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



Kindergarten  Grade 1  Grade 2  Grade 3  Grade 4  Grade 5  Grade 6  Grade 7  Grade 8  Algebra I 
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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. §111.2. Kindergarten, 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. §111.3. Grade 1, 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. §111.4. 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. 
§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. §111.7. Grade 5, Adopted 2012. 
§111.25. Implementation of Texas Essential Knowledge and Skills for Mathematics, Middle School, Adopted 2012. Source: The provisions of this §111.25 adopted to be effective September 10, 2012, 37 TexReg 7109. §111.26. Grade 6, Adopted 2012. 
§111.25. Implementation of Texas Essential Knowledge and Skills for Mathematics, Middle School, Adopted 2012. Source: The provisions of this §111.25 adopted to be effective September 10, 2012, 37 TexReg 7109. §111.27. Grade 7, Adopted 2012. 
§111.25. Implementation of Texas Essential Knowledge and Skills for Mathematics, Middle School, Adopted 2012. Source: The provisions of this §111.25 adopted to be effective September 10, 2012, 37 TexReg 7109. §111.28. Grade 8, Adopted 2012. 
§111.38. Implementation of Texas Essential Knowledge and Skills for Mathematics, High School, Adopted 2012. Source: The provisions of this §111.38 adopted to be effective September 10, 2012, 37 TexReg 7109. §111.39. Algebra I, Adopted 2012 (One Credit). 
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 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 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 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 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 problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving 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 problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving 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 problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving 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 problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving 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 problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving 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 problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving 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 problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving 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 problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving 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 problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving 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 problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental math, estimation, and number sense to solve problems. Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, 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 Kindergarten 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 1 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 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.

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.

The primary focal areas in Grade 6 are number and operations; proportionality; expressions, equations, and relationships; and measurement and data. Students use concepts, algorithms, and properties of rational numbers to explore mathematical relationships and to describe increasingly complex situations. Students use concepts of proportionality to explore, develop, and communicate mathematical relationships. Students use algebraic thinking to describe how a change in one quantity in a relationship results in a change in the other. Students connect verbal, numeric, graphic, and symbolic representations of relationships, including equations and inequalities. Students use geometric properties and relationships, as well as spatial reasoning, to model and analyze situations and solve problems. Students communicate information about geometric figures or situations by quantifying attributes, generalize procedures from measurement experiences, and use the procedures to solve problems. Students use appropriate statistics, representations of data, and reasoning to draw conclusions, evaluate arguments, and make recommendations. While the use of all types of technology is important, the emphasis on algebra readiness skills necessitates the implementation of graphing technology.

The primary focal areas in Grade 7 are number and operations; proportionality; expressions, equations, and relationships; and measurement and data. Students use concepts, algorithms, and properties of rational numbers to explore mathematical relationships and to describe increasingly complex situations. Students use concepts of proportionality to explore, develop, and communicate mathematical relationships, including number, geometry and measurement, and statistics and probability. Students use algebraic thinking to describe how a change in one quantity in a relationship results in a change in the other. Students connect verbal, numeric, graphic, and symbolic representations of relationships, including equations and inequalities. Students use geometric properties and relationships, as well as spatial reasoning, to model and analyze situations and solve problems. Students communicate information about geometric figures or situations by quantifying attributes, generalize procedures from measurement experiences, and use the procedures to solve problems. Students use appropriate statistics, representations of data, and reasoning to draw conclusions, evaluate arguments, and make recommendations. While the use of all types of technology is important, the emphasis on algebra readiness skills necessitates the implementation of graphing technology.

The primary focal areas in Grade 8 are proportionality; expressions, equations, relationships, and foundations of functions; and measurement and data. Students use concepts, algorithms, and properties of real numbers to explore mathematical relationships and to describe increasingly complex situations. Students use concepts of proportionality to explore, develop, and communicate mathematical relationships. Students use algebraic thinking to describe how a change in one quantity in a relationship results in a change in the other. Students connect verbal, numeric, graphic, and symbolic representations of relationships, including equations and inequalities. Students begin to develop an understanding of functional relationships. Students use geometric properties and relationships, as well as spatial reasoning, to model and analyze situations and solve problems. Students communicate information about geometric figures or situations by quantifying attributes, generalize procedures from measurement experiences, and use the procedures to solve problems. Students use appropriate statistics, representations of data, and reasoning to draw conclusions, evaluate arguments, and make recommendations. While the use of all types of technology is important, the emphasis on algebra readiness skills necessitates the implementation of graphing technology.

