MAT-03.AR Domain 

(AR) Number and Operations  Learners will develop a foundational understanding of the number system, operations, and computational fluency to create connections and solve problems within and across concepts.

Sub-Categories

• (OA) Operations and Algebraic Thinking
  Learners will analyze patterns and relationships to generate and interpret numerical expressions.
• (RP) Ratios and Proportional Relationships
  Learners will use ratios, rates, and proportions to model relationships and solve problems.
• (EE) Expressions and Equations
  Learners will look for, generate, and make sense of patterns, relationships, and algebraic symbols to represent mathematical models while adapting approaches in novel situations.
• (F) Functions
  Learners will develop a foundational knowledge of functions and use them to model relationships between quantities.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

3rd Grade (MAT) Targeted Standard     (AR) Algebraic Reasoning  (OA) Operations and Algebraic Thinking Learners will analyze patterns and relationships to generate and interpret numerical expressions.

Proficiency Scale

Progressions

Operations – Basic Facts

• MAT-00.AR.OA.01 Automatically add and subtract within 5.
• MAT-01.AR.OA.01 Automatically add and subtract within 10.
• MAT-02.AR.OA.01 Automatically add and subtract within 20.
• MAT-03.AR.OA.01 Using mental strategies, multiply and divide basic facts within 100. Automatically multiply and divide up to 5 x 5 and 10s facts.
• MAT-04.AR.OA.01 Automatically multiply and divide through 10 x 10.
• MAT-05.AR.OA.01 Automatically multiply and divide through 12 x 12.

3rd Grade (MAT) Targeted Standard     (AR) Algebraic Reasoning  (OA) Operations and Algebraic Thinking Learners will analyze patterns and relationships to generate and interpret numerical expressions.

Proficiency Scale

Progressions

Properties of Operations

• MAT-02.AR.OA.02 Apply the properties of operations to solve addition and subtraction equations and justify thinking.
• MAT-03.AR.OA.02 Apply the properties of operations to solve multiplication and division equations and justify thinking.
• MAT-04.AR.OA.02 Identify and apply the properties of operations for addition, subtraction, multiplication, and division and justify thinking.
• MAT-05.AR.OA.02 Analyze problems using the order of operations to solve and evaluate expressions while justifying thinking.
• MAT-06.AR.EE.03 Identify when two expressions are equivalent. Apply the properties of operations to generate equivalent expressions.
• MAT-07.AR.EE.01 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions involving variables, integers, and/or non-negative fractions and decimals with an emphasis on writing equivalent expressions.
• MAT-08.AR.EE.05 Solve linear equations with rational number coefficients and variables on both sides, including equations that require using the distributive property and/or combining and collecting like terms. Interpret the number of solutions. Give examples of linear equations in one variable with one solution, infinitely showing solutions or no solutions.
• MAT-09.AR.05 Justify each step in solving a linear equation that may or may not have a solution.

Equations/Expressions

• MAT-01.AR.OA.06 Use the +, -, and = symbols accurately in an equation.
• MAT-02.AR.OA.02 Apply the properties of operations to solve addition and subtraction equations and justify thinking.
• MAT-03.AR.OA.02 Apply the properties of operations to solve multiplication and division equations and justify thinking.
• MAT-03.AR.OA.03 Solve word two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.
• MAT-03.AR.OA.04 Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.
• MAT-03.AR.OA.05 Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.
• MAT-04.AR.OA.03 Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders.
• MAT-04.AR.OA.05 Interpret multiplication equations as a comparison. Represent multiplicative comparisons as multiplication equations.
• MAT-05.AR.OA.02 Analyze problems using the order of operations to solve and evaluate expressions while justifying thinking.
• MAT-05.AR.OA.03 Write simple expressions that record calculations with numbers. Interpret numerical expressions without evaluating them.
• MAT-06.AR.EE.01 Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.
• MAT-06.AR.EE.02 Read and evaluate algebraic expressions, including expressions with whole number exponents and grouping symbols. Write algebraic expressions to represent simple and authentic situations.
• MAT-06.AR.EE.04 Describe the concept of a solution of an equation or an inequality. Determine whether a given number is a solution to an equation or an inequality.
• MAT-06.AR.EE.05 Write and solve equations of the form of x + p = q and px = q for cases in which p and q are non-negative whole numbers or decimals, including authentic problems.
• MAT-07.AR.EE.02 Write and solve equations of the form px + q = r and p(x + q) = r , including in authentic problems.
• MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.
• MAT-08.AR.EE.02 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a non-negative rational number.
• MAT-08.AR.EE.06 Read, write, and evaluate numerical and algebraic expressions, including expressions involving absolute value. Solve and graph equations of the form |x| = r where r is a nonnegative rational number.
• MAT-09.AR.01 Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.
• MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
• MAT-12.AR.03 Interpret expressions that represent a quantity in context.
• MAT-12.AR.02 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.

