(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.

MAT-06.AR.EE.03 Identify when two expressions are equivalent. Apply the properties of operations to generate equivalent expressions.

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.03Identify 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.

Equivalent Expressions

MAT-06.AR.EE.03Identify 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.01 Use 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.