In Algebra I, students will build on the knowledge and skills for mathematics in Grades 68, which provide a foundation in linear relationships, number and operations, and proportionality. Students will study linear, quadratic, and exponential functions and their related transformations, equations, and associated solutions. Students will connect functions and their associated solutions in both mathematical and realworld situations. Students will use technology to collect and explore data and analyze statistical relationships. In addition, students will study polynomials of degree one and two, radical expressions, sequences, and laws of exponents. Students will generate and solve linear systems with two equations and two variables and will create new functions through transformations.

The primary focal areas in Kindergarten are understanding counting and cardinality, understanding addition as joining and subtraction as separating, and comparing objects by measurable attributes.

The primary focal areas in Grade 1 are understanding and applying place value, solving problems involving addition and subtraction, and composing and decomposing twodimensional shapes and threedimensional solids.

The primary focal areas in Grade 2 are making comparisons within the base10 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 35, 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 realworld relationships using number pairs in a table and verbal descriptions. In geometry and measurement, students will identify and classify twodimensional 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 35, 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 multistep problems involving the four operations with whole numbers with expressions and equations and generate and analyze patterns. In geometry and measurement, students will classify twodimensional figures, measure angles, and convert units of measure. In data analysis, students will represent and interpret data.

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 35, the number set is limited to positive rational numbers. In number and operations, students will apply place value and identify parttowhole 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 twodimensional figures, connect geometric attributes to the measures of threedimensional figures, use units of measure, and represent location using a coordinate plane. In data analysis, students will represent and interpret data.

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.

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.

Students develop number and operations through several fundamental concepts. Students know number names and the counting sequence. Counting and cardinality lay a solid foundation for number. Students apply the principles of counting to make the connection between numbers and quantities.

Students use relationships within the numeration system to understand the sequential order of the counting numbers and their relative magnitude.

Students develop an understanding of the base10 place value system and place value concepts. The students' understanding of base10 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 use meanings of numbers to create strategies for solving problems and responding to practical situations involving addition and subtraction.

Students extend their use of addition and subtraction beyond the actions of joining and separating to include comparing and combining. Students use properties of operations and the relationship between addition and subtraction to solve problems. By comparing a variety of solution strategies, students use efficient, accurate, and generalizable methods to perform operations.

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 multidigit whole numbers.








Â Students identify characteristics of objects that can be measured and directly compare objects according to these measurable attributes.

Students use basic shapes and spatial reasoning to model objects in their environment and construct more complex shapes. Students are able to identify, name, and describe basic twodimensional shapes and threedimensional solids.

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.

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.





K.1
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

1.1
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

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:

5.1
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

6.1
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

7.1
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

8.1
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

A.1
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

K.1A
Apply mathematics to problems arising in everyday life, society, and the workplace.

1.1A
Apply mathematics to problems arising in everyday life, society, and the workplace.

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 
5.1A
Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard 
6.1A
Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard 
7.1A
Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard 
8.1A
Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard 
A.1A
Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard 
K.1B
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.

1.1B
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.

2.1B
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.

3.1B
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
Process Standard 
4.1B
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
Process Standard 
5.1B
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
Process Standard 
6.1B
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
Process Standard 
7.1B
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
Process Standard 
8.1B
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
Process Standard 
A.1B
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
Process Standard 
K.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.

1.1C
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.

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 
5.1C
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 
6.1C
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 
7.1C
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 
8.1C
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 
A.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 
K.1D
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

1.1D
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

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 
5.1D
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Process Standard 
6.1D
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Process Standard 
7.1D
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Process Standard 
8.1D
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Process Standard 
A.1D
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Process Standard 
K.1E
Create and use representations to organize, record, and communicate mathematical ideas.

1.1E
Create and use representations to organize, record, and communicate mathematical ideas.

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 
5.1E
Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard 
6.1E
Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard 
7.1E
Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard 
8.1E
Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard 
A.1E
Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard 
K.1F
Analyze mathematical relationships to connect and communicate mathematical ideas.

1.1F
Analyze mathematical relationships to connect and communicate mathematical ideas.

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 
5.1F
Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard 
6.1F
Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard 
7.1F
Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard 
8.1F
Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard 
A.1F
Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard 
K.1G
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

1.1G
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

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 
5.1G
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard 
6.1G
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard 
7.1G
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard 
8.1G
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard 
A.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

Counting and Recognizing Whole Numbers

Counting and Recognizing Whole Numbers








K.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. The student is expected to:

1.2
Number and operations. The student applies mathematical process standards 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:

2.2
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:








K.2A
Count forward and backward to at least 20 with and without objects.










