### AR.Math.Content.HSA.SSE: Seeing Structure in Expressions

#### AR.Math.Content.HSA.SSE.A: Interpret the structure of expressions.

AR.Math.Content.HSA.SSE.A.1: Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression using appropriate vocabulary, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity.

AR.Math.Content.HSA.SSE.A.2: Use the structure of an expression to identify ways to rewrite it.

#### AR.Math.Content.HSA.SSE.B: Write expressions in equivalent forms to solve problems.

AR.Math.Content.HSA.SSE.B.3: 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. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. Use the properties of exponents to transform expressions for exponential functions.

### AR.Math.Content.HSA.APR: Arithmetic with Polynomials and Rational Expressions

#### AR.Math.Content.HSA.APR.A: Perform arithmetic operations on polynomials.

AR.Math.Content.HSA.APR.A.1: Add, subtract, and multiply polynomials. Understand that polynomials, like the integers, are closed under addition, subtraction, and multiplication.

#### AR.Math.Content.HSA.APR.B: Understand the relationship between zeros and factors of polynomials.

AR.Math.Content.HSA.APR.B.2: Know and apply the Factor and Remainder Theorems: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

AR.Math.Content.HSA.APR.B.3: Identify zeros of polynomials when suitable factorizations are available. Use the zeros to construct a rough graph of the function defined by the polynomial.

#### AR.Math.Content.HSA.APR.C: Use polynomial identities to solve problems.

AR.Math.Content.HSA.APR.C.5: Know and apply the Binomial Theorem for the expansion of (x + y) n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.

### AR.Math.Content.HSA.CED: Creating Equations

#### AR.Math.Content.HSA.CED.A: Create equations that describe numbers or relationships.

AR.Math.Content.HSA.CED.A.1: Create equations and inequalities in one variable and use them to solve problems.

AR.Math.Content.HSA.CED.A.2: Create equations in two or more variables to represent relationships between quantities. Graph equations, in two variables, on a coordinate plane.

AR.Math.Content.HSA.CED.A.3: Represent and interpret constraints by equations or inequalities, and by systems of equations and/or inequalities. Interpret solutions as viable or nonviable options in a modeling and/or real-world context.

AR.Math.Content.HSA.CED.A.4: Rearrange literal equations using the properties of equality.

### AR.Math.Content.HSA.REI: Reasoning with Equations and Inequalities

#### AR.Math.Content.HSA.REI.A: Understand solving equations as a process of reasoning and explain the reasoning.

AR.Math.Content.HSA.REI.A.1: Assuming that equations have a solution, construct a solution and justify the reasoning used.

AR.Math.Content.HSA.REI.A.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

#### AR.Math.Content.HSA.REI.B: Solve equations and inequalities in one variable.

AR.Math.Content.HSA.REI.B.3: Solve linear equations, inequalities and absolute value equations in one variable, including equations with coefficients represented by letters.

AR.Math.Content.HSA.REI.B.4: Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions. Solve quadratic equations (as appropriate to the initial form of the equation) by: inspection of a graph, taking square roots, completing the square, using the quadratic formula, factoring. Recognize complex solutions and write them as a±bi for real numbers a and b.

#### AR.Math.Content.HSA.REI.C: Solve systems of equations and inequalities graphically.

AR.Math.Content.HSA.REI.C.5: Solve systems of equations in two variables using substitution and elimination. Understand that the solution to a system of equations will be the same when using substitution and elimination.

AR.Math.Content.HSA.REI.C.6: Solve systems of equations algebraically and graphically.

AR.Math.Content.HSA.REI.C.7: Solve systems of equations consisting of linear equations and nonlinear equations in two variables algebraically and graphically.

AR.Math.Content.HSA.REI.C.8: Represent a system of linear equations as a single matrix equation in a vector variable.

#### AR.Math.Content.HSA.REI.D: Solve systems of equations.

AR.Math.Content.HSA.REI.D.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

AR.Math.Content.HSA.REI.D.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); Find the solutions approximately by: using technology to graph the functions (Algebra 1 and Algebra 2), making tables of values (Algebra 1 and Algebra 2), finding successive approximations (Algebra 1 and Algebra 2). Include cases (but not limited to) where f(x) and/or g(x) are: linear (Algebra 1 and Algebra 2), polynomial (Algebra 1 and Algebra 2), rational (Algebra 2), absolute value (Algebra 1), exponential (Introduction in Algebra 1, Mastery in Algebra 2), logarithmic functions (Algebra 2).

AR.Math.Content.HSA.REI.D.12: Solve linear inequalities and systems of linear inequalities in two variables by graphing.

Correlation last revised: 9/16/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.