Learning Standards

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.

Compound Interest

Operations with Radical Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

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

Compound Interest

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

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

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Exponents and Power Rules

Factoring Special Products

Modeling the Factorization of *x*^{2}+*bx*+*c*

Multiplying Exponential Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Using Algebraic Expressions

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.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Quadratics in Factored Form

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.

Dividing Exponential Expressions

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.

Addition of Polynomials

Dividing Polynomials Using Synthetic Division

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).

Dividing Polynomials Using Synthetic Division

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.

Graphs of Polynomial Functions

Modeling the Factorization of *x*^{2}+*bx*+*c*

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Vertex Form

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.

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

Exploring Linear Inequalities in One Variable

Solving Two-Step Equations

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

Exploring Linear Inequalities in One Variable

Linear Inequalities in Two Variables

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

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

Absolute Value Equations and Inequalities

Arithmetic Sequences

Exploring Linear Inequalities in One Variable

Geometric Sequences

Linear Inequalities in Two Variables

Modeling One-Step Equations

Solving Equations on the Number Line

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

Using Algebraic Equations

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.

Exponential Functions

Linear Functions

Modeling and Solving Two-Step Equations

Point-Slope Form of a Line

Points, Lines, and Equations

Solving Equations by Graphing Each Side

Standard Form of a Line

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

Addition and Subtraction of Functions

Quadratics in Polynomial Form

Quadratics in Vertex Form

Translating and Scaling Functions

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

Absolute Value Equations and Inequalities

Circles

Linear Functions

Point-Slope Form of a Line

Quadratics in Polynomial Form

Quadratics in Vertex Form

Solving Equations on the Number Line

Standard Form of a Line

Using Algebraic Equations

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.

Linear Inequalities in Two Variables

Linear Programming

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

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.

Area of Triangles

Solving Formulas for any Variable

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

Area of Triangles

Solving Formulas for any Variable

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

Area of Triangles

Solving Formulas for any Variable

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

Area of Triangles

Solving Formulas for any Variable

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.

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations on the Number Line

Solving Two-Step Equations

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

Area of Triangles

Compound Inequalities

Exploring Linear Inequalities in One Variable

Linear Inequalities in Two Variables

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations I

Solving Algebraic Equations II

Solving Equations by Graphing Each Side

Solving Equations on the Number Line

Solving Formulas for any Variable

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

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.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Roots of a Quadratic

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

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.

Solving Equations by Graphing Each Side

Solving Linear Systems (Standard Form)

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.

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

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

Solving Linear Systems (Matrices and Special Solutions)

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).

Solving Linear Systems (Matrices and Special Solutions)

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).

Absolute Value Equations and Inequalities

Circles

Parabolas

Point-Slope Form of a Line

Points, Lines, and Equations

Standard Form of 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.

Cat and Mouse (Modeling with Linear Systems)

Point-Slope Form of a Line

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Standard Form of a Line

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.

Linear Inequalities in Two Variables

Linear Programming

Systems of Linear Inequalities (Slope-intercept form)

Correlation last revised: 1/22/2020