AR.Math.Content.HSA.SSE: Seeing Structure in Expressions

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

AR.Math.Content.HSA.SSE.A.1: Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression using appropriate vocabulary, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity.

Compound Interest
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Translating and Scaling Functions
Using Algebraic Expressions

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

Equivalent Algebraic Expressions II
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II

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

AR.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. Factor a quadratic expression to reveal the zeros of the function it defines. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. Use the properties of exponents to transform expressions for exponential functions.

Dividing Exponential Expressions
Exponents and Power Rules
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Quadratics in Vertex Form
Simplifying Algebraic Expressions II

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

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

AR.Math.Content.HSA.APR.A.1: Add, subtract, and multiply polynomials. Understand that polynomials, like the integers, are closed under addition, subtraction, and multiplication.

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of x²+bx+c

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

AR.Math.Content.HSA.APR.B.2: Know and apply the Factor and Remainder Theorems: 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
Polynomials and Linear Factors

AR.Math.Content.HSA.APR.B.3: Identify zeros of polynomials when suitable factorizations are available. 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

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

AR.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

AR.Math.Content.HSA.CED: Creating Equations

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

AR.Math.Content.HSA.CED.A.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
Exponential Growth and Decay
Geometric Sequences
Modeling and Solving Two-Step Equations
Quadratic Inequalities
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

AR.Math.Content.HSA.CED.A.2: Create equations in two or more variables to represent relationships between quantities. Graph equations, in two variables, on a coordinate plane.

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

AR.Math.Content.HSA.CED.A.3: Represent and interpret constraints by equations or inequalities, and by systems of equations and/or inequalities. Interpret solutions as viable or nonviable options in a modeling and/or real-world context.

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

AR.Math.Content.HSA.CED.A.4: Rearrange literal equations using the properties of equality.

Area of Triangles
Solving Formulas for any Variable

AR.Math.Content.HSA.REI: Reasoning with Equations and Inequalities

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

AR.Math.Content.HSA.REI.A.1: Assuming that equations have a solution, construct a solution and justify the reasoning used.

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

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

Radical Functions

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

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

Absolute Value Equations and Inequalities
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 on the Number Line
Solving Formulas for any Variable
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

AR.Math.Content.HSA.REI.B.4: Solve quadratic equations in one variable. 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. Solve quadratic equations (as appropriate to the initial form of the equation) by: inspection of a graph, taking square roots, completing the square, using the quadratic formula, factoring. Recognize complex solutions and write them as a±bi for real numbers a and b.

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

AR.Math.Content.HSA.REI.C: Solve systems of equations and inequalities graphically.

AR.Math.Content.HSA.REI.C.5: Solve systems of equations in two variables using substitution and elimination. Understand that the solution to a system of equations will be the same when using substitution and elimination.

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

AR.Math.Content.HSA.REI.C.6: Solve systems of 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)

AR.Math.Content.HSA.REI.C.7: Solve systems of equations consisting of linear equations and nonlinear equations in two variables 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)

AR.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)

AR.Math.Content.HSA.REI.D: Solve systems of equations.

AR.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.

Absolute Value Equations and Inequalities
Circles
Ellipses
Hyperbolas
Parabolas
Point-Slope Form of a Line
Points, Lines, and Equations
Standard Form of a Line

AR.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 by: using technology to graph the functions (Algebra 1 and Algebra 2), making tables of values (Algebra 1 and Algebra 2), finding successive approximations (Algebra 1 and Algebra 2). Include cases (but not limited to) where f(x) and/or g(x) are: linear (Algebra 1 and Algebra 2), polynomial (Algebra 1 and Algebra 2), rational (Algebra 2), absolute value (Algebra 1), exponential (Introduction in Algebra 1, Mastery in Algebra 2), logarithmic functions (Algebra 2).

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

AR.Math.Content.HSA.REI.D.12: Solve linear inequalities and systems of linear inequalities in two variables by graphing.

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