Vertical Alignment

The Vertical Viewer is designed to demonstrate the vertical alignment of the state standards (TEKS) throughout the grade levels and provide further clarity of the depth and complexity of the standards. The TEKS Resource System Vertical Viewer tool utilizes the vertical alignment provided by the Texas Education Agency (TEA).

To access PDF versions of the TEA Vertical Alignment charts for Mathematics, click here.

Select the grade levels you wish to view (up to five at a time) by checking or unchecking the desired boxes below. To find a specific word or phrase, use your browser's search function by pressing CRTL + F at the same time.

TEKS Mathematical Vertical Alignment

Kindergarten
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
Algebra I
Grade 2 Grade 3 Grade 4
Introduction
Introduction
Introduction

§111.1. Implementation of Texas Essential Knowledge and Skills for Mathematics, Elementary, Adopted 2012.

Source: The provisions of this §111.1 adopted to be effective September 10, 2012, 37 TexReg 7109.

§111.4. Grade 2, Adopted 2012.

§111.1. Implementation of Texas Essential Knowledge and Skills for Mathematics, Elementary, Adopted 2012.

Source: The provisions of this §111.1 adopted to be effective September 10, 2012, 37 TexReg 7109.

§111.5. Grade 3, Adopted 2012.

§111.1. Implementation of Texas Essential Knowledge and Skills for Mathematics, Elementary, Adopted 2012.

Source: The provisions of this §111.1 adopted to be effective September 10, 2012, 37 TexReg 7109.

§111.6. Grade 4, Adopted 2012.

