpretations of historical events that are based on different perspectives and evidence from primary and secondary sources.* (D2) Analyzing major historical eras, major enduring themes, turning points, events, consequences, and people in the history of Maine, the United States and various regions of the world.* (D3) Explaining the history of democratic ideals and constitutional principles and their importance in the history of the United States and the world.* (D4) Making decisions related to the classroom, school, community, civic organization, Maine, or beyond; applying appropriate and relevant social studies knowledge and skills, including research skills, and other relevant information.* 

History 2: Students understand historical aspects of unity and diversity in the community, the state, including Maine Native American communities, and the United States by: 

(F1) Explaining how both unity and diversity have played and continue to play important roles in the history of Maine and the United States. (F2) Identifying a variety of cultures through time, including comparisons of native and immigrant groups in the United States, and eastern and western societies in the world. (F3) Identifying major turning points and events in the history of Maine Native Americans and various historical and recent immigrant groups in Maine, the United States, and other cultures in the world. 
(D1) Explaining how both unity and diversity have played and continue to play important roles in the history of the World. (D2) Comparing a variety of cultures through time, including comparisons of native and immigrant groups in the United States, and eastern and western societies in the world. (D3) Describing major turning points and events in the history of Maine Native Americans and various historical and recent immigrant groups in Maine, the United States, and other cultures in the world. 
Strand 
History 

Standard 
Students draw on concepts and processes using primary and secondary sources from history to develop historical perspective and understand issues of continuity and change in the community, Maine, the United States, and the world. 

Adolescence 

Grades 9Diploma 

Performance Expectations 
History 1: Students understand major eras, major enduring themes, and historic influences in United States and world history, including the roots of democratic philosophy, ideals, and institutions in the world by: 

(F1) By explaining that history includes the study of the past based on the examination of a variety of primary and secondary sources and how history can help one better understand and make informed decisions about the present and future.* (F2) Analyzing and critiquing major historical eras: major enduring themes, turning points, events, consequences, and people in the history of the United States and the implications for the present and future. (F3) Tracing and critiquing the roots and evolution of democratic ideals and constitutional principles in the history of the United States using historical sources. (F4) Developing individual and collaborative decisions/plans by considering multiple points of view, weighing pros and cons, building on the ideas of others, and sharing information in an attempt to sway the opinions of others.* 
(D1) Analyzing and critiquing varying interpretations of historic people, issues, or events, and explain how evidence from primary and secondary sources is used to support and/or refute different interpretations.* (D2) Analyzing and critiquing major historical eras: major enduring themes, turning points, events, consequences, and people in the history of the world and the implications for the present and future. (D3) Tracing and critiquing the roots and evolution of democratic ideals and constitutional principles in the history of the world using historical sources. (D4) Making a decision related to the classroom, school, community, civic organization, Maine, United States, or international entity by applying appropriate and relevant social studies knowledge and skills, including research skills, ethical reasoning skills, and other relevant information.* 

History 2: Students understand historical aspects of unity and diversity in the United States, the world, and Native American communities by: 

(F1) Identifying and critiquing issues characterized by unity and diversity in the history of the United States, and describing their effects, using primary and secondary sources.* (F2) Identifying and analyzing major turning points and events in the history of Native Americans and various historical and recent immigrant groups in the United States, making use of primary and secondary sources.* 
(D1) Identifying and critiquing issues characterized by unity and diversity in the history of other nations, and describing their effects, using primary and secondary sources.* (D2) Making use of primary and secondary sources, identifying and analyzing major turning points and events in the history of world cultures as it pertains to various historical and recent migrant groups.* 
Definitions:
Strand: A body of knowledge in a content area identified by a simple title.
Standard: Enduring understandings and skills that students can apply and transfer to contexts that are new to the student.
Performance Expectation: Building blocks to the standard and measurable articulations of what the student understands and can do.
VISUAL AND PERFORMING ARTS
SUMMARY: The Maine Department of Education Regulation 132  The Maine Learning Results: Parameters for Essential Instruction establishes parameters for essential teaching and learning in grades Kindergarten through Diploma across eight content areas and supports the goals outlined in the Guiding Principles. The Maine Learning Results: Parameters for Essential Instruction will inform the blueprint for item development of the largescale State assessments aligned to the federal accountability standards found in Maine Department of Education Regulation 131  The Federal, State, and Local Accountability Standards. High school, middle school, and elementary school programming in Maine's publicly supported schools must be aligned to the knowledge and skills described in the Maine Learning Results: Parameters for Essential Instruction.
The Maine Department of Education Regulation 132  The Maine Learning Results: Parameters for Essential Instruction augments and expands upon the content standards for federal accountability (Maine Department of Education Regulation 131: The Maine Federal, State, and Local Accountability Standards) by describing details for essential teaching and learning for eight content areas. These learning goals identify the knowledge and skills required for college, career, and citizenship in the 21st Century.
THE GUIDING PRINCIPLES  The knowledge and skills described in the Maine Department of Education Regulation 132 support Maine students in achieving the goals established in Maine's Guiding Principles.The Guiding Principles state that each Maine student must leave school as:
A. A clear and effective communicator who:
B. A selfdirected and lifelong learner who:
C. A creative and practical problem solver who: [1995, c. 649, §1 (new).]
D. A responsible and involved citizen who:
E. An integrative and informed thinker who:
The visual and performing arts are an essential part of every child's education. Engagement in a wellrounded visual and performing arts education positively impacts students' academic, social and emotional outcomes.1 Arts education supports lifelong learning and creative problem solving. It enhances a student's understanding of the world around them through multiple viewpoints and critical thinking. Through the arts, students become active and involved citizens who can clearly communicate their thoughts and ideas through various mediums. Arts integration opportunities provide authentic learning experiences for students, connecting the visual and performing arts with other content areas of the curriculum. Research shows that students who are continually involved in visual and performing arts opportunities are more successful in school, more connected within their communities, and perform better academically.
This update of the Maine Learning Results includes separate standards for music, dance, theater, visual arts and media arts. Though Media Arts is a new standalone discipline, like other disciplines within the arts, it may be covered in other VPA classrooms or as a standalone course.
The National Core Arts Standards (NCAS, 2014) define the arts as Dance, Media Arts, Music, Theatre, and Visual Art. In addition to the NCAS other sources were referenced in the creation of these Maine Standards. The format of this document defines Strands to guide educational practices in each Arts discipline. These Strands form the foundation of educational excellence that support students in their journey from early learning experiences in kindergarten through graduation from high school. Teachers and their learning community are meant to collaborate on these foundational standards. These standards are meant as a foundation for teachers to build upon as districts meet the needs of their students. The standards also provide administrators and district decisionmakers with critical information for developing and expanding standardsbased arts programs. Standards are process oriented, building on skills and concepts as they progress through the grades. The writing of these standards reflects backward design, the process of designing learning experiences and instructional techniques to achieve learning goals.
A successful visual and performing arts education is supported through highly qualified teachers, schedules that support visual and performing arts, facilities and materials designed for visual and performing arts education, and a strong collaboration between the visual and performing arts and other disciplines. The key to success is a culture within the community and the school that supports a strong arts education. This document is set forth as a guide toward attaining that goal.[2]
How to Represent the Visual and Performing Arts Standards and Performance Expectations
The Dance Standards
Dance, like language, is found in all human societies. It is an essential component in the process of socialization in all cultures. By honoring personal expression through time and space, dance contributes to the sense of self as no other art form can. Everyone has the instrument of dance  one's own body. Dance education can enhance awareness of the body's physical development, increase recognition of one's place in the physical world, and heighten the sense of self. The human body is the vehicle through which learning occurs. Body and mind are inseparable. In a safe environment, a child is free to discover and rediscover the self. The purpose of dance education is to build on the primitive body movements that begin before birth and to discover and experiment with increasingly more complex interconnections of body and mind, enhancing the physical, intellectual, social and emotional development of the child. Basic dance education plays an important role in this developmental process and should be provided to all children. Such a basic dance education includes opportunities in creative dance, improvisation, choreography, technique, social and contemporary forms and multicultural experiences. The use of dance increases the understanding of one's own culture and other cultures of the world. The creativity and discipline of dance contributes to balanced development of the whole person. Maine students need dance education in their public education because:
Maine's Dance Education Heritage 3
Maine has a long history of dance in education. From the dance styles of the Wabanaki nations to the 19th century May Pole dances at "Normal" schools to today's dances inspired by contemporary music or dances from the heritage of New Mainers dance has a profound effect upon children in Maine. Dance in education in Maine has many interweaving strands. As in other states throughout the country, dance in education began in the physical education programs of state and private colleges. Courses in rhythm, folk dance, square dance, and social dance have existed since the 1880s. University and college drama and music programs have included dance events in the training of teachers for many years. Dance in education has been offered through physical education, drama, and music programs; in individual classrooms; through gifted and talented programs; or through schoolbased programs organized by individuals or groups in the community. Private dance studios throughout the state have provided instruction in such areas as modern dance, ballet, jazz, hip hop, tap, African dance, Latin dance, acrobatics, clogging and ballroom dance. Each dance form has produced offshoots emphasizing increased specialization. A wide variety of dance instruction exists throughout the state of Maine in private studios, however the opportunity for learning in and through dance and creative movement should be accessible to all children through their public education. Public agencies and organizations such as the Maine Arts Commission, the Arts Education Program of the National Endowment for the Arts, The National Dance Education Organization (NDEO), The Maine Alliance for Arts Education (MAAE), VSA Maine, Dance Education in Maine Schools (DEMS), and The Maine Association for Health, Physical Education, Recreation and Dance (MAHPERD) have provided financial and technical support for the development of dance in public education over the years. Maine schools are ready for the development and inclusion of dance in the curriculum. The expression of a child's personal stories through movement and the resulting enhancement of learning, social skills, and selfesteem can be crucial to that child's development.
Strand 
A. DANCE 

