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.04 Create linear and exponential equations in two or more variables to represent relationships between quantities.
MAT-05.NO.NBT.07 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
MAT-06.AR.EE.01 Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.
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.01 Explain how the definition of rational exponents follows from extending the properties of integer exponents; rewrite simple expressions involving radicals and rational exponents using the properties of exponents.
MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
MAT-09.AR.06 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.
MAT-09.AR.04Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with proper labels and scales.
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-0.AR.F.08 Identify situations that can be modeled with linear, quadratic, and exponential functions. Justify the most appropriate model for a situation based on the rate of change over equal intervals. Include situations in which a quantity grows or decays.
MAT-12.NO.01 Rewrite complex expressions involving radicals and rational exponents using the properties of exponents.
MAT-12.NO.02 Perform basic operations on advanced radicals and simplify radicals to write equivalent expressions.
MAT-12.AR.07 Create equations and inequalities and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions.
MAT-12.AR.08 Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
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.F.06 Apply the inverse relationship between exponents and logarithms to solve problems.
MAT-12.AR.F.15 Use properties of logarithms to express the solution to abct = d where a, c, and d are real numbers and b is a positive real number. Evaluate the logarithm using technology when appropriate.
Unit Size and Scale
MAT-06.NO.NS.02 Write, interpret, and explain statements of order for rational numbers on a number line diagram and in authentic contexts.
MAT-09.NO.03 Choose and interpret the scale and the origin in graphs and data displays.
MAT-09.NO.04 Define appropriate quantities and units for the purpose of descriptive modeling.
MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
MAT-09.AR.04Create 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-10.GM.14 Verify experimentally and justify the properties of dilations given by a center and a scale factor.
MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
MAT-12.NO.04 Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
MAT-12.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
MAT-12.AR.08 Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
Linear Equations
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.03 Explain the characteristics of a linear relationship, including identifying the slope and yintercept in tables, graphs, equations, and descriptions.
MAT-08.AR.EE.04 Represent linear relationships using tables, graphs, equations, and descriptions when given a relationship in one of these forms.
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, many solutions, or no solutions.
MAT-09.AR.03 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.
MAT-09.AR.04Create 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-09.AR.05 Justify each step in solving a linear equation that may or may not have a solution.
MAT-09.AR.06 Solve linear equations and inequalities (to include compound inequalities) in one variable.
MAT-09.AR.07 Solve a system of linear equations graphically and algebraically. Create and solve a system of linear equations in context and interpret the results.
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.07 Create equations and inequalities and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions.
MAT-12.AR.08 Create equations in two or more variables to represent relationships between quantities.
Graph equations on coordinate axes with appropriate labels and scales.
MAT-12.AR.09 Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context.
MAT-12.AR.12 Solve simple rational and radical equations in one variable and identify extraneous solutions.
MAT-12.AR.F.14 Write arithmetic and geometric sequences both recursively and with an explicit formula and convert between the two forms. Use sequences to model situations.
MAT-12.AR.15 Apply the Factor and Remainder Theorems to determine efficiently whether a liner expression is a factor of a polynomial expression.
MAT-12.AR.16 Using graphs, technology, tables, or successive approximations, show that the solution(s) to the equation f(x) = g(x) is the x-value(s) that result in the y-values of f(x) and g(x) being the same.
MAT-12.AR.17 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
MAT-12.AR.18 Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
MAT-12.NO.13 Apply the Fundamental Theorem of Algebra to find all roots of a polynomial equation and determine the nature (i.e., integer, rational, irrational, real, complex) of the roots.
MAT-12.AR.19 Solve a system of equations in three or more variables with matrices (using technology).
MAT-12.AR.F.23 Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions and interpret them in context.
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.04Create 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.
Proficiency Scale