Learners will look for, generate, and make sense of patterns, relationships, and algebraic symbols to represent mathematical models while adopting approaches and solutions in novel situations.

MAT-09.AR.01 Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.

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.01Use 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

Factor Pairs/Multiples

MAT-04.AR.OA.04 Find factor pairs and multiples within the range of 1-36 while classifying numbers as prime or composite.

MAT-05.AR.OA.04 Find factor pairs and multiples within the range of 1-100 while classifying numbers as prime or composite.

MAT-06.NO.O.04 Determine the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.

MAT-09.AR.01Use 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.02 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.04 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

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.

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.01Use 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.

Equivalent Expressions

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 the 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.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-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.

MAT-09.AR.01Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.

MAT-09.AR.02 Rearrange formulas to isolate a quantity or variable(s) of interest using the same reasoning as in solving equations.

MAT-09.AR.07 Rearrange multi-variable formulas to highlight a quantity of interest.

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-12.NO.02 Perform operations on complex radical expressions to write a simplified equivalent expression.

MAT-12.AR.01 Rearrange multi-variable formulas to highlight a quantity of interest.

MAT-12.AR.02 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.

MAT-12.AR.04 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

MAT-12.AR.05 Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system analogous to rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.

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.GM.01 Write the equation of a conic section given its special features. Convert between the standard form and general form equations of conic sections.

MAT-12.GM.02 Identify key features of a conic section given its equation. Apply properties of conic sections in context.

MAT-12.NO.12 Extend polynomial identities to the complex numbers.

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.01Use 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.