Standard 
A1  Generate and conceptualize artistic ideas and work. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Respond in movement to a variety of stimuli (for example, music/sound, text, objects, images, symbols, observed dance). b. Explore different ways to do basic locomotor and nonlocomotor movements by changing at least one of the elements of dance. 
a. Explore movement inspired by a variety of stimuli (for example, music/sound, text, objects, images, symbols, observed dance, experiences) and identify the source. b. Explore a variety of locomotor and nonlocomotor movements by experimenting with and changing the elements of dance. 
a. Explore movement inspired by a variety of stimuli (for example, music/sound, text, objects, images, symbols, observed dance, experiences) and suggest additional sources for movement ideas. b. Combine a variety of movements while manipulating the elements of dance. 
Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Experiment with a variety of selfidentified stimuli (for example, music/sound, text, objects, images, notation, observed dance, experiences) for movement. b. Explore a given movement problem. Select and demonstrate a solution. 
a. Identify ideas for choreography generated from a variety of stimuli (for example, music/sound, text, objects, images, notation, observed dance, experiences). b. Develop a movement problem and manipulate the elements of dance as tools to find a solution. 
a. Build content for choreography using several stimuli (for example, music/sound, text, objects, images, notation, observed dance, experiences, literary forms, natural phenomena, current news, social events). b. Construct and solve multiple movement problems to develop choreographic content. 
Strand 
A. DANCE 

Standard 
A1  Generate and conceptualize artistic ideas and work. 

Early Adolescence 

Grades 68 

Performance Expectations 
a. Implement movement from a variety of stimuli (for example, music, observed dance, literary forms, notation, natural phenomena, personal experience/recall, current news, or social events) to develop dance content for an original dance study or dance. b. Identify and select personal preferences to create an original dance study or dance. Use genrespecific dance terminology to articulate and justify choices made in movement development to communicate intent. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Accomplished 
Grades 9Diploma Advanced 

Performance Expectations 
a. Explore a variety of stimuli for sourcing movement to develop an improvisational or choreographed dance study. Analyze the process and the relationship between the stimuli and the movement. b. Experiment with the elements of dance to explore personal movement preferences and strengths and select movements that challenge skills and build on strengths in an original dance study or dance. 
a. Synthesize content generated from stimulus materials to choreograph dance studies or dances using original or codified movement. b. Apply personal movement preferences and strengths with the movement vocabulary of several dance styles or genres to choreograph an original dance study or dance that communicates an artistic intent. Compare personal choices to those made by wellknown choreographers. 
a. Synthesize content generated from stimulus material. Experiment and take risks to discover a personal voice to communicate artistic intent. b. Expand personal movement preferences and strengths to discover unexpected solutions that communicate the artistic intent of an original dance. Analyze the unexpected solutions and explain why they were effective in expanding artistic intent. 
Strand 
A. DANCE 

Standard 
A2  Organize and develop artistic ideas and work. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Improvise dance that has a beginning, middle, and end. b. Express an idea, feeling, or image, through improvised movement moving alone or with a partner. 
a. Improvise a series of movements that have a beginning, middle, and end, and describe movement choices. b. Choose movements that express an idea or emotion, or that follow a musical phrase. 
a. Improvise a dance phrase with a beginning, a middle that has a main idea, and a clear end. b. Choose movements that express a main idea or emotion, or that follow a musical phrase. Explain reasons for movement choices. 
Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Identify and experiment with choreographic devices to create simple movement patterns and dance structures (for example, AB, ABA, theme and development). b. Develop a dance phrase that expresses and communicates an idea or feeling. Discuss the effect of the movement choices. 
a. Manipulate or modify choreographic devices to expand movement possibilities and create a variety of movement patterns and structures. Discuss movement choices. b. Develop a dance study that expresses and communicates a main idea. Discuss the reasons and effectiveness of the movement choices. 
a. Manipulate or modify a variety of choreographic devices to expand choreographic possibilities and develop a main idea. Explain reasons for movement choices. b. Develop a dance study by selecting a specific movement vocabulary to communicate a main idea. Discuss how the dance communicates nonverbally. 
Grades 68 

Performance Expectations 
a. Collaborate to select and apply a variety of choreographic devices and dance structures to choreograph an original dance study or dance with a clear artistic intent. Articulate the group process for making movement and structural choices. b. Define and apply artistic criteria to choreograph a dance that communicates personal or cultural meaning. Discuss how the criteria clarify or intensify the meaning of the dance. 
Strand 
A. DANCE 

Standard 
A2  Organize and develop artistic ideas and work. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Accomplished 
Grades 9Diploma Advanced 

Performance Expectations 
a. Collaborate to design a dance using choreographic devices and dance structures to support an artistic intent. Explain how the dance structures clarify the artistic intent. b. Develop an artistic statement for an original dance study or dance. Discuss how the use of movement elements, choreographic devices and dance structures serve to communicate the artistic statement. 
a. Work individually and collaboratively to design and implement a variety of choreographic devices and dance structures to develop original dances. Analyze how the structure and final composition inform the artistic intent. b. Develop an artistic statement that reflects a personal aesthetic for an original dance study or dance. Select and demonstrate movements that support the artistic statement. 
a. Demonstrate fluency and personal voice in designing and choreographing original dances. Justify choreographic choices and explain how they are used to intensify artistic intent. b. Construct an artistic statement that communicates a personal, cultural and artistic perspective. 
Strand 
A. Dance 

Standard 
A3  Refine and complete artistic work. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Apply suggestions for changing movement through guided improvisational experiences. b. Depict a dance movement by drawing a picture or using a symbol. 
a. Explore suggestions to change movement from guided improvisations and/or short remembered sequences. b. Depict several different types of movements 
a. Explore movement inspired by a variety of stimuli (for example, music/sound, text, objects, images, symbols, observed dance, experiences) and suggest additional sources for movement ideas. b. Combine a variety of movements while manipulating the elements of dance. 
Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Experiment with a variety of selfidentified stimuli (for example, music/sound, text, objects, images, notation, observed dance, experiences) for movement. b. Explore a given movement problem. Select and demonstrate a solution. 
a. Identify ideas for choreography generated from a variety of stimuli (for example, music/sound, text, objects, images, notation, observed dance, experiences). b. Develop a movement problem and manipulate the elements of dance as tools to find a solution. 
a. Build content for choreography using several stimuli (for example, music/sound, text, objects, images, notation, observed dance, experiences, literary forms, natural phenomena, current news, social events). b. Construct and solve multiple movement problems to develop choreographic content. 
Strand 
A. DANCE 

Standard 
A3  Refine and complete artistic work. 

Early Adolescence 

Grades 68 

Performance Expectations 
a. Implement movement from a variety of stimuli (for example, music, observed dance, literary forms, notation, natural phenomena, personal experience/recall, current news, or social events) to develop dance content for an original dance study or dance. b. Identify and select personal preferences to create an original dance study or dance. Use genrespecific dance terminology to articulate and justify choices made in movement development to communicate intent. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Accomplished 
Grades 9Diploma Advanced 

Performance Expectations 
a. Explore a variety of stimuli for sourcing movement to develop an improvisational or choreographed dance study. Analyze the process and the relationship between the stimuli and the movement. b. Experiment with the elements of dance to explore personal movement preferences and strengths and select movements that challenge skills and build on strengths in an original dance study or dance. 
a. Synthesize content generated from stimulus materials to choreograph dance studies or dances using original or codified movement. b. Apply personal movement preferences and strengths with the movement vocabulary of several dance styles or genres to choreograph an original dance study or dance that communicates an artistic intent. Compare personal choices to those made by wellknown choreographers. 
a. Synthesize content generated from stimulus material. Experiment and take risks to discover a personal voice to communicate artistic intent. b. Expand personal movement preferences and strengths to discover unexpected solutions that communicate the artistic intent of an original dance. Analyze the unexpected solutions and explain why they were effective in expanding artistic intent. 
Strand 
A. DANCE 

Standard 
B1  Select, analyze, and interpret artistic work for presentation. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Make still and moving body shapes that show lines (for example, straight, bent, and curved), levels, and vary in size (large/small). b. Demonstrate tempo contrasts with movements that match to tempo of sound stimuli. c. Identify and apply different characteristics to movements (for example, slow, smooth, or wavy). 
a. Demonstrate locomotor and nonlocomotor movements that change body shapes, levels, and facings. Move in straight, curved, and zigzagged pathways. Find and return to place in space. Move with others to form straight lines and circles. b. Relate quick, moderate, and slow movements to duration in time. Recognize steady beat and move to varying tempi of steady beat. c. Demonstrate movement characteristics along with movement vocabulary (for example, use adverbs and adjectives that apply to movement such as a bouncy leap, a floppy fall, a jolly jump, and joyful spin). 
a. Demonstrate clear directionality and intent when performing locomotor and nonlocomotor movements that change body shapes, facings, and pathways in space. Identify symmetrical and asymmetrical body shapes and examine relationships between body parts. Differentiate between circling and turning as two separate ways of continuous directional change. b. Identify the length of time a move or phrase takes (for example, whether it is long or short). Identify and move on the downbeat in duple and triple meter. Correlate metric phrasing with movement phrasing. c. Select and apply appropriate characteristics to movements (for example, selecting specific adverbs and adjectives and apply them to movements). Demonstrate kinesthetic awareness while dancing the movement characteristics. d. 
Strand 
A. DANCE 

Standard 
B1  Select, analyze, and interpret artistic work for presentation. 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Judge spaces as distance traveled and use space threedimensionally. Demonstrate shapes with positive and negative space. Perform movement sequences in and through space with intentionality and focus. b. Fulfill specified duration of time with improvised locomotor and nonlocomotor movements. Differentiate between "in time" and "out of time" to music. Perform movements that are the same or of a different time orientation to accompaniment. Use metric and kinesthetic phrasing. c. Change use of energy and dynamics by modifying movements and applying specific characteristics to heighten the effect of their intent. 
a. Make static and dynamic shapes with positive and negative space. Perform elevated shapes (jump shapes) with soft landings and movement sequences alone and with others, establishing relationships with other dancers through focus of eyes. b. Accompany other dancers using a variety of percussive instruments and sounds. Respond in movement to even and uneven rhythms. Recognize and respond to tempo changes as they occur in dance and music. c. Analyze movements and phrases for use of energy and dynamic changes and use adverbs and adjectives to describe them. Based on the analysis, refine the phrases by incorporating a range of movement characteristics. 
a. Integrate static and dynamic shapes and floor and air pathways into dance sequences. Establish relationships with other dancers through focus of eyes and other body parts. Convert inward focus to outward focus for projecting out to far space. b. Dance to a variety of rhythms generated from internal and external sources. Perform movement phrases that show the ability to respond to changes in time. c. Contrast bound and freeflowing movements. Motivate movement from both central initiation (torso) and peripheral initiation (distal) and analyze the relationship between initiation and energy. 
Strand 
A. DANCE 
Standard 
B1  Select, analyze, and interpret artistic work for presentation. 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Expand movement vocabulary of floor and air pattern designs. Incorporate and modify body designs from different dance genres and styles for the purpose of expanding movement vocabulary to include differently designed shapes and movements for interest and contrast. b. Vary durational approach in dance phrasing by using timing accents and variations within a phrase to add interest kinesthetically, rhythmically, and visually. c. Compare and contrast movement characteristics from a variety of dance genres or styles. Discuss specific characteristics and use adverbs and adjectives to describe them. Determine what dancers must do to perform them clearly. 
Strand 
A. DANCE 

Standard 
B1  Select, analyze, and interpret artistic work for presentation. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Accomplished 
Grades 9Diploma Advanced 

Performance Expectations 
a. Develop partner and ensemble skills that enable contrasting level changes through lifts, balances, or other means while maintaining a sense of spatial design and relationship. Use space intentionally during phrases and through transitions between phrases. Establish and break relationships with others as appropriate to the choreography. b. Use syncopation and accent movements related to different tempi. Take rhythmic cues from different aspects of accompaniment. Integrate breath phrasing with metric and kinesthetic phrasing. c. Connect energy and dynamics to movements by applying them in and through all parts of the body. Develop total body awareness so that movement phrases demonstrate variances of energy and dynamics. 
a. Dance alone and with others with spatial intention. Expand partner and ensemble skills to greater ranges and skill. Execute complex floor and air sequences with others while maintaining relationships through focus and intentionality. b. Perform dance studies and compositions that use time and tempo in unpredictable ways. Use internal rhythms and kinetics as phrasing tools. Dance "in the moment." c. Initiate movement phrases by applying energy and dynamics. Vary energy and dynamics over the length of a phrase and transition smoothly out of the phrase and into the next phrase, paying close attention to its movement initiation and energy 
a. Use the broadest range of movement in space for artistic and expressive clarity. Use inward and outward focus to clarify movement and intent. Establish and break relationships with other dancers and audience as appropriate to the dance. b. Modulate time factors for artistic interest and expressive acuity. Demonstrate time complexity in phrasing with and without musical accompaniment. Use multiple and complex rhythms at the same time. Work with and against rhythm of accompaniment or sound environments. c. Modulate dynamics to clearly express intent while performing dance phrases and choreography. Perform movement sequences expressively using a broad dynamic range and employ dynamic skills for establishing relationships with other dancers and projecting to the audience. 
Strand 
A. Dance 

Standard 
B2  Develop and refine artistic technique and work for presentation. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Demonstrate sameside and crossbody locomotor and nonlocomotor movements, body patterning movements, and body shapes. b. Move safely in general space and start and stop on cue during activities, group formations, and creative explorations while maintaining personal space. c. Move body parts in relation to other body parts and repeat and recall movements upon request. 
a. Demonstrate a range of locomotor and nonlocomotor movements, body patterning, body shapes, and directionality. b. Move safely in general space through a range of activities and group formations while maintaining personal space. c. Modify movements and spatial arrangements upon request. 
a. Demonstrate a range of locomotor and nonlocomotor movements, body patterning, and dance sequences that require moving through space using a variety of different pathways. b. Move safely in a variety of spatial relationships and formations with other dancers, sharing and maintaining personal space. c. Repeat movements with an awareness of self and others in space. Selfadjust and modify movements or placement upon request. 
Strand 
A. DANCE 

Standard 
B2  Develop and refine artistic technique and work for presentation. 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Replicate body shapes, movement characteristics, and movement patterns in a dance sequence with awareness of body alignment and core support. b. Adjust body use to coordinate with a partner or other dancers to safely change levels, directions, and pathway designs. c. Recall movement sequences with a partner or in group dance activities. Apply the teacher's constructive feedback and selfcheck to improve dance skills. 
a. Demonstrate fundamental dance skills (i.e., alignment, coordination, balance, core support, kinesthetic awareness) and movement qualities when replicating patterns and sequences of locomotor and nonlocomotor movements. b. Execute techniques that extend movement range, build strength, and develop endurance. Explain the relationship between execution of technique, safe body use, and healthful nutrition. c. Coordinate phrases and timing with other dancers by cueing off each other and responding to stimuli cues (i.e., music, text, lighting). Reflect on feedback from others to inform personal dance performance goals. 
a. Recall and execute a series of dance phrases using fundamental dance skills (i.e., alignment, coordination, balance, core support, kinesthetic awareness, clarity of movement). b. Demonstrate safe body use practices during technical exercises and movement combinations. Discuss how these practices, along with healthful eating habits, promote strength, flexibility, endurance, and injury prevention. c. Collaborate with peer ensemble members to repeat sequences, synchronize actions, and refine spatial relationships to improve performance quality. Apply feedback from others to establish personal performance goals. 
Strand 
A. DANCE 
Standard 
B2  Develop and refine artistic technique and work for presentation. 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Incorporate technical dance skills (i.e., functional alignment, coordination, balance, core support, clarity of movement, weight shifts, flexibility/range of motion) to replicate, recall, and execute spatial designs and musical or rhythmic dance phrases. b. Evaluate personal healthful practices in dance activities and everyday life including nutrition and injury prevention. Discuss choices made, the effects experiences, and methods for improvement. c. Collaborate with peers to discover strategies for achieving performance accuracy, clarity, and expressiveness. Articulate personal performance goals and practice to reach those goals. Document personal improvement over time (e.g., journaling, portfolio, or timeline.) 
Strand 
A. DANCE 

Standard 
B2  Develop and refine artistic technique and work for presentation. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Accomplished 
Grades 9Diploma Advanced 

Performance Expectations 
a. Incorporate technical dance skills (i.e., functional alignment, coordination, balance, core support, clarity of movement, weight shifts, flexibility/range of motion) to retain and execute dance choreography. b. Develop a plan for healthful practices in dance activities and everyday life including nutrition and injury prevention. Discuss implementation of the plan and how it supports personal performance goals. c. Collaborate with peers to establish and implement a rehearsal plan to meet performance goals. Use a variety of strategies to analyze and evaluate performances of self and others. Articulate performance goals and justify reasons for selecting particular practice strategies. 
a. Dance with sensibility toward other dancers while executing complex spatial, rhythmic, and dynamic sequences to meet performance goals. b. Apply anatomical principles and healthful practices to a range of technical dance skills for achieving fluency of movement. Follow a personal nutrition plan that supports health for everyday life. c. Plan and execute collaborative and independent practice and rehearsal processes with attention to technique and artistry, informed by personal performance goals. Reflect on personal achievements. 
a. Apply bodymind principles to technical dance skills in complex choreography when performing solo, partnering, or dancing in ensemble works in a variety of dance genres and styles. Selfevaluate performances and discuss and analyze performance ability with others. b. Research healthful and safe practices for dancers and modify personal practice based on findings. Discuss how research informs practice. c. Initiate, plan, and direct rehearsals with attention to technical details and fulfilling artistic expression. Use a range of rehearsal strategies to achieve performance excellence. 
Strand 
A. DANCE 

Standard 
B3  Convey meaning through the presentation of artistic work. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Dance for and with others in a designated space. b. Select a prop to use as part of a dance. 
a. Dance for others in a space where the audience observes from a different space. b. Explore the use of simple props to enhance performance. 
a. Dance for and with others in a space where the audience observes from a different space. b. Use limited production elements (i.e., hand props, simple scenery, or media projections) to enhance performance. 
Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Identify the main areas of a performance space using production terminology (i.e., stage right, stage left, upstage, downstage, etc.) b. Explore simple production elements (i.e., costumes, scenery, props, etc.) in a dance performed for an audience in a designated specific performance space. 
a. Consider how to establish a formal performance space from an informal setting (i.e., gymnasium, outside courtyard, etc.) b. Identify, explore, and experiment with a variety of production elements to heighten the artistic intent and audience experience. 
a. Demonstrate the ability to adapt dance to alternative performance venues by modifying spacing and movements to the performance space. b. Identify, explore, and select production elements that heighten and intensify the artistic intent of a dance that are adaptable to various performance spaces. 
Strand 
A. DANCE 
Standard 
B3  Convey meaning through the presentation of artistic work. 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Recognize needs and adapt movements to a performance space. Use performance etiquette and practices during class, rehearsal, and performance. Accept postperformance notes from the choreographer and make corrections as needed to apply to future performances. b. Compare and contrast a variety of possible production elements that would intensify and heighten the artistic intent of the work. Select choices and explain reasons for those selections using production terminology. 
Strand 
A. DANCE 

Standard 
B3  Convey meaning through the presentation of artistic work. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Accomplished 
Grades 9Diploma Advanced 

Performance Expectations 
a. Demonstrate leadership qualities (i.e., commitment, dependability, responsibility, cooperation) when preparing performances. Demonstrate performance etiquette and practices during class, rehearsal, and performance. Accept postperformance notes from the choreographer and make corrections as needed for future performances. Document the rehearsal and performance process and evaluate methods and strategies using dance and production terminology. b. Evaluate possible designs for the production elements of a performance, selecting and executing the ideas that would intensify and heighten the artistic intent of the dances. 
a. Demonstrate leadership qualities when preparing performances. Model performance etiquette and practices during class, rehearsal, and performance. Implement performance strategies to enhance projection. Accept postperformance notes from the choreographer and apply corrections to future performances. Document the rehearsal and performance process and evaluate methods and strategies using dance and production terminology. b. Work collaboratively to produce a dance concert on a stage or alternative space, planning the production elements that would be necessary to fulfill the artistic intent of the dance works. 
a. Demonstrate leadership qualities when preparing performances. Model performance etiquette and practices during class, rehearsal, and performance. Enhance performances using a broad repertoire of strategies for dynamic projection. Develop a professional portfolio (e.g., resume and head shot photo) that documents the rehearsal and performance process with fluency in professional dance and production terminology. b. Work collaboratively to produce dance concerts in a variety of venues, designing and organizing the production elements necessary to fulfill the artistic intent of the dance works. 
Strand 
A. DANCE 

Standard 
C1  Perceive and analyze artistic work. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Find a movement that repeats in a dance. b. Demonstrate or describe observed or performed dance movements. 
a. Find a movement that repeats in a dance to make a pattern. b. Demonstrate and describe observed or performed dance movements from a specific genre or culture. 
a. Find movements in a dance that develop a pattern. b. Demonstrate and describe movements in dances from different genres or cultures. 
Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Find a movement pattern that creates a movement phrase in a dance work. b. Demonstrate and explain how one dance genre is different from another, or how one cultural movement practice is different from another. 
a. Find patterns of movement in dance works that create a style or theme. b. Demonstrate and explain how dance styles differ within a genre or within a cultural movement practice. 
a. Find meaning or artistic intent from the patterns of movement in a dance work. b. Using basic dance terminology, describe the qualities and characteristics of a style used in a dance from one's own cultural movement practice. Using basic dance terminology, compare them to the qualities and characteristics of style found in a different dance genre, style, or cultural movement practice. 
Strand 
A. DANCE 

Standard 
C1  Perceive and analyze artistic work. 