3rd Grade (MAT) Targeted Standard     (AR) Algebraic Reasoning  (OA) Operations and Algebraic Thinking Learners will analyze patterns and relationships to generate and interpret numerical expressions.

Proficiency Scale

Progressions

Solve Problems Using Operations

• MAT-00.AR.OA.04 Solve authentic word problems with addition by putting together or adding to within 10.
• MAT-01.AR.OA.06 Use the +, -, and = symbols accurately in an equation.
• MAT-01.AR.OA.04 Solve authentic word problems with addition, including three numbers and unknowns, within 20.
• MAT-02.AR.OA.03 Solve one- and two-step authentic word problems with addition within 100, including the use of unknowns.
• MAT-00.AR.OA.05 Solve authentic word problems with subtraction by taking apart or taking from within 10.
• MAT-01.AR.OA.05 Solve authentic word problems with subtraction, including unknowns, within 20.
• MAT-02.AR.OA.04 Solve one- and two-step authentic word problems with subtraction within 100, including the use of unknowns.
• MAT-02.AR.OA.05 Use repeated addition to find the total number of objects arranged in a rectangular array.
• MAT-03.AR.OA.03 Solve two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.
• MAT-03.AR.OA.04 Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.
• MAT-03.AR.OA.05 Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.
• MAT-04.AR.OA.03 Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders. Represent problems using equations, including a symbol as an unknown.

Equations/Expressions

• MAT-01.AR.OA.06 Use the +, -, and = symbols accurately in an equation.
• MAT-02.AR.OA.02 Apply the properties of operations to solve addition and subtraction equations and justify thinking.
• MAT-03.AR.OA.02 Apply the properties of operations to solve multiplication and division equations and justify thinking.
• MAT-03.AR.OA.03 Solve word two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.
• MAT-03.AR.OA.04 Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.
• MAT-03.AR.OA.05 Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.
• MAT-04.AR.OA.03 Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders.
• MAT-04.AR.OA.05 Interpret multiplication equations as a comparison. Represent multiplicative comparisons as multiplication equations.
• MAT-05.AR.OA.02 Analyze problems using the order of operations to solve and evaluate expressions while justifying thinking.
• MAT-05.AR.OA.03 Write simple expressions that record calculations with numbers. Interpret numerical expressions without evaluating them.
• MAT-06.AR.EE.01 Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.
• MAT-06.AR.EE.02 Read and evaluate algebraic expressions, including expressions with whole number exponents and grouping symbols. Write algebraic expressions to represent simple and authentic situations.
• MAT-06.AR.EE.04 Describe the concept of a solution of an equation or an inequality. Determine whether a given number is a solution to an equation or an inequality.
• MAT-06.AR.EE.05 Write and solve equations of the form of x + p = q and px = q for cases in which p and q are non-negative whole numbers or decimals, including authentic problems.
• MAT-07.AR.EE.02 Write and solve equations of the form px + q = r and p(x + q) = r , including in authentic problems.
• MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.
• MAT-08.AR.EE.02 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a non-negative rational number.
• MAT-08.AR.EE.06 Read, write, and evaluate numerical and algebraic expressions, including expressions involving absolute value. Solve and graph equations of the form |x| = r where r is a nonnegative rational number.
• MAT-09.AR.01 Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.
• MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
• MAT-12.AR.03 Interpret expressions that represent a quantity in context.
• MAT-12.AR.02 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.

3rd Grade (MAT) Targeted Standard     (AR) Algebraic Reasoning  (OA) Operations and Algebraic Thinking Learners will analyze patterns and relationships to generate and interpret numerical expressions.

Proficiency Scale

Progressions

Solve Problems Using Operations

• MAT-00.AR.OA.04 Solve authentic word problems with addition by putting together or adding to within 10.
• MAT-01.AR.OA.06 Use the +, -, and = symbols accurately in an equation.
• MAT-01.AR.OA.04 Solve authentic word problems with addition, including three numbers and unknowns, within 20.
• MAT-02.AR.OA.03 Solve one- and two-step authentic word problems with addition within 100, including the use of unknowns.
• MAT-00.AR.OA.05 Solve authentic word problems with subtraction by taking apart or taking from within 10.
• MAT-01.AR.OA.05 Solve authentic word problems with subtraction, including unknowns, within 20.
• MAT-02.AR.OA.04 Solve one- and two-step authentic word problems with subtraction within 100, including the use of unknowns.
• MAT-02.AR.OA.05 Use repeated addition to find the total number of objects arranged in a rectangular array.
• MAT-03.AR.OA.03 Solve two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.
• MAT-03.AR.OA.04 Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.
• MAT-03.AR.OA.05 Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.
• MAT-04.AR.OA.03 Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders. Represent problems using equations, including a symbol as an unknown.

Equations/Expressions

• MAT-01.AR.OA.06 Use the +, -, and = symbols accurately in an equation.
• MAT-02.AR.OA.02 Apply the properties of operations to solve addition and subtraction equations and justify thinking.
• MAT-03.AR.OA.02 Apply the properties of operations to solve multiplication and division equations and justify thinking.
• MAT-03.AR.OA.03 Solve word two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.
• MAT-03.AR.OA.04 Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.
• MAT-03.AR.OA.05 Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.
• MAT-04.AR.OA.03 Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders.
• MAT-04.AR.OA.05 Interpret multiplication equations as a comparison. Represent multiplicative comparisons as multiplication equations.
• MAT-05.AR.OA.02 Analyze problems using the order of operations to solve and evaluate expressions while justifying thinking.
• MAT-05.AR.OA.03 Write simple expressions that record calculations with numbers. Interpret numerical expressions without evaluating them.
• MAT-06.AR.EE.01 Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.
• MAT-06.AR.EE.02 Read and evaluate algebraic expressions, including expressions with whole number exponents and grouping symbols. Write algebraic expressions to represent simple and authentic situations.
• MAT-06.AR.EE.04 Describe the concept of a solution of an equation or an inequality. Determine whether a given number is a solution to an equation or an inequality.
• MAT-06.AR.EE.05 Write and solve equations of the form of x + p = q and px = q for cases in which p and q are non-negative whole numbers or decimals, including authentic problems.
• MAT-07.AR.EE.02 Write and solve equations of the form px + q = r and p(x + q) = r , including in authentic problems.
• MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.
• MAT-08.AR.EE.02 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a non-negative rational number.
• MAT-08.AR.EE.06 Read, write, and evaluate numerical and algebraic expressions, including expressions involving absolute value. Solve and graph equations of the form |x| = r where r is a nonnegative rational number.
• MAT-09.AR.01 Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.
• MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
• MAT-12.AR.03 Interpret expressions that represent a quantity in context.
• MAT-12.AR.02 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.

3rd Grade (MAT) Targeted Standard     (AR) Algebraic Reasoning  (OA) Operations and Algebraic Thinking Learners will analyze patterns and relationships to generate and interpret numerical expressions.

Proficiency Scale

Progressions

Solve Problems Using Operations

• MAT-00.AR.OA.04 Solve authentic word problems with addition by putting together or adding to within 10.
• MAT-01.AR.OA.06 Use the +, -, and = symbols accurately in an equation.
• MAT-01.AR.OA.04 Solve authentic word problems with addition, including three numbers and unknowns, within 20.
• MAT-02.AR.OA.03 Solve one- and two-step authentic word problems with addition within 100, including the use of unknowns.
• MAT-00.AR.OA.05 Solve authentic word problems with subtraction by taking apart or taking from within 10.
• MAT-01.AR.OA.05 Solve authentic word problems with subtraction, including unknowns, within 20.
• MAT-02.AR.OA.04 Solve one- and two-step authentic word problems with subtraction within 100, including the use of unknowns.
• MAT-02.AR.OA.05 Use repeated addition to find the total number of objects arranged in a rectangular array.
• MAT-03.AR.OA.03 Solve two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.
• MAT-03.AR.OA.04 Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.
• MAT-03.AR.OA.05 Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.
• MAT-04.AR.OA.03 Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders. Represent problems using equations, including a symbol as an unknown.

Equations/Expressions

• MAT-01.AR.OA.06 Use the +, -, and = symbols accurately in an equation.
• MAT-02.AR.OA.02 Apply the properties of operations to solve addition and subtraction equations and justify thinking.
• MAT-03.AR.OA.02 Apply the properties of operations to solve multiplication and division equations and justify thinking.
• MAT-03.AR.OA.03 Solve word two-step authentic word problems using addition and subtraction within 1000, including equations with a letter as an unknown.
• MAT-03.AR.OA.04 Use strategies and visual models to solve authentic word problems with multiplication within 100, including unknowns, using grouping models and equations.
• MAT-03.AR.OA.05 Use strategies and visual models to solve authentic word problems with division within 100, including unknowns, using grouping models and equations.
• MAT-04.AR.OA.03 Solve multi-step authentic word problems using the four operations, including problems with interpreted remainders.
• MAT-04.AR.OA.05 Interpret multiplication equations as a comparison. Represent multiplicative comparisons as multiplication equations.
• MAT-05.AR.OA.02 Analyze problems using the order of operations to solve and evaluate expressions while justifying thinking.
• MAT-05.AR.OA.03 Write simple expressions that record calculations with numbers. Interpret numerical expressions without evaluating them.
• MAT-06.AR.EE.01 Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.
• MAT-06.AR.EE.02 Read and evaluate algebraic expressions, including expressions with whole number exponents and grouping symbols. Write algebraic expressions to represent simple and authentic situations.
• MAT-06.AR.EE.04 Describe the concept of a solution of an equation or an inequality. Determine whether a given number is a solution to an equation or an inequality.
• MAT-06.AR.EE.05 Write and solve equations of the form of x + p = q and px = q for cases in which p and q are non-negative whole numbers or decimals, including authentic problems.
• MAT-07.AR.EE.02 Write and solve equations of the form px + q = r and p(x + q) = r , including in authentic problems.
• MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.
• MAT-08.AR.EE.02 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a non-negative rational number.
• MAT-08.AR.EE.06 Read, write, and evaluate numerical and algebraic expressions, including expressions involving absolute value. Solve and graph equations of the form |x| = r where r is a nonnegative rational number.
• MAT-09.AR.01 Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.
• MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
• MAT-12.AR.03 Interpret expressions that represent a quantity in context.
• MAT-12.AR.02 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.

3rd Grade (MAT) Targeted Standard     (AR) Algebraic Reasoning  (OA) Operations and Algebraic Thinking Learners will analyze patterns and relationships to generate and interpret numerical expressions.

Proficiency Scale

Progressions

Patterns

• MAT-00.AR.OA.06 Recognize, duplicate, complete, and extend repeating patterns in a variety of contexts (e.g., shape, color, size, objects, sounds, and movement).
• MAT-01.AR.OA.07 Identify, create, complete, and extend patterns that are repeating, increasing, and decreasing in a variety of contexts.
• MAT-02.AR.OA.06 Identify a group of objects from 0 to 20 as even or odd by showing even numbers as a sum of two equal parts.
• MAT-03.AR.OA.06 Identify arithmetic patterns and explain them using the properties of operations.
• MAT-04.AR.OA.06 Generate a number or shape pattern that follows a given rule while identifying apparent features of the pattern that were not explicit in the rule itself.
• MAT-05.AR.OA.05 Generate two numerical patterns using two given rules and form ordered pairs consisting of corresponding terms from the two patterns. (Graphing on a coordinate plane).
• MAT-09.AR.01 Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.
• MAT-12.AR.2 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.