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(AR) Algebraic Reasoning

MAT-01.AR

BPSS-MAT-GM logo  MAT-01.AR Domain 
BPSS-MAT-AR logo

(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.

MAT-01.AR.OA.01

BPSS-MAT-NO logo 1st Grade (MAT) Targeted Standard  
  (AR) Algebraic Reasoning 
(OA) Operations and Algebraic Thinking
Learners will analyze patterns and relationships to generate and interpret numerical expressions.
MAT-01.AR.OA.01 Automatically add and subtract within 10.*

proficiency scale iconProficiency 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.

MAT-01.AR.OA.02

BPSS-MAT-NO logo 1st Grade (MAT) Targeted Standard  
  (AR) Algebraic Reasoning 
(OA) Operations and Algebraic Thinking
Learners will analyze patterns and relationships to generate and interpret numerical expressions.
MAT-01.AR.OA.02 For any number from 1 to 19, find the number that makes 20 when added to the given number, sharing the answer with a model, drawing, or equation.

proficiency scale iconProficiency Scale

Progressions

Adding On

  • MAT-00.AR.OA.02 For any number from 1 to 9, find the number that makes 10 when added to the given number, sharing the answer with a model, drawing, or equation. 
  • MAT-01.AR.OA.02 For any number from 1 to 19, find the number that makes 20 when added to the given number, sharing the answer with a model, drawing, or equation.

MAT-01.AR.OA.03

BPSS-MAT-NO logo 1st Grade (MAT) Targeted Standard  
  (AR) Algebraic Reasoning 
(OA) Operations and Algebraic Thinking
Learners will analyze patterns and relationships to generate and interpret numerical expressions.
MAT-01.AR.OA.03 Decompose numbers less than or equal to 20 into pairs in more than one way.

proficiency scale iconProficiency Scale

Progressions

Decompose Numbers and/or Expressions

  • MAT-00.AR.OA.03 Decompose numbers less than or equal to 10 into pairs in more than one way using verbal explanations, objects, or drawings. 
  • MAT-01.AR.OA.03 Decompose numbers less than or equal to 20 in more than one way. 
  • MAT-09.AR.01 Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it. 
  • MAT-09.AR.F.06 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function. 
  • MAT-09.AR.F.11 Interpret the parameters in a linear, quadratic, or exponential function in context. 
  • MAT-12.AR.01 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it. 
  • MAT-12.AR.03 Interpret expressions that represent a quantity in context. 
  • MAT-12.AR.06 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, division, or technology for the more complicated examples. 
  • MAT-12.AR.F.03 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function. 
  • MAT-12.AR.20 Apply the Binomial Theorem for the expansion of (ax + by)n in powers of x and y for a positive integer n and integers a and b

MAT-01.AR.OA.04

BPSS-MAT-NO logo 1st Grade (MAT) Targeted Standard  
  (AR) Algebraic Reasoning 
(OA) Operations and Algebraic Thinking
Learners will analyze patterns and relationships to generate and interpret numerical expressions.
MAT-01.AR.OA.04 Solve authentic word problems with addition, including three numbers and unknowns, within 20.*

proficiency scale iconProficiency 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.

MAT-01.AR.OA.05

BPSS-MAT-NO logo 1st Grade (MAT) Targeted Standard  
  (AR) Algebraic Reasoning 
(OA) Operations and Algebraic Thinking
Learners will analyze patterns and relationships to generate and interpret numerical expressions.
MAT-01.AR.OA.05 Solve authentic word problems with subtraction, including unknowns, within 20.*

proficiency scale iconProficiency 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.

MAT-01.AR.OA.06

BPSS-MAT-NO logo 1st Grade (MAT) Targeted Standard  
  (AR) Algebraic Reasoning 
(OA) Operations and Algebraic Thinking
Learners will analyze patterns and relationships to generate and interpret numerical expressions.
MAT-01.AR.OA.06 Distinguish and use the +, -, and = symbols accurately in an equation.*

proficiency scale iconProficiency 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.

MAT-01.AR.OA.07

BPSS-MAT-NO logo 1st Grade (MAT) Targeted Standard  
  (AR) Algebraic Reasoning 
(OA) Operations and Algebraic Thinking
Learners will analyze patterns and relationships to generate and interpret numerical expressions.
MAT-01.AR.OA.07 Identify, create, complete, and extend patterns that are repeating, increasing, and decreasing in a variety of contexts.

proficiency scale iconProficiency 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.02 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.