Early Adolescence 

Grades 68 

Performance Expectations 
a. Describe, demonstrate, and discuss patterns of movement and their relationships to dance in the context of artistic intent. b. Using genrespecific dance terminology, explain how the elements of dance are used in a variety of different genres, styles, or cultural movement practices to communicate intent. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Accomplished 
Grades 9Diploma Advanced 

Performance Expectations 
a. Analyze recurring patterns of movement and their relationships in dance in the context of artistic intent. b. Using genrespecific dance terminology, analyze the use of elements of dance in a variety of different genres, styles, and cultural movement practices within a cultural context to communicate intent. 
a. Analyze dance works and provide examples of recurring patterns of movement and their relationships that create structure and meaning in dance. b. Using genrespecific dance terminology, analyze and compare the movement patterns and their relationships in a variety of different genres, styles, or cultural movement practices and explain how their differences impact communication and intent within a cultural context. 
a. Analyze dance works from a variety of dance genres and styles and explain how recurring patterns of movement and their relationships create wellstructured and meaningful choreography. b. Using genrespecific dance terminology, explain how dance communicates aesthetic and cultural values in a variety of genres, styles, and/or cultural movement practices. 
Strand 
A. Dance 

Standard 
C2  Interpret intent and meaning in artistic work. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Using simple dance terminology, observe and describe movement. 
Using simple dance terminology, select movements from a dance that suggest ideas and explain how the movement captures the idea. 
Using simple dance terminology and context clues from movement, identify meaning and intent in a dance. 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Using basic dance terminology, select specific content clues from movement. Explain how they relate to the main idea of the dance. 
Using basic dance terminology, relate movements, ideas, and context to decipher meaning in a dance. 
Using basic dance terminology, interpret meaning in a dance based on its movements. Explain how the movements communicate the main idea of the dance. 

Early Adolescence 

Grades 68 

Performance Expectations 
Using genrespecific dance terminology, explain how the artistic expression of a dance is achieved through the elements of dance, use of body, dance technique, dance structure, and context. Explain how these communicate the intent of the dance. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Accomplished 
Grades 9Diploma Advanced 

Performance Expectations 
Using genrespecific dance terminology, select and compare different dances and discuss their intent and artistic expression. Explain how the relationships among the elements of dance, use of body, dance technique, and context enhance meaning and support intent. 
Using genrespecific dance terminology, analyze and discuss how the elements of dance, execution of dance movement principles, and context contribute to artistic expression. 
Using genrespecific dance terminology, analyze and interpret how the elements of dance, execution of dance movement principles, and context contribute to artistic expression across different genres, styles, or cultural movement practices. 
Strand 
A. DANCE 

Standard 
C3  Apply criteria to evaluate artistic work. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Find a movement that was noticed in a dance. Demonstrate that movement and explain why it attracted attention. 
Identify and demonstrate several movements in advance that attracted attention. Describe the characteristics that make the movements interesting and talk about why they were chosen. 
Observe or demonstrate dances from a genre or culture. Using simple dance terminology, discuss movements and other aspects of the dances that make the dances work well. 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Select dance movements from specific genres, styles, or cultures. Identify characteristic movements from these dances and, using basic dance terminology, describe the ways in which they are alike and different. 
Using basic dance terminology, discuss and demonstrate the characteristics that make a dance artistic and apply those characteristic movements to dances observed and performed in a specific genre, style, or cultural movement practice. 
Define the characteristics of dance that make a dance artistic and meaningful. Relate them to the elements of dance in genres, styles, or cultural movement practices. Using basic dance terminology, describe characteristics that make a dance artistic and meaningful. 

Early Adolescence 

Grades 68 

Performance Expectations 
Discuss the characteristics and artistic intent of a dance from a genre, style, or cultural movement practice and develop artistic criteria to critique the dance using genrespecific dance terminology. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Accomplished 
Grades 9Diploma Advanced 

Performance Expectations 
Analyze and discuss the artistic expression of a dance using dance terminology and evaluative criteria. 
Compare and contrast two or more dances using evaluative criteria and dance terminology to critique artistic expression, considering societal values and a range of perspectives. 
Define personal artistic preferences to critique dance. Consider societal and personal values, and a range of artistic expression. Discuss perspectives with peers and justify viewpoints. 
Strand 
A. Dance 

Standard 
D1  Synthesize and relate knowledge and personal experiences to make art. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. Recognize and name an emotion that is experienced when watching, improvising, or performing dance and relate it to a personal experience. b. Observe a work of visual art. Describe and then express through movement something of interest about the artwork and ask questions for discussion concerning the artwork. 
a. Find a familiar experience expressed or portrayed in a dance. Identify the movements that communicate this experience. b. Observe and discuss illustrations from a story, identifying and demonstrating ideas for dance movement. 
a. Describe, create, and/or perform a dance that expresses personal meaning and explain how certain movements express this personal meaning. b. Respond to a dance work using an inquirybased approach (i.e., think, wonder, etc.). Create movement using ideas from responses and explain how certain movements express a specific idea. 
Strand 
A. DANCE 

Standard 
D1  Synthesize and relate knowledge and personal experiences to make art. 

Childhood 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Compare the relationships expressed in a dance to relationships with others. Explain how they are similar and different. b. Ask and research a question about a key aspect of a dance that communicates a perspective about an issue or event. Explore the key aspect through movement. Share movements and describe how the movements help to remember or discover new qualities in these key aspects. Communicate the new learning in oral, written, or movement form. 
a. Relate the main idea or content in a dance to other experiences. Explain how the main idea of a dance is similar to or different from one's own experiences, relationships, ideas or perspectives. b. Develop and research a question relating to a topic of study in school using multiple sources of references. Select key aspects about the topic and choreograph movements that communicate the information. Discuss what was learned from creating the dance and describe how the topic might be communicated using another form of expression. 
a. Compare two dances with contrasting themes. Discuss feelings and ideas evoked by each. Describe how the themes and movements relate to points of view and experiences. b. Choose a topic, concept, or content from another discipline of study and research how other art forms have expressed the topic. Create a dance study that expresses the idea. Explain how the dance study expressed the idea and discuss how this learning process is similar to, or different from, other learning situations. 
Strand 
A. DANCE 
Standard 
D1  Synthesize and relate knowledge and personal experiences to make art. 
Early Adolescence 

Grades 68 

Performance Expectations 
a. Observe the movement characteristics or qualities observed in a specific dance genre. Describe differences and similarities about what was observed to one's attitudes and movement preferences. b. Conduct research using a variety of resources to find information about a social issue of great interest. Use the information to create a dance study that expresses a specific point of view on the topic. Discuss whether the experience of creating and sharing the dance reinforces personal views or offers new knowledge and perspectives. 
Strand 
A. DANCE 

Standard 
D1  Synthesize and relate knowledge and personal experiences to make art. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Accomplished 
Grades 9Diploma Advanced 

Performance Expectations 
a. Analyze a dance to determine the ideas expressed by the choreographer. Explain how the perspectives expressed by the choreographer may impact one's own interpretation. Provide evidence to support one's analysis. b. Collaboratively identify a dance related question or problem. Conduct research through interviews, research databases, text, media, or movement. Analyze and apply information gathered by creating a group dance that answers the question posed. Discuss how the dance communicates new perspectives or realizations. Compare orally and in writing the process used in choreography to that of other creative, academic, or scientific procedures. 
a. Analyze a dance that is related to content learned in other subjects and research its context. Synthesize information learned and share new ideas about its impact on one's perspective. b. Use established research methods and techniques to investigate a topic. Collaborate with others to identify questions and solve movement problems that pertain to the topic. Create and perform a piece of choreography. Discuss orally or in writing the insights relating to knowledge gained through the research process, the synergy of collaboration, and the transfer of learning from this project to other learning situations. 
a. Review original choreography developed over time with respect to its content and context and its relationship to personal perspectives. Reflect on and analyze the variables that contributed to changes in one's personal growth. b. Investigate various dance related careers through a variety of research methods and techniques. Select those careers of most interest. Develop and implement a Capstone Project that reflects a possible career choice. 
Strand 
A. DANCE 

Standard 
D2  Relate artistic ideas and works with societal, cultural, and historical contexts to deepen understanding. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Describe or demonstrate the movements in a dance that was watched or performed. 
Watch and/or perform a dance from a different culture and discuss or demonstrate the types of movement danced. 
Observe a dance and relate the movement to the people or environment in which the dance was created and performed. 
Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Find a relationship between movement in a dance from a culture, society, or community and the culture from which the dance is derived. Explain what the movements communicate about key aspects of the culture, society, or community. 
Select and describe movements in a specific genre or style and explain how the movements relate to the culture, society, historical period, or community from which the dance originated. 
Describe how the movement characteristics and qualities of a dance in a specific genre or style communicate the ideas and perspectives of the culture, historical period, or community from which the genre or style originated 
Early Adolescence 

Grades 68 

Performance Expectations 
Interpret and show how the movement and qualities of a dance communicate its cultural, historical, and/or community purpose or meaning. 
Strand 
A. DANCE 

Standard 
D2  Relate artistic ideas and works with societal, cultural, and historical contexts to deepen understanding. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Accomplished 
Grades 9Diploma Advanced 

Performance Expectations 
Analyze and discuss dances from selected genres or styles and/or historical time periods and formulate reasons for the similarities and differences between them in relation to the ideas and perspectives of the peoples from which the dances originate. 
Analyze dances from several genres or styles, historical time periods, and/or world dance forms. Discuss how dance movement characteristics, techniques, and artistic criteria relate to the ideas and perspectives of the peoples from which the dances originate. 
Analyze dances from several genres or styles, historical time periods, and/or world dance forms. Discuss how dance movement characteristics, techniques, and artistic criteria relate to the ideas and perspectives of the peoples from which the dances originate, and how the analysis has expanded one's dance literacy. 
The Music Standards
Music plays an important role in our society; it is in every part of our lives. The study of music aids in brain development, listening skills, social and emotional growth, language development, and brings joy throughout one's life. Music serves as a medium for crosscultural understanding and as a reflection of creator, performer, and consumer. Bennett Reimer, aesthetic music education philosopher, states, "Music and the other arts are basic ways that humans know themselves and their world; they are basic modes of cognition."[4] Therefore, it is important that our educational system provides opportunities for the study of music for all students. Jerome Bruner, a major advocate of the spiral curriculum, argues that any person can learn any topic, as long as the level of complexity is appropriate for the learner.[5]
The Maine Learning Results for Music are written with an inclusive lens, considering all types of notation, skills, ensembles, and knowledge acquisition. These standards are written so that they flow in a natural progression through the grade levels. However, there is also the understanding that students come to the music classroom with varied musical experiences and varying levels of exposure. Differentiation for students is assumed in the music classroom with the goal of each student reaching proficiency. The advanced level is written with the more experienced student in mind, or for districts with diplomas that have specialized certificates. It is also recognized that performance classes have a slightly different focus than nonperformance classes and that, although all standards should be explored in all music classes, the rigor of each standard could be different.
Strand 
B. MUSIC 

Standard 
A1  Listen to, apply criteria, and interpret the artist's intended meaning. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Listen and respond to diverse music experiences by singing, playing, moving, etc. 
With guidance, identify characteristics and themes within diverse music experiences. 
With guidance, discuss music characteristics 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Discuss, compare, and contrast diverse music experiences. 
a. Compare, contrast, and describe music ideas using appropriate terminology for music elements. b. Explore music elements that convey the song's purpose. 
a. Describe and interpret music ideas using appropriate terminology for music elements. b. Explore the personal, cultural, and historical background of an artist to gain perspective on their intent. 

Early Adolescence 

Grades 68 

Performance Expectations 
a. Explore music examples and analyze the music through the lens of the elements of music. b. Reflect on the personal, cultural, and historical contexts of a music example and/or composer/performer to enhance personal connection and understanding of the music. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Advanced 

Performance Expectations 
a. Analyze and evaluate music examples through the lens of the elements of music. b. Reflect on the artist's intent as well as the personal, historical, and cultural contexts of a music example to enhance personal connection and understanding of the music. 
a. Analyze and evaluate a body of musical work through the lens of the elements of music. b. Justify interpretations of the expressive intent and meaning of music works by comparing and synthesizing varied researched sources, including reference to other art forms. 
Strand 
B. MUSIC 

Standard 
A2  Interpret and express music through movement. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Explore expressive qualities of music through movement. 
Respond to expressive qualities of music through movement. 
Represent expressive qualities of music through movement. 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Compare and contrast the elements of music through movement. 
Demonstrate an understanding of the expressive qualities of music through movement. 
Demonstrate an understanding of the elements and expressive qualities of music through structured and improvised movement. 

Early Adolescence 

Grades 68 

Performance Expectations 
Demonstrate and apply the elements and expressive qualities of specific music examples through structured and/or improvised movement. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Advanced 

Performance Expectations 
With guidance, interpret specific music examples by planning and generating structured and/or improvised movements that express the elements, expressive qualities, and implied meaning of each example. 
Interpret specific music examples by planning and generating structured and/or improvised movements that express the elements, expressive qualities, and implied meaning of each example. 
Strand 
B. MUSIC 

Standard 
B1  Connect with a variety of musical experiences through relationships between music and personal understandings. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Explore music that represents a range of emotions. 
With guidance, identify emotions and personal connections that relate to a selected piece of music. 
With guidance, discuss emotions and personal connections that relate to a selected piece of music. 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Explore how personal interests and skills relate to choices when experiencing music. 
Explore how personal interests and skills relate to choices when creating, performing, and responding to music. 
Demonstrate and explore how personal interests and skills relate to choices when creating, performing, and responding to music. 

Early Adolescence 

Grades 68 

Performance Expectations 
Identify various uses of music in daily life, describe the characteristics that make music suitable for a specific use, and demonstrate individual preference for music in those contexts. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Advanced 

Performance Expectations 
Explore and evaluate personal benefits of listening to, performing, and creating music, and the role that music plays in developing empathy. 
Discuss and debate the nature of music appreciation and justify music's value to individuals in a society. 
Strand 
B. MUSIC 

Standard 
B2  Connect with a variety of musical experiences through the relations between music, the other arts, and other disciplines. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Explore how music is used for a variety of purposes and occasions. 
Explore how music relates to other disciplines when experiencing music. 
With guidance, identify relationships between music and another art or discipline outside the arts. 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
With guidance, discuss relationships between music and another art or discipline outside the arts. 
Identify relationships between music and another art or discipline outside the arts. 
Demonstrate and explore how music relates to other disciplines when creating, performing, and responding to music. 