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.
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.
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.
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.
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.
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.
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 2 are expected to perform their work without the use of calculators.
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 3 are expected to perform their work without the use of calculators.
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.
The primary focal areas in Grade 2 are making comparisons within the base-10 place value system, solving problems with addition and subtraction within 1,000, and building foundations for multiplication.
The primary focal areas in Grade 3 are place value, operations of whole numbers, and understanding fractional units. 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 focus on applying place value, comparing and ordering whole numbers, connecting multiplication and division, and understanding and representing fractions as numbers and equivalent fractions. In algebraic reasoning, students will use multiple representations of problem situations, determine missing values in number sentences, and represent real-world relationships using number pairs in a table and verbal descriptions. In geometry and measurement, students will identify and classify two-dimensional figures according to common attributes, decompose composite figures formed by rectangles to determine area, determine the perimeter of polygons, solve problems involving time, and measure liquid volume (capacity) or weight. In data analysis, students will represent and interpret data.
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.
Students develop an understanding of the base-10 place value system and place value concepts. The students' understanding of base-10 place value includes ideas of counting in units and multiples of thousands, hundreds, tens, and ones and a grasp of number relationships, which students demonstrate in a variety of ways.
Students identify situations in which addition and subtraction are useful to solve problems. Students develop a variety of strategies to use efficient, accurate, and generalizable methods to add and subtract multi-digit whole numbers.
Students use the relationship between skip counting and equal groups of objects to represent the addition or subtraction of equivalent sets, which builds a strong foundation for multiplication and division.
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.
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.
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.
2.1
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
3.1
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
4.1
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
2.1A
Apply mathematics to problems arising in everyday life, society, and the workplace.
3.1A
Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard
4.1A
Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard
2.1B
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.
3.1B
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.
Process Standard
4.1B
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.
Process Standard
2.1C
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.
3.1C
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.
Process Standard
4.1C
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.
Process Standard
2.1D
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
3.1D
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Process Standard
4.1D
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Process Standard
2.1E
Create and use representations to organize, record, and communicate mathematical ideas.
3.1E
Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard
4.1E
Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard
2.1F
Analyze mathematical relationships to connect and communicate mathematical ideas.
3.1F
Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard
4.1F
Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard
2.1G
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
3.1G
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard
4.1G
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard
Counting and Recognizing Whole Numbers
2.2
Number and operations. The student applies mathematical process standards to understand how to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system related to place value. The student is expected to:
2.2C
Generate a number that is greater than or less than a given whole number up to 1,200.
Comparing and Ordering Numbers
Comparing and Ordering Numbers
Comparing and Ordering Numbers
2.2
Number and operations. The student applies mathematical process standards to understand how to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system related to place value. The student is expected to:
3.2
Number and operations. The student applies mathematical process standards to represent and compare whole numbers and understand relationships related to place value. The student is expected to:
4.2
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:
2.2D
Use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =).
3.2D
Compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =.
Readiness Standard
4.2C
Compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or =.
Supporting Standard
4.2F
Compare and order decimals using concrete and visual models to the hundredths.
Supporting Standard
Representing and Relating Numbers Using Number Lines
Representing and Relating Numbers Using Number Lines
Representing and Relating Numbers Using Number Lines
2.2
Number and operations. The student applies mathematical process standards to understand how to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system related to place value. The student is expected to:
3.2
Number and operations. The student applies mathematical process standards to represent and compare whole numbers and understand relationships related to place value. The student is expected to:
4.2
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:
2.2E
Locate the position of a given whole number on an open number line.
3.2C
Represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers.
Supporting Standard
4.2H
Determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line.
Supporting Standard
3.3
Number and operations. The student applies mathematical process standards to represent and explain fractional units. The student is expected to:
4.2G
Relate decimals to fractions that name tenths and hundredths.
Readiness Standard
3.3A
Represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines.
Supporting Standard
4.2E
Represent decimals, including tenths and hundredths, using concrete and visual models and money.
Supporting Standard
2.2F
Name the whole number that corresponds to a specific point on a number line.
3.3B
Determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line.
Supporting Standard
Composing and Decomposing Numbers: Place Value
Composing and Decomposing Numbers: Place Value
Composing and Decomposing Numbers: Place Value
2.2
Number and operations. The student applies mathematical process standards to understand how to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system related to place value. The student is expected to:
3.2
Number and operations. The student applies mathematical process standards to represent and compare whole numbers and understand relationships related to place value. The student is expected to:
4.2
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:
2.2A
Use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones.
3.2A
Compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate.
Readiness Standard
2.2B
Use standard, word, and expanded forms to represent numbers up to 1,200.
4.2B
Represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals.
Readiness Standard
3.2B
Describe the mathematical relationships found in the base-10 place value system through the hundred thousands place.
Supporting Standard
4.2A
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.
Supporting Standard
4.2E
Represent decimals, including tenths and hundredths, using concrete and visual models and money.
Supporting Standard
Representing Fraction Concepts
Representing Fraction Concepts
Representing Fraction Concepts
2.3
Number and operations. The student applies mathematical process standards to recognize and represent fractional units and communicates how they are used to name parts of a whole. The student is expected to:
3.3
Number and operations. The student applies mathematical process standards to represent and explain fractional units. The student is expected to:
4.3
Number and operations. The student applies mathematical process standards to represent and generate fractions to solve problems. The student is expected to:
2.3A
Partition objects into equal parts and name the parts, including halves, fourths, and eighths, using words.
3.3A
Represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines.
Supporting Standard
2.3D
Identify examples and non-examples of halves, fourths, and eighths.
2.3C
Use concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole.
3.3E
Solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8.
Supporting Standard
2.3B
Explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part.
3.3C
Explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number.
Supporting Standard
3.3D
Compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b.
Supporting Standard
4.3A
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.
Supporting Standard
4.3B
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.
Supporting Standard
4.3G
Represent fractions and decimals to the tenths or hundredths as distances from zero on a number line.
Supporting Standard
Determining Equivalence and Comparing Part-to-Whole Relationships
Determining Equivalence and Comparing Part-to-Whole Relationships
3.3
Number and operations. The student applies mathematical process standards to represent and explain fractional units. The student is expected to:
4.3
Number and operations. The student applies mathematical process standards to represent and generate fractions to solve problems. The student is expected to:
3.3F
Represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines.
Readiness Standard
3.3G
Explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model.
Supporting Standard
4.3C
Determine if two given fractions are equivalent using a variety of methods.
Supporting Standard
3.3H
Compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models.
Readiness Standard
4.3D
Compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <.
Readiness Standard
4.2
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:
4.2G
Relate decimals to fractions that name tenths and hundredths.
Readiness Standard
Adding and Subtracting Whole Numbers, Decimals, and Rational Numbers
Adding and Subtracting Whole Numbers, Decimals, and Rational Numbers
Adding and Subtracting Whole Numbers, Decimals, and Rational Numbers
2.4
Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve addition and subtraction problems with efficiency and accuracy. The student is expected to:
3.4
Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy. The student is expected to:
4.4
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: