Texas Administrative Code
Title 19 - EDUCATION
Part 2 - TEXAS EDUCATION AGENCY
Chapter 111 - TEXAS ESSENTIAL KNOWLEDGE AND SKILLS FOR MATHEMATICS
Subchapter A - ELEMENTARY
Section 111.6 - Grade 4, Adopted 2012
Universal Citation: 19 TX Admin Code ยง 111.6
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 4 are expected to perform their work without the use of
calculators.
(4) The primary focal
areas in Grade 4 are use of operations, fractions, and decimals and describing
and analyzing geometry and measurement. 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 represent points on a number line that
correspond to a given fraction or terminating decimal. In algebraic reasoning,
students will represent and solve multi-step problems involving the four
operations with whole numbers with expressions and equations and generate and
analyze patterns. In geometry and measurement, students will classify
two-dimensional figures, measure angles, and convert units of measure. 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 whole
numbers and decimals and understand relationships related to place value. The
student is expected to:
(A) interpret the
value of each place-value position as 10 times the position to the right and as
one-tenth of the value of the place to its left;
(B) represent the value of the digit in whole
numbers through 1,000,000,000 and decimals to the hundredths using expanded
notation and numerals;
(C) compare
and order whole numbers to 1,000,000,000 and represent comparisons using the
symbols >, <, or =;
(D) round
whole numbers to a given place value through the hundred thousands
place;
(E) represent decimals,
including tenths and hundredths, using concrete and visual models and
money;
(F) compare and order
decimals using concrete and visual models to the hundredths;
(G) relate decimals to fractions that name
tenths and hundredths; and
(H)
determine the corresponding decimal to the tenths or hundredths place of a
specified point on a number line.
(3) Number and operations. The student
applies mathematical process standards to represent and generate fractions to
solve problems. The student is expected to:
(A) represent a fraction a/b
as a sum of fractions 1/b, where a and
b are whole numbers and b > 0, including
when a > b;
(B)
decompose a fraction in more than one way into a sum of fractions with the same
denominator using concrete and pictorial models and recording results with
symbolic representations;
(C)
determine if two given fractions are equivalent using a variety of
methods;
(D) compare two fractions
with different numerators and different denominators and represent the
comparison using the symbols >, =, or <;
(E) represent and solve addition and
subtraction of fractions with equal denominators using objects and pictorial
models that build to the number line and properties of operations;
(F) evaluate the reasonableness of sums and
differences of fractions using benchmark fractions 0, 1/4, 1/2, 3/4, and 1,
referring to the same whole; and
(G) represent fractions and decimals to the
tenths or hundredths as distances from zero on a number line.
(4) Number and operations. The
student applies mathematical process standards to develop and use strategies
and methods for whole number computations and decimal sums and differences in
order to solve problems with efficiency and accuracy. The student is expected
to:
(A) add and subtract whole numbers and
decimals to the hundredths place using the standard algorithm;
(B) determine products of a number and 10 or
100 using properties of operations and place value understandings;
(C) represent the product of 2 two-digit
numbers using arrays, area models, or equations, including perfect squares
through 15 by 15;
(D) use
strategies and algorithms, including the standard algorithm, to multiply up to
a four-digit number by a one-digit number and to multiply a two-digit number by
a two-digit number. Strategies may include mental math, partial products, and
the commutative, associative, and distributive properties;
(E) represent the quotient of up to a
four-digit whole number divided by a one-digit whole number using arrays, area
models, or equations;
(F) use
strategies and algorithms, including the standard algorithm, to divide up to a
four-digit dividend by a one-digit divisor;
(G) round to the nearest 10, 100, or 1,000 or
use compatible numbers to estimate solutions involving whole numbers;
and
(H) solve with fluency one- and
two-step problems involving multiplication and division, including interpreting
remainders.
(5)
Algebraic reasoning. The student applies mathematical process standards to
develop concepts of expressions and equations. The student is expected to:
(A) represent multi-step problems involving
the four operations with whole numbers using strip diagrams and equations with
a letter standing for the unknown quantity;
(B) represent problems using an input-output
table and numerical expressions to generate a number pattern that follows a
given rule representing the relationship of the values in the resulting
sequence and their position in the sequence;
(C) use models to determine the formulas for
the perimeter of a rectangle (l + w + l + w or
2l + 2w), including the special form for
perimeter of a square (4s) and the area of a rectangle
(l x w); and
(D) solve problems related to perimeter and
area of rectangles where dimensions are whole numbers.
(6) Geometry and measurement. The student
applies mathematical process standards to analyze geometric attributes in order
to develop generalizations about their properties. The student is expected to:
(A) identify points, lines, line segments,
rays, angles, and perpendicular and parallel lines;
(B) identify and draw one or more lines of
symmetry, if they exist, for a two-dimensional figure;
(C) apply knowledge of right angles to
identify acute, right, and obtuse triangles; and
(D) classify two-dimensional figures based on
the presence or absence of parallel or perpendicular lines or the presence or
absence of angles of a specified size.
(7) Geometry and measurement. The student
applies mathematical process standards to solve problems involving angles less
than or equal to 180 degrees. The student is expected to:
(A) illustrate the measure of an angle as the
part of a circle whose center is at the vertex of the angle that is "cut out"
by the rays of the angle. Angle measures are limited to whole
numbers;
(B) illustrate degrees as
the units used to measure an angle, where 1/360 of any circle is one degree and
an angle that "cuts" n /360 out of any circle whose center is
at the angle's vertex has a measure of n degrees. Angle
measures are limited to whole numbers;
(C) determine the approximate measures of
angles in degrees to the nearest whole number using a protractor;
(D) draw an angle with a given measure;
and
(E) determine the measure of an
unknown angle formed by two non-overlapping adjacent angles given one or both
angle measures.
(8)
Geometry and measurement. The student applies mathematical process standards to
select appropriate customary and metric units, strategies, and tools to solve
problems involving measurement. The student is expected to:
(A) identify relative sizes of measurement
units within the customary and metric systems;
(B) convert measurements within the same
measurement system, customary or metric, from a smaller unit into a larger unit
or a larger unit into a smaller unit when given other equivalent measures
represented in a table; and
(C)
solve problems that deal with measurements of length, intervals of time, liquid
volumes, mass, and money using addition, subtraction, multiplication, or
division as appropriate.
(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 data on a frequency table, dot
plot, or stem-and-leaf plot marked with whole numbers and fractions;
and
(B) solve one- and two-step
problems using data in whole number, decimal, and fraction form in a frequency
table, dot plot, or stem-and-leaf plot.
(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) distinguish between fixed and variable
expenses;
(B) calculate profit in a
given situation;
(C) compare the
advantages and disadvantages of various savings options;
(D) describe how to allocate a weekly
allowance among spending; saving, including for college; and sharing;
and
(E) describe the basic purpose
of financial institutions, including keeping money safe, borrowing money, and
lending.
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