Early Adolescence 

Grades 68 

Performance Expectations 
a. Demonstrate and explore skills and concepts that are similar across disciplines. b. Describe and explore how the study of music integrates with other disciplines and professions. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Advanced 

Performance Expectations 
a. Analyze skills and concepts that are similar across disciplines. b. Analyze the impact of music on other disciplines and professions. 
a. Justify the use of music in specific artistic works that combine the other arts. b. Evaluate the impact of music on other disciplines and professions. 
Strand 
B. MUSIC 

Standard 
B3  Connect with a variety of musical experiences through the relationships between music and history and culture. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Explore music from a variety of societal, cultural, and historical contexts and respond through singing, listening, or moving. 
With guidance, experience repertoire from a variety of societal, cultural, and historical contexts by singing, moving, and playing in a manner appropriate to the context of the music. 
With guidance, discuss characteristics of music from a variety of societal, cultural, and historical contexts. 
Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Explore and discuss characteristics of music from a variety of societal, cultural, and historical contexts. 
Explore characteristics of music from a variety of societal, cultural, and historical contexts when creating, performing, and responding to music. 
Demonstrate and explore characteristics of music from a variety of societal, cultural, and historical contexts when creating, performing, and responding to music. 
Strand 
B. MUSIC 

Standard 
B3  Connect with a variety of musical experiences through the relationships between music and history and culture. 

Early Adolescence 

Grades 68 

Performance Expectations 
a. Identify and describe the distinguishing characteristics of musical works from a variety of genres, styles, historical periods, and cultures. b. Compare and contrast, in various cultures and historical periods, the functions of music, the roles of musicians, and the conditions under which participation in music typically occurs. c. Explore unfamiliar musical works by genre, style, historical period, and/or culture and defend the classification. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Advanced 

Performance Expectations 
a. Identify and describe the stylistic features of known musical works that serve to define their aesthetic tradition and historical or cultural context. b. Identify and explore music and musicians that influenced societal change and/or politics and describe how they reflected culture at a particular time in history. c. With guidance, classify unfamiliar musical works by genre, style, historical period, and/or culture and defend the classification. 
a. Analyze and articulate the stylistic features of known musical works that serve to define their aesthetic tradition and historical or cultural context. b. Analyze music and musicians that influenced societal change and/or politics and describe how they reflected culture at a particular time in history. c. Classify unfamiliar musical works by genre, style, historical period, and/or culture and defend the classification. 
Strand 
B. MUSIC 

Standard 
C1  Perform a rich and diverse repertoire of music. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. With guidance, explore vocal range, pitch flexibility, and types of voices (i.e., whisper, speak, sing, call/shout, thinking/audiate.) b. With guidance, explore a variety of classroom instruments. c. With guidance, perform simple songs and echo phrases. 
a. With guidance, sing in head voice and demonstrate types of voices. b. With guidance, perform on a variety of classroom instruments with proper posture and basic techniques. c. With guidance, perform a variety of melodies and callandresponse songs. 
a. Sing in head voice with proper posture. b. Perform on a variety of classroom instruments with appropriate hand placement. c. Explore and perform basic forms in music (i.e., binary, ternary, rondo, etc.) 
Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. Sing in head voice with increasing pitch accuracy using proper posture. b. Perform songs on a variety of classroom instruments with appropriate technique, and in various tonalities and meters. c. Explore and perform music in basic forms with increasing technical accuracy at a consistent tempo. 
a. Sing in head voice with increasing pitch accuracy using proper posture and breath support. b. Perform songs on a variety of classroom instruments with appropriate technique in various tonalities and meters, and with appropriate dynamics. c. Explore and perform music in basic forms with increasing accuracy, proper technique, and at a consistent tempo. 
a. Sing in head voice with increasing pitch accuracy, with proper posture, breath support, and appropriate tone. b. Perform songs on a variety of classroom instruments with appropriate technique, in various tonalities and meters, with appropriate dynamics and articulations. c. Perform a rich and diverse repertoire with increasing technical accuracy and proper technique at a consistent tempo. 
Strand 
B. MUSIC 

Standard 
C1  Perform a rich and diverse repertoire of music. 

Early Adolescence 

Grades 68 

Performance Expectations 
a. Explore the function of the voice/instrument to support healthy singing/playing habits. b. Accurately and expressively sing and/or play a rich and diverse repertoire of music using appropriate skills throughout a limited range. c. Perform a rich and diverse repertoire of music that includes changes in tempo, key, and meter. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Advanced 

Performance Expectations 
a. Practice healthy playing/singing habits. b. Accurately and expressively sing and/or play a rich and diverse repertoire of music using appropriate skills throughout an expanded range. c. Perform a rich and diverse repertoire that requires attention to phrasing and interpretation, and the ability to perform various meters and rhythms in a variety of keys. 
a. Model healthy playing/singing habits and explore the longterm impacts of playing/singing. b. Accurately and expressively sing and/or play a rich and diverse repertoire of music using appropriate skills throughout an advanced range. c. Perform a rich and diverse repertoire that includes a wide range, difficult technical passages, nuanced interpretation, and greater part independence. 
Strand 
B. MUSIC 

Standard 
C2  Apply criteria and feedback to rehearse and recreate musical experiences. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Share short songs as a group with others, in formal and/or informal settings. 
Share short songs as a group with others, in formal and/or informal settings. With guidance, apply teacherprovided feedback. 
Share sort songs as a group with others, in formal and/or informal settings. As a group, reflect on performances and apply feedback. 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Demonstrate short songs alone or with others, in formal and/or informal settings. With guidance, reflect on performances and apply feedback. 
Recreate music experiences alone or with others, in formal and/or informal settings. With guidance, reflect on performances and apply feedback. 
Recreate music experiences alone or with others, in formal and/or informal settings. Reflect on and refine performances by applying feedback. 

Early Adolescence 

Grades 68 

Performance Expectations 
Analyze, evaluate, and refine music experiences using criteria and feedback from the teacher. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Advanced 

Performance Expectations 
Analyze, evaluate, and refine music experiences using criteria and feedback from the teacher and others. 
Analyze, evaluate, and refine personal elements of music experiences independent of guidance from the composer, conductor, or fellow musicians. 
Strand 
B. MUSIC 

Standard 
D1  Audiate and communicate musical ideas. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
With substantial guidance, explore the concept of audiation. 
As a group, audiate and perform the motions of a poem and/or song. 
With guidance, independently audiate and perform the motions of a poem and/or song. 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Demonstrate the ability to audiate with increasing accuracy by recreating familiar musical ideas alone. 
Demonstrate the ability to audiate by accurately recreating familiar musical ideas alone. 
Demonstrate the ability to audiate by accurately recreating familiar and unfamiliar musical ideas alone. 

Early Adolescence 

Grades 68 

Performance Expectations 
Demonstrate the ability to audiate by accurately recreating familiar and unfamiliar musical excerpts or pieces. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Advanced 

Performance Expectations 
Demonstrate the ability to audiate the elements of music in a given excerpt or piece and perform it. 
Demonstrate the ability to audiate the elements of music in a given excerpt or piece and perform it in a musical or culturally authentic way. 
Strand 
B. MUSIC 

Standard 
D2  Read and communicate musical ideas using terms and symbols. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
a. With guidance, explore vocal flexibility and songs within an appropriate vocal range. b. With guidance, use movement to explore pulse in duple and triple meter. c. With guidance, explore music opposites (e.g., loud/soft, high/low, fast/slow, etc.) 
a. With guidance, show melodic contour and echo a variety of tonal patterns and/or fragments vocally. b. With guidance, maintain a steady pulse in duple and triple meter. c. With guidance, identify music opposites using applicable descriptors. 
a. With guidance, recognize familiar tonal patterns and songs performed instrumentally and/or on a neutral syllable. b. With guidance, recognize rhythms of familiar songs and poems, performed instrumentally and/or on a neutral syllable. c. With guidance, discuss expressive qualities of music using applicable descriptors. 
Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
a. With guidance, echo and decode, with increasing accuracy, a variety of tonal and rhythmic patterns and songs performed instrumentally and/or vocally. b. Discuss and describe expressive qualities of music using applicable descriptors. 
a. Echo and decode, with accuracy, a variety of tonal and rhythmic patterns and songs performed instrumentally and/or vocally. With guidance, read a variety of tonal and rhythmic patterns patterns. b. Identify (visually and aurally) and describe common expressive musical symbols and elements. 
a. Echo, decode, and read, with accuracy, a variety of tonal and rhythmic patterns and songs performed instrumentally and/or vocally. b. Identify (visually and aurally), describe, and demonstrate musical terms and elements. 
Strand 
B. MUSIC 

Standard 
D2  Read and communicate musical ideas using terms and symbols. 

Early Adolescence 

Grades 68 

Performance Expectations 
a. Read the terms and symbols for a piece of music to inform a performance or critique. b. Apply musical terms and symbols to express musical ideas to other musicians. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Advanced 

Performance Expectations 
a. Read and interpret the terms and symbols for a piece of music to inform a performance or critique. b. Analyze musical terms and symbols to express musical ideas to other musicians. 
a. Fluently read and interpret familiar and unfamiliar musical terms and symbols while performing. b. Evaluate the ability of musical terms and symbols to express subtle musical ideas to other musicians. 
Strand 
B. MUSIC 

Standard 
E1  Generate and conceptualize musical ideas. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
With guidance, explore vocal and instrumental sounds. 
With guidance, improvise/create short answers, rhythmic patterns, beat motions, and/or word substitutions. 
With guidance, vocally and instrumentally improvise/create short melodies and rhythms. 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Improvise/create melodic and rhythmic phrases to express a musical idea. 
Improvise/create, both vocally and instrumentally, melodic and rhythmic phrases to express a musical idea with increasing complexity. 
Improvise/create, both vocally and instrumentally, melodic and rhythmic phrases to express a musical idea which conveys a specific purpose. 

Early Adolescence 

Grades 68 

Performance Expectations 
Generate a wide variety of musical ideas using a set of criteria. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Advanced 

Performance Expectations 
Generate a wide variety of musical ideas with heightened expressive qualities by incorporating your personal feelings, opinions, and experiences. 
Generate a wide variety of musical ideas considering historical and cultural contexts. 
Strand 
B. MUSIC 

Standard 
E2  Organize and develop musical ideas to achieve a creative goal. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Explore visual and kinesthetic representations of sound. 
With guidance, choose visual and kinesthetic representations of sound. 
With guidance, plan and arrange visual and kinesthetic representations of sound. 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
With guidance, plan and create rhythmic and melodic patterns through multiple pathways. 
Plan, create, and notate rhythmic and melodic patterns through multiple pathways. 
Plan, create, notate, and refine rhythmic and melodic patterns to convey musical ideas. 

Early Adolescence 

Grades 68 

Performance Expectations 
Use a goaloriented process to select, develop ideas, and combine elements of music to improvise, compose, or arrange music. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Advanced 

Performance Expectations 
Plan, select, and combine musical ideas to achieve a musical goal. 
Plan, select, and combine music from multiple genres to achieve a musical goal. 
Strand 
B. MUSIC 

Standard 
E3  Refine and complete music work. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
With guidance, explore ways to change a familiar song or poem. 
With guidance, apply collaborative alterations to a familiar song or poem. 
With guidance, apply individually selected alterations to a familiar song or poem. 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
With guidance, identify ways to use feedback toward musical ideas. 
With guidance, use feedback to refine musical ideas. 
Use feedback to refine musical ideas. 

Early Adolescence 

Grades 68 

Performance Expectations 
Refine musical works using given criteria. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Advanced 

Performance Expectations 
Refine musical works using feedback and considering audience and venue to better achieve a musical goal. 
Refine musical works seeking feedback from other artists in the music community. 
Strand 
B. MUSIC 

Standard 
F1  Identify positive inter and intrapersonal skills that impact the quality of a musician's art and participation in the arts. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
Demonstrate taking turns and active listening skills. 
Explore cooperative skills (individual and group responsibilities) in order to perform as a group. 
With guidance, demonstrate active participation and communication skills in group music making (e.g., basic problem solving, compromise, inclusion, personal responsibility, etc.) 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
Demonstrate active participation and communication skills in group music making (e.g., basic problem solving, compromise, inclusion, personal responsibility, etc.) 
Identify skills and habits that support group musicmaking goals. 
Identify and demonstrate skills and habits that positively affect group musicmaking goals. 

Early Adolescence 

Grades 68 

Performance Expectations 
Demonstrate positive interpersonal skills and analyze how interpersonal skills affect participation in the arts. 

Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Advanced 

Performance Expectations 
Demonstrate positive interpersonal skills and reflect on the impact of interpersonal skills on personal success in the arts. 
Demonstrate positive leadership skills and reflect on the impact of leadership skills on personal success in the arts. 
Strand 
B. MUSIC 

Standard 
F2  Make technical and expressive adjustments to meet the goals of the performing group. 

Childhood 

Kindergarten 
Grade 1 
Grade 2 

Performance Expectations 
With guidance, perform songs and poems as a group and respond to teacher cues (i.e., my turnyour turn, startstop, etc.) 
With guidance, perform words, motions, and/or instruments of songs and poems in time with the group. 
With guidance, apply simple visual cues from a conductor to a performance. 

Grade 3 
Grade 4 
Grade 5 

Performance Expectations 
With guidance apply simple visual and auditory cues from others. 
With guidance, use visual and auditory cues from others to adjust a performance. 
Use visual and auditory cues from others to adjust a performance. 

Early Adolescence 

Grades 68 

Performance Expectations 
Employ strategies to address expressive challenges in a varied repertoire of music, and evaluate success using feedback from ensemble peers and other sources to refine performances. 

Early Adolescence 

Grades 9Diploma Proficient 
Grades 9Diploma Advanced 

Performance Expectations 
Select strategies to address expressive challenges in a varied repertoire of music, and evaluate success using feedback from ensemble peers and other sources to refine performances. 
Develop strategies to address expressive challenges in a varied repertoire of music, and evaluate success using feedback from ensemble peers and other sources to refine performances. 
The Media Arts Standards
The media arts standards are designed to enable students to achieve media arts literacy. Media arts standards assume the diverse forms and categories of media arts as a distinct, standalone arts discipline, whose basic categories include the following areas: photography, imaging, sound, animation, video, web design, graphic design, interactive design, combinations utilizing mixed traditional art forms and emerging forms, multimedia, augmented reality and virtual design. The standards for media arts do not address the use of specific media, rather they provide benchmarks that art educators can adapt to specific media. Technology is embedded, integrated, or used as a tool in the media arts, but the emphasis is on process, so that the standards will remain relevant even as technology evolves.
Literacy in media arts is broad, diverse, and addresses creative, conceptual, and technical competencies that exist globally. Media arts are the emerging basis for communications, design, and social interaction in our increasingly digitally centered world, and Maine's strong tradition of art creation that supports a creative economy. Therefore, students should gain experience in production and design that has realworld relevance and applications that can include the following