CCS.Math.Content.HSA-SSE: Seeing Structure in Expressions

CCS.Math.Content.HSA-SSE.A: Interpret the structure of expressions

CCS.Math.Content.HSA-SSE.A.1: Interpret expressions that represent a quantity in terms of its context.

CCS.Math.Content.HSA-SSE.A.1.a: Interpret parts of an expression, such as terms, factors, and coefficients.

Arithmetic Sequences
Compound Interest

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

Compound Interest

CCS.Math.Content.HSA-SSE.A.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

CCS.Math.Content.HSA-SSE.B: Write expressions in equivalent forms to solve problems

CCS.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.

CCS.Math.Content.HSA-SSE.B.3.a: Factor a quadratic expression to reveal the zeros of the function it defines.

Quadratics in Factored Form

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

Quadratics in Vertex Form

CCS.Math.Content.HSA-APR: Arithmetic with Polynomials and Rational Expressions

CCS.Math.Content.HSA-APR.A: Perform arithmetic operations on polynomials

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

Addition and Subtraction of Functions
Addition of Polynomials
Dividing Polynomials Using Synthetic Division
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

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

CCS.Math.Content.HSA-APR.B.2: Know and apply the Remainder Theorem: 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).

Dividing Polynomials Using Synthetic Division

CCS.Math.Content.HSA-APR.B.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Polynomials and Linear Factors

CCS.Math.Content.HSA-APR.C: Use polynomial identities to solve problems

CCS.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.

Binomial Probabilities

CCS.Math.Content.HSA-CED: Creating Equations

CCS.Math.Content.HSA-CED.A: Create equations that describe numbers or relationships

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

Absolute Value Equations and Inequalities
Exploring Linear Inequalities in One Variable
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Roots of a Quadratic
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

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

Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Quadratics in Polynomial Form
Quadratics in Vertex Form
Rational Functions
Translating and Scaling Sine and Cosine Functions

CCS.Math.Content.HSA-CED.A.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 Programming

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

Roots of a Quadratic
Solving Formulas for any Variable

CCS.Math.Content.HSA-REI: Reasoning with Equations and Inequalities

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

CCS.Math.Content.HSA-REI.A.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
Quadratics in Factored Form
Solving Algebraic Equations II
Solving Two-Step Equations

CCS.Math.Content.HSA-REI.B: Solve equations and inequalities in one variable

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

Exploring Linear Inequalities in One Variable
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

CCS.Math.Content.HSA-REI.B.4: Solve quadratic equations in one variable.

CCS.Math.Content.HSA-REI.B.4.a: 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. Derive the quadratic formula from this form.

Roots of a Quadratic

CCS.Math.Content.HSA-REI.B.4.b: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Quadratics in Factored Form
Roots of a Quadratic

CCS.Math.Content.HSA-REI.C: Solve systems of equations

CCS.Math.Content.HSA-REI.C.5: Prove 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 Linear Systems (Standard Form)

CCS.Math.Content.HSA-REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Cat and Mouse (Modeling with Linear Systems)
Cat and Mouse (Modeling with Linear Systems) - Metric
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

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

Solving Linear Systems (Matrices and Special Solutions)

CCS.Math.Content.HSA-REI.C.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)

CCS.Math.Content.HSA-REI.D: Represent and solve equations and inequalities graphically

CCS.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, often forming a curve (which could be a line).

Absolute Value Equations and Inequalities
Exponential Functions
Introduction to Exponential Functions
Point-Slope Form of a Line
Quadratics in Polynomial Form
Standard Form of a Line

CCS.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, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Absolute Value Equations and Inequalities
Cat and Mouse (Modeling with Linear Systems)
Cat and Mouse (Modeling with Linear Systems) - Metric
Radical Functions
Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)

CCS.Math.Content.HSA-REI.D.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
Systems of Linear Inequalities (Slope-intercept form)