K.2B
Read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures.










K.2C
Count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order.










K.2D
Recognize instantly the quantity of a small group of objects in organized and random arrangements.

1.2A
Recognize instantly the quantity of structured arrangements.









K.2E
Generate a set using concrete and pictorial models that represents a number that is more than, less than, and equal to a given number up to 20.










K.2F
Generate a number that is one more than or one less than another number up to at least 20.

1.2D
Generate a number that is greater than or less than a given whole number up to 120.

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

Comparing and Ordering Numbers

Comparing and Ordering Numbers

Comparing and Ordering Numbers

Comparing and Ordering Numbers


Comparing and Ordering Numbers


K.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. The student is expected to:

1.2
Number and operations. The student applies mathematical process standards 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:

2.2
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:

5.2
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:

6.2
Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to:


8.2
Number and operations. The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to:


K.2G
Compare sets of objects up to at least 20 in each set using comparative language.

1.2E
Use place value to compare whole numbers up to 120 using comparative language.

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 
5.2B
Compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =.
Readiness Standard 
6.2D
Order a set of rational numbers arising from mathematical and realworld contexts.
Readiness Standard 

8.2D
Order a set of real numbers arising from mathematical and realworld contexts.
Readiness Standard 

K.2H
Use comparative language to describe two numbers up to 20 presented as written numerals.





1.2F
Order whole numbers up to 120 using place value and open number lines.





1.2G
Represent the comparison of two numbers to 100 using the symbols >, <, or =.








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

Representing and Relating Numbers Using Number Lines


Representing and Relating Numbers Using Number Lines


Representing and Relating Numbers Using Number Lines



1.2
Number and operations. The student applies mathematical process standards 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:

2.2
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:


6.2
Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to:


8.2
Number and operations. The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to:



1.2F
Order whole numbers up to 120 using place value and open number lines.

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 

6.2B
Identify a number, its opposite, and its absolute value.
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 

6.2C
Locate, compare, and order integers and rational numbers using a number line.
Supporting Standard 

8.2B
Approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line.
Supporting Standard 








Representing and Classifying Numbers

Representing and Classifying Numbers

Representing and Classifying Numbers








6.2
Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to:

7.2
Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to:

8.2
Number and operations. The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to:








6.2A
Classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers.
Supporting Standard 
7.2A
Extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers.
Supporting Standard 
8.2A
Extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers.
Supporting Standard 

Composing and Decomposing Numbers: Place Value

Composing and Decomposing Numbers: Place Value

Composing and Decomposing Numbers: Place Value

Composing and Decomposing Numbers: Place Value

Composing and Decomposing Numbers: Place Value

Composing and Decomposing Numbers: Place Value



Composing and Decomposing Numbers: Place Value


K.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. The student is expected to:

1.2
Number and operations. The student applies mathematical process standards 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:

2.2
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:

5.2
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:



8.2
Number and operations. The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to:


K.2I
Compose and decompose numbers up to 10 with objects and pictures.

1.2B
Use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones.

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 




8.2C
Convert between standard decimal notation and scientific notation.
Supporting Standard 


1.2C
Use objects, pictures, and expanded and standard forms to represent numbers up to 120.

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 
5.2A
Represent the value of the digit in decimals through the thousandths using expanded notation and numerals.
Supporting Standard 







3.2B
Describe the mathematical relationships found in the base10 place value system through the hundred thousands place.
Supporting Standard 
4.2A
Interpret the value of each placevalue position as 10 times the position to the right and as onetenth 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


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:


6.2
Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. 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 nonexamples 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 nonzero 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 

6.2E
Extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0.
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 ParttoWhole Relationships

Determining Equivalence and Comparing ParttoWhole Relationships


Determining Equivalence and Comparing ParttoWhole 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:


6.5
Proportionality. The student applies mathematical process standards to solve problems involving proportional relationships. 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 

6.5C
Use equivalent fractions, decimals, and percents to show equal parts of the same whole.
Supporting 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

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


Adding and Subtracting Whole Numbers, Decimals, and Rational Numbers



K.3
Number and operations. The student applies mathematical process standards to develop an understanding of addition and subtraction situations in order to solve problems. The student is expected to:

1.3
Number and operations. The student applies mathematical process standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems. The student is expected to:

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:

5.3
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:
