Texas Essential Knowledge and Skills (TEKS): Grade 4
Skills available for Texas fourth-grade math standards
Strand
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1
Mathematical process standards
1 The student uses mathematical processes to acquire and demonstrate mathematical understanding.
A apply mathematics to problems arising in everyday life, society, and the workplace;
Addition and subtraction
Multiplication and division
Money
Measurement
Time
Perimeter and area
Angles
Data and graphs
A apply mathematics to problems arising in everyday life, society, and the workplace;
Addition and subtraction
Multiplication and division
Money
Measurement
Time
Perimeter and area
Angles
Data and graphs
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;
Place value
Addition and subtraction
Multiplication
Division
Identify reasonable answers
Money
Time
Perimeter and area
Data and graphs
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;
Place value
Addition and subtraction
Multiplication
Division
Identify reasonable answers
Money
Time
Perimeter and area
Data and graphs
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;
Add and subtract whole numbers
Multiply whole numbers
Divide whole numbers
Estimation
Compare and order fractions
Add and subtract fractions
Decimals
Angles
Data and graphs
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;
Add and subtract whole numbers
Multiply whole numbers
Divide whole numbers
Estimation
Compare and order fractions
Add and subtract fractions
Decimals
Angles
Data and graphs
D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
Multi-step problems
Patterns and tables
Fractions
Perimeter and area
Lines and angles
Two-dimensional figures
D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
Multi-step problems
Patterns and tables
Fractions
Perimeter and area
Lines and angles
Two-dimensional figures
E create and use representations to organize, record, and communicate mathematical ideas;
Multiplication
Division
Multi-step problems
Expressions and equations
Patterns and tables
Fractions
Decimals
Data and graphs
E create and use representations to organize, record, and communicate mathematical ideas;
Multiplication
Division
Multi-step problems
Expressions and equations
Patterns and tables
Fractions
Decimals
Data and graphs
F analyze mathematical relationships to connect and communicate mathematical ideas; and
Place value
Multiplication and division
Patterns and tables
Fractions and decimals
Measurement
Perimeter and area
Angles
Two-dimensional shapes
F analyze mathematical relationships to connect and communicate mathematical ideas; and
Place value
Multiplication and division
Patterns and tables
Fractions and decimals
Measurement
Perimeter and area
Angles
Two-dimensional shapes
G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Multi-step problems
Fractions
Patterns and tables
Two-dimensional shapes
G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Multi-step problems
Fractions
Patterns and tables
Two-dimensional shapes
2-4
Number and operations
2 The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value.
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;
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;
Whole numbers
Decimals
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;
Whole numbers
Decimals
C compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or =;
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;
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;
Read and write decimals
Visual models
Money
E represent decimals, including tenths and hundredths, using concrete and visual models and money;
Read and write decimals
Visual models
Money
F compare and order decimals using concrete and visual models to the hundredths;
Compare decimals
Order decimals
F compare and order decimals using concrete and visual models to the hundredths;
Compare decimals
Order decimals
G relate decimals to fractions that name tenths and hundredths; and
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.
H determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line.
3 The student applies mathematical process standards to represent and generate fractions to solve problems.
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;
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;
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;
Model equivalent fractions
Equivalent fractions
C determine if two given fractions are equivalent using a variety of methods;
Model equivalent fractions
Equivalent fractions
D compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <;
Comparison strategies
Compare fractions
Order fractions
D compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <;
Comparison strategies
Compare fractions
Order fractions
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;
Addition
Subtraction
Mixed operations
Real-world problems
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;
Addition
Subtraction
Mixed operations
Real-world problems
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
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.
G represent fractions and decimals to the tenths or hundredths as distances from zero on a number line.
4 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.
A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm;
Add whole numbers
Subtract whole numbers
Add and subtract decimals
A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm;
Add whole numbers
Subtract whole numbers
Add and subtract decimals
B determine products of a number and 10 or 100 using properties of operations and place value understandings;
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;
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;
Multiplication facts
Multiply 1-digit numbers using models
Multiply 1-digit numbers
Multiply 2-digit numbers using models
Multiply 2-digit numbers
Multiplication strategies
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;
Multiplication facts
Multiply 1-digit numbers using models
Multiply 1-digit numbers
Multiply 2-digit numbers using models
Multiply 2-digit numbers
Multiplication strategies
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;
Divide 2-digit numbers
Divide larger numbers
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;
Divide 2-digit numbers
Divide larger numbers
F use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor;
Division facts
Divide 2-digit numbers
Divide larger numbers
Division strategies
F use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor;
Division facts
Divide 2-digit numbers
Divide larger numbers
Division strategies
G round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers; and
Estimate sums
Estimate differences
Estimate products
Estimate quotients
Mixed operations
G round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers; and
Estimate sums
Estimate differences
Estimate products
Estimate quotients
Mixed operations
H solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders.
Multiplication facts
Multiplication word problems
Division facts
Division word problems
Interpret remainders
Multi-step problems
H solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders.
Multiplication facts
Multiplication word problems
Division facts
Division word problems
Interpret remainders
Multi-step problems
5
Algebraic reasoning
5 The student applies mathematical process standards to develop concepts of expressions and equations.
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;
Write variable expressions
Write variable equations
Use strip diagrams
Solve word problems
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;
Write variable expressions
Write variable equations
Use strip diagrams
Solve word problems
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;
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
Perimeter
Area
Area and perimeter
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
Perimeter
Area
Area and perimeter
D solve problems related to perimeter and area of rectangles where dimensions are whole numbers.
Perimeter
Area
Area and perimeter
D solve problems related to perimeter and area of rectangles where dimensions are whole numbers.
Perimeter
Area
Area and perimeter
6-8
Geometry and measurement
6 The student applies mathematical process standards to analyze geometric attributes in order to develop generalizations about their properties.
A identify points, lines, line segments, rays, angles, and perpendicular and parallel lines;
Parallel, perpendicular, and intersecting lines
Points, lines, and angles
Angles
A identify points, lines, line segments, rays, angles, and perpendicular and parallel lines;
Parallel, perpendicular, and intersecting lines
Points, lines, and angles
Angles
B identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure;
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
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.
Triangles
Quadrilaterals
Polygons
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.
Triangles
Quadrilaterals
Polygons
7 The student applies mathematical process standards to solve problems involving angles less than or equal to 180 degrees.
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;
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;
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;
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
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.
E determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures.
8 The student applies mathematical process standards to select appropriate customary and metric units, strategies, and tools to solve problems involving measurement.
A identify relative sizes of measurement units within the customary and metric systems;
Customary units
Metric units
A identify relative sizes of measurement units within the customary and metric systems;
Customary units
Metric units
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
Customary units
Metric units
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
Customary units
Metric units
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.
Measurement
Time
Money
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.
Measurement
Time
Money
9
Data analysis
9 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
Frequency tables
Line plots
Stem-and-leaf plots
A represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions; and
Frequency tables
Line plots
Stem-and-leaf plots
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.
Frequency tables
Line plots
Stem-and-leaf plots
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.
Frequency tables
Line plots
Stem-and-leaf plots
10
Personal financial literacy
10 The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security.
A distinguish between fixed and variable expenses;
A distinguish between fixed and variable expenses;
B calculate profit in a given situation;
B calculate profit in a given situation;
C compare the advantages and disadvantages of various savings options;
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
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.
E describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending.