Texas Administrative Code
Title 19 - EDUCATION
Part 2 - TEXAS EDUCATION AGENCY
Chapter 111 - TEXAS ESSENTIAL KNOWLEDGE AND SKILLS FOR MATHEMATICS
Subchapter A - ELEMENTARY
Section 111.7 - Grade 5, Adopted 2012
Universal Citation: 19 TX Admin Code ยง 111.7
Current through Reg. 49, No. 38; September 20, 2024
(a) Introduction.
(1) The desire to achieve educational
excellence is the driving force behind the Texas essential knowledge and skills
for mathematics, guided by the college and career readiness standards. By
embedding statistics, probability, and finance, while focusing on computational
thinking, mathematical fluency, and solid understanding, Texas will lead the
way in mathematics education and prepare all Texas students for the challenges
they will face in the 21st century.
(2) The process standards describe ways in
which students are expected to engage in the content. The placement of the
process standards at the beginning of the knowledge and skills listed for each
grade and course is intentional. The process standards weave the other
knowledge and skills together so that students may be successful problem
solvers and use mathematics efficiently and effectively in daily life. The
process standards are integrated at every grade level and course. When
possible, students will apply mathematics to problems arising in everyday life,
society, and the workplace. Students will use a problem-solving model that
incorporates analyzing given information, formulating a plan or strategy,
determining a solution, justifying the solution, and evaluating the
problem-solving process and the reasonableness of the solution. Students will
select appropriate tools such as real objects, manipulatives, algorithms, paper
and pencil, and technology and techniques such as mental math, estimation,
number sense, and generalization and abstraction to solve problems. Students
will effectively communicate mathematical ideas, reasoning, and their
implications using multiple representations such as symbols, diagrams, graphs,
computer programs, and language. Students will use mathematical relationships
to generate solutions and make connections and predictions. Students will
analyze mathematical relationships to connect and communicate mathematical
ideas. Students will display, explain, or justify mathematical ideas and
arguments using precise mathematical language in written or oral
communication.
(3) For students to
become fluent in mathematics, students must develop a robust sense of number.
The National Research Council's report, "Adding It Up," defines procedural
fluency as "skill in carrying out procedures flexibly, accurately, efficiently,
and appropriately." As students develop procedural fluency, they must also
realize that true problem solving may take time, effort, and perseverance.
Students in Grade 5 are expected to perform their work without the use of
calculators.
(4) The primary focal
areas in Grade 5 are solving problems involving all four operations with
positive rational numbers, determining and generating formulas and solutions to
expressions, and extending measurement to area and volume. These focal areas
are supported throughout the mathematical strands of number and operations,
algebraic reasoning, geometry and measurement, and data analysis. In Grades
3-5, the number set is limited to positive rational numbers. In number and
operations, students will apply place value and identify part-to-whole
relationships and equivalence. In algebraic reasoning, students will represent
and solve problems with expressions and equations, build foundations of
functions through patterning, identify prime and composite numbers, and use the
order of operations. In geometry and measurement, students will classify
two-dimensional figures, connect geometric attributes to the measures of
three-dimensional figures, use units of measure, and represent location using a
coordinate plane. In data analysis, students will represent and interpret
data.
(5) Statements that contain
the word "including" reference content that must be mastered, while those
containing the phrase "such as" are intended as possible illustrative
examples.
(b) Knowledge and skills.
(1) Mathematical process
standards. The student uses mathematical processes to acquire and demonstrate
mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in
everyday life, society, and the workplace;
(B) use a problem-solving model that
incorporates analyzing given information, formulating a plan or strategy,
determining a solution, justifying the solution, and evaluating the
problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects,
manipulatives, paper and pencil, and technology as appropriate, and techniques,
including mental math, estimation, and number sense as appropriate, to solve
problems;
(D) communicate
mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as
appropriate;
(E) create and use
representations to organize, record, and communicate mathematical
ideas;
(F) analyze mathematical
relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify
mathematical ideas and arguments using precise mathematical language in written
or oral communication.
(2) Number and operations. The student
applies mathematical process standards to represent, compare, and order
positive rational numbers and understand relationships as related to place
value. The student is expected to:
(A)
represent the value of the digit in decimals through the thousandths using
expanded notation and numerals;
(B)
compare and order two decimals to thousandths and represent comparisons using
the symbols >, <, or =; and
(C) round decimals to tenths or
hundredths.
(3) Number
and operations. The student applies mathematical process standards to develop
and use strategies and methods for positive rational number computations in
order to solve problems with efficiency and accuracy. The student is expected
to:
(A) estimate to determine solutions to
mathematical and real-world problems involving addition, subtraction,
multiplication, or division;
(B)
multiply with fluency a three-digit number by a two-digit number using the
standard algorithm;
(C) solve with
proficiency for quotients of up to a four-digit dividend by a two-digit divisor
using strategies and the standard algorithm;
(D) represent multiplication of decimals with
products to the hundredths using objects and pictorial models, including area
models;
(E) solve for products of
decimals to the hundredths, including situations involving money, using
strategies based on place-value understandings, properties of operations, and
the relationship to the multiplication of whole numbers;
(F) represent quotients of decimals to the
hundredths, up to four-digit dividends and two-digit whole number divisors,
using objects and pictorial models, including area models;
(G) solve for quotients of decimals to the
hundredths, up to four-digit dividends and two-digit whole number divisors,
using strategies and algorithms, including the standard algorithm;
(H) represent and solve addition and
subtraction of fractions with unequal denominators referring to the same whole
using objects and pictorial models and properties of operations;
(I) represent and solve multiplication of a
whole number and a fraction that refers to the same whole using objects and
pictorial models, including area models;
(J) represent division of a unit fraction by
a whole number and the division of a whole number by a unit fraction such as
1/3 ÷ 7 and 7 ÷ 1/3 using objects and pictorial models, including
area models;
(K) add and subtract
positive rational numbers fluently; and
(L) divide whole numbers by unit fractions
and unit fractions by whole numbers.
(4) Algebraic reasoning. The student applies
mathematical process standards to develop concepts of expressions and
equations. The student is expected to:
(A)
identify prime and composite numbers;
(B) represent and solve multi-step problems
involving the four operations with whole numbers using equations with a letter
standing for the unknown quantity;
(C) generate a numerical pattern when given a
rule in the form y = ax or y = x + a and
graph;
(D) recognize the difference
between additive and multiplicative numerical patterns given in a table or
graph;
(E) describe the meaning of
parentheses and brackets in a numeric expression;
(F) simplify numerical expressions that do
not involve exponents, including up to two levels of grouping;
(G) use concrete objects and pictorial models
to develop the formulas for the volume of a rectangular prism, including the
special form for a cube (V = l x w x
h,V = s x s x
s, and V = Bh); and
(H) represent and solve problems related to
perimeter and/or area and related to volume.
(5) Geometry and measurement. The student
applies mathematical process standards to classify two-dimensional figures by
attributes and properties. The student is expected to classify two-dimensional
figures in a hierarchy of sets and subsets using graphic organizers based on
their attributes and properties.
(6) Geometry and measurement. The student
applies mathematical process standards to understand, recognize, and quantify
volume. The student is expected to:
(A)
recognize a cube with side length of one unit as a unit cube having one cubic
unit of volume and the volume of a three-dimensional figure as the number of
unit cubes (n cubic units) needed to fill it with no gaps or
overlaps if possible; and
(B)
determine the volume of a rectangular prism with whole number side lengths in
problems related to the number of layers times the number of unit cubes in the
area of the base.
(7)
Geometry and measurement. The student applies mathematical process standards to
select appropriate units, strategies, and tools to solve problems involving
measurement. The student is expected to solve problems by calculating
conversions within a measurement system, customary or metric.
(8) Geometry and measurement. The student
applies mathematical process standards to identify locations on a coordinate
plane. The student is expected to:
(A)
describe the key attributes of the coordinate plane, including perpendicular
number lines (axes) where the intersection (origin) of the two lines coincides
with zero on each number line and the given point (0, 0); the
x- coordinate, the first number in an ordered pair, indicates
movement parallel to the x- axis starting at the origin; and
the y- coordinate, the second number, indicates movement
parallel to the y- axis starting at the origin;
(B) describe the process for graphing ordered
pairs of numbers in the first quadrant of the coordinate plane; and
(C) graph in the first quadrant of the
coordinate plane ordered pairs of numbers arising from mathematical and
real-world problems, including those generated by number patterns or found in
an input-output table.
(9) Data analysis. The student applies
mathematical process standards to solve problems by collecting, organizing,
displaying, and interpreting data. The student is expected to:
(A) represent categorical data with bar
graphs or frequency tables and numerical data, including data sets of
measurements in fractions or decimals, with dot plots or stem-and-leaf
plots;
(B) represent discrete
paired data on a scatterplot; and
(C) solve one- and two-step problems using
data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or
scatterplot.
(10)
Personal financial literacy. The student applies mathematical process standards
to manage one's financial resources effectively for lifetime financial
security. The student is expected to:
(A)
define income tax, payroll tax, sales tax, and property tax;
(B) explain the difference between gross
income and net income;
(C) identify
the advantages and disadvantages of different methods of payment, including
check, credit card, debit card, and electronic payments;
(D) develop a system for keeping and using
financial records;
(E) describe
actions that might be taken to balance a budget when expenses exceed income;
and
(F) balance a simple
budget.
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