### A.SSE: Seeing Structure in Expressions

#### 1.1: Interpret the structure of expressions.

A.SSE.1: Interpret expressions that represent a quantity in terms of its context.

A.SSE.1a: Interpret parts of an expression, such as terms, factors, and coefficients.

A.SSE.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)^n as the product of P and (1 + r)^n.

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

#### 1.2: Write expressions in equivalent forms to solve problems.

A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A.SSE.3a: Factor a quadratic expression to reveal the zeros of the function it defines.

A.SSE.3b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

A.SSE.3c: Use the properties of exponents to transform expressions for exponential functions.

### A.APR: Arithmetic with Polynomials and Rational Expressions

#### 2.1: Perform arithmetic operations on polynomials.

A.APR.1: Add, subtract, and multiply polynomials.

A.APR.2: Factor higher degree polynomials; identifying that some polynomials are prime.

A.APR.3: Know and apply the Remainder Theorem: For a polynomial p(x) and a number c, the remainder on division by (x - c) is p(c), so p(c) = 0 if and only if (x - c) is a factor of p(x).

#### 2.2: Use polynomial identities to solve problems.

A.APR.4: Generate polynomial identities from a pattern.

A.APR.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. The Binomial Theorem can be proven by mathematical induction or by a combinatorial argument.

### A.CED: Creating Equations

#### 3.1: Create equations that describe numbers or relationships.

A.CED.1: Apply and extend previous understanding to create equations and inequalities in one variable and use them to solve problems.

A.CED.2: Apply and extend previous understanding to create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A.CED.3: 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.

A.CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

### A.REI: Reasoning with Equations and Inequalities

#### 4.1: Understand solving equations as a process of reasoning and explain the reasoning.

A.REI.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

#### 4.2: Solve equations and inequalities in one variable.

A.REI.2: Apply and extend previous understanding to solve equations, inequalities, and compound inequalities in one variable, including literal equations and inequalities.

A.REI.3: Solve equations in one variable and give examples showing how extraneous solutions may arise.

A.REI.3a: Solve rational, absolute value and square root equations.

A.REI.4: Solve radical and rational exponent equations and inequalities in one variable, and give examples showing how extraneous solutions may arise.

A.REI.5: Solve quadratic equations and inequalities.

A.REI.5a: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives no real solutions.

A.REI.5b: Solve quadratic equations with complex solutions written in the form a ± bi for real numbers a and b.

A.REI.5c: Use the method of completing the square to transform and solve any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions.

#### 4.3: Solve systems of equations.

A.REI.6: Analyze and solve pairs of simultaneous linear equations.

A.REI.6a: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

A.REI.6c: Solve real-world and mathematical problems leading to two linear equations in two variables.

A.REI.7: Represent a system of linear equations as a single matrix equation and solve (incorporating technology) for matrices of dimension 3 × 3 or greater.

#### 4.4: Represent and solve equations and inequalities graphically.

A.REI.8: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

A.REI.9: Solve an equation f(x) = g(x) by graphing y = f(x) and y = g(x) and finding the x-value of the intersection point. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

A.REI.10: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Correlation last revised: 9/15/2020

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