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

Factor a quadratic expression to reveal the zeros of the function it defines.

Use the properties of exponents to transform exponential expressions.

Complete the square in a quadratic expression to produce an equivalent expression.

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.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.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.04Choose 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.

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.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.04Choose 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.