HS.A-SSE: Seeing Structure in Expressions

1.1: Interpret the structure of expressions

HS.A-SSE.1: Interpret expressions that represent a quantity in terms of its context.

HS.A-SSE.1.a: 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

HS.A-SSE.1.b: Interpret complicated expressions by examining one or more of their parts as a single entity.

Compound Interest
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

HS.A-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
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Using Algebraic Expressions

1.2: Write expressions in equivalent forms to solve problems

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

HA.A.SSE.3.a: Factor a quadratic expression to reveal the zeros of the function it defines.

Modeling the Factorization of x2+bx+c
Quadratics in Factored Form

HA.A.SSE.3.b: Complete the square in a quadratic expression to produce an equivalent expression.

Quadratics in Vertex Form

HS.A-APR: Arithmetic with Polynomials and Rational Expressions

2.1: Perform arithmetic operations on polynomials

HS.A-APR.1.i: Add, subtract, and multiply polynomials.

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

HS.A-APR.1.ii: Understand that polynomials form a system comparable to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.

Addition of Polynomials

2.2: Understand the relationship between zeros and factors of polynomials

HS.A-APR.2: Apply the Remainder Theorem.

Dividing Polynomials Using Synthetic Division

HS.A-APR.3.i: Identify zeros of polynomials when suitable factorizations are available.

Modeling the Factorization of x2+bx+c
Polynomials and Linear Factors

HS.A-APR.3.ii: Use the zeros to construct a rough graph of the function defined by the polynomial.

Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form

2.3: Use polynomial identities to solve problems

HS.A-APR.5: Apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n.

Binomial Probabilities

HS.A-CED: Creating Equations and Inequalities

3.1: Create equations that describe numbers or relationships

HS.A-CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Absolute Value Equations and Inequalities
Arithmetic Sequences
Compound Interest
Exploring Linear Inequalities in One Variable
Exponential Functions
General Form of a Rational Function
Geometric Sequences
Introduction to Exponential Functions
Linear Inequalities in Two Variables
Logarithmic Functions
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Rational Functions
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Translating and Scaling Functions
Using Algebraic Equations

HS.A-CED.2.i: Create equations in two or more variables to represent relationships between quantities.

Absolute Value Equations and Inequalities
Circles
Linear Functions
Point-Slope Form of a Line
Solving Equations on the Number Line
Standard Form of a Line
Using Algebraic Equations

HS.A-CED.2.ii: Graph equations on coordinate axes with appropriate labels and scales.

Absolute Value Equations and Inequalities
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form
Standard Form of a Line

HS.A-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
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

HS.A-CED.4: Rearrange formulas to isolate a quantity of interest, using the same reasoning as in solving equations.

Area of Triangles
Solving Formulas for any Variable

HS.A-REI: Reasoning with Equations and Inequalities

4.1: Understand solving equations as a process of reasoning and explain the reasoning

HS.A-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

HS.A-REI.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Radical Functions

4.2: Solve equations and inequalities in one variable

HS.A-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 II
Solving Equations on the Number Line
Solving Formulas for any Variable
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

HS.A-REI.4: Solve quadratic equations in one variable.

HS.A-REI.4.a.i: 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

HS.A-REI.4.a.ii: Derive the quadratic formula from this form.

Roots of a Quadratic

HS.A-REI.4.b.i: 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.

Modeling the Factorization of x2+bx+c
Roots of a Quadratic

HS.A-REI.4.b.ii: Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b.

Points in the Complex Plane
Roots of a Quadratic

4.3: Solve systems of equations

HS.A-REI.6: Solve systems of linear equations exactly and approximately, focusing on 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)

HS.A-REI.8: Represent a system of linear equations as a single matrix equation.

Solving Linear Systems (Matrices and Special Solutions)

HS.A-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)

4.4: Represent and solve equations and inequalities graphically

HS.A-REI.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
Parabolas
Point-Slope Form of a Line
Points, Lines, and Equations
Standard Form of a Line

HS.A-REI.11: Using graphs, technology, tables, or successive approximations, show that the solution(s) to the equation f(x) = g(x) are the x-value(s) that result in the y-values of f(x) and g(x) being the same.

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

HS.A-REI.12.i: Graph the solutions to a linear inequality in two variables as a half-plane.

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

HS.A-REI.12.ii: Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

Correlation last revised: 9/24/2019

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