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.

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
Translating and Scaling Functions
Using Algebraic Expressions

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 ax²+bx+c
Modeling the Factorization of x²+bx+c
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Simplifying Trigonometric Expressions
Solving Algebraic Equations II
Using Algebraic Expressions

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.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+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.

Quadratics in Vertex Form

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

Dividing Exponential Expressions
Exponents and Power Rules

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.

Addition and Subtraction of Functions
Addition of 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.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).

Dividing Polynomials Using Synthetic Division
Polynomials and Linear Factors

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 x²+bx+c
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form

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.

Factoring Special Products

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.

Binomial Probabilities

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

Binomial Probabilities

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

Binomial Probabilities

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.

Absolute Value Equations and Inequalities
Arithmetic Sequences
Compound Interest
Exploring Linear Inequalities in One Variable
Geometric Sequences
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Quadratic Inequalities
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Using Algebraic Equations

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

Absolute Value Equations and Inequalities
Arithmetic Sequences
Compound Interest
Exploring Linear Inequalities in One Variable
Geometric Sequences
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Quadratic Inequalities
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Using Algebraic 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.

Absolute Value Equations and Inequalities
Circles
Compound Interest
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Solving Equations on the Number Line
Standard Form of a Line
Using Algebraic Equations

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.

Linear Inequalities in Two Variables
Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

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.

Area of Triangles
Solving Formulas for any Variable

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: 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.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Formulas for any Variable
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.

Radical Functions

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.

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.

Roots of a Quadratic

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.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Points in the Complex Plane
Roots of a Quadratic

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

Roots of a Quadratic

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.

Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

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

Cat and Mouse (Modeling with Linear Systems)
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.6a: Limit to pairs of linear equations in two variables.

Cat and Mouse (Modeling with Linear Systems)
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.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).

Absolute Value Equations and Inequalities
Circles
Ellipses
Hyperbolas
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)