### OH.Math.HSA.SSE: Seeing Structure in Expressions

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

OH.Math.HSA.SSE.1: Interpret expressions that represent a quantity in terms of its context.

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

OH.Math.HSA.SSE.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity.

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

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

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

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

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

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

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

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

OH.Math.HSA.APR.1: Understand that polynomials form a system analogous to the integers, namely, that they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

OH.Math.HSA.APR.1b: Extend to polynomial expressions beyond those expressions that simplify to forms that are linear or quadratic.

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

OH.Math.HSA.APR.2: Understand and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a). In particular, p(a) = 0 if and only if (x - a) is a factor of p(x).

OH.Math.HSA.APR.3: Identify zeros of polynomials, when factoring is reasonable, and use the zeros to construct a rough graph of the function defined by the polynomial.

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

OH.Math.HSA.APR.4: Prove polynomial identities and use them to describe numerical relationships.

OH.Math.HSA.APR.5: Know and apply the Binomial Theorem for the expansion of (?? + ??)? in powers of ?? and ?? for a positive integer ??, where ?? and ?? are any numbers.

2.3.2.1: For example by using coefficients determined for by Pascal’s Triangle.

2.3.2.2: The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.

### OH.Math.HSA.CED: Creating Equations

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

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

3.1.1.1: Include equations and inequalities arising from linear, quadratic, simple rational, and exponential functions.

OH.Math.HSA.CED.1a: Focus on applying linear and simple exponential expressions.

OH.Math.HSA.CED.1c: Extend to include more complicated function situations with the option to solve with technology.

OH.Math.HSA.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

OH.Math.HSA.CED.2a: Focus on applying linear and simple exponential expressions.

OH.Math.HSA.CED.2b: Focus on applying simple quadratic expressions.

OH.Math.HSA.CED.2c: Extend to include more complicated function situations with the option to graph with technology.

OH.Math.HSA.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.

OH.Math.HSA.CED.3a: While functions will often be linear, exponential, or quadratic, the types of problems should draw from more complicated situations.

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

OH.Math.HSA.CED.4a: Focus on formulas in which the variable of interest is linear or square.

OH.Math.HSA.CED.4b: Focus on formulas in which the variable of interest is linear.

OH.Math.HSA.CED.4c: Focus on formulas in which the variable of interest is linear or square.

OH.Math.HSA.CED.4d: While functions will often be linear, exponential, or quadratic, the types of problems should draw from more complicated situations.

### OH.Math.HSA.REI: Reasoning with Equations and Inequalities

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

OH.Math.HSA.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.

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

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

OH.Math.HSA.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

OH.Math.HSA.REI.4: Solve quadratic equations in one variable.

OH.Math.HSA.REI.4a: 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.

OH.Math.HSA.REI.4b: Solve quadratic equations as appropriate to the initial form of the equation by inspection, e.g., for x² = 49; taking square roots; completing the square; applying the quadratic formula; or utilizing the Zero-Product Property after factoring.

OH.Math.HSA.REI.4c: Derive the quadratic formula using the method of completing the square.

#### OH.Math.HSA.REI.C: Solve systems of equations.

OH.Math.HSA.REI.5: Verify that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

OH.Math.HSA.REI.6: Solve systems of linear equations algebraically and graphically.

OH.Math.HSA.REI.6a: Limit to pairs of linear equations in two variables.

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

OH.Math.HSA.REI.9: 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).

#### OH.Math.HSA.REI.D: Represent and solve equations and inequalities graphically.

OH.Math.HSA.REI.10: 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).

OH.Math.HSA.REI.11: Explain why the x-coordinates of the points where the graphs of the equation y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, making tables of values, or finding successive approximations.

OH.Math.HSA.REI.12: 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.