A.SSE: Seeing Structure in Expressions

1.1: Interpret the structure of expressions.

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

A.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

A.SSE.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)^n as the product of P and (1 + r)^n.

Compound Interest
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

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.

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

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

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

A.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

A.APR: Arithmetic with Polynomials and Rational Expressions

2.1: Perform arithmetic operations on polynomials.

A.APR.1: Add, subtract, and multiply polynomials.

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

A.APR.2: Factor higher degree polynomials; identifying that some polynomials are prime.

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

A.APR.3: Know and apply the Remainder Theorem: For a polynomial p(x) and a number c, the remainder on division by (x - c) is p(c), so p(c) = 0 if and only if (x - c) is a factor of p(x).

Dividing Polynomials Using Synthetic Division

2.2: Use polynomial identities to solve problems.

A.APR.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. The Binomial Theorem can be proven by mathematical induction or by a combinatorial argument.

Binomial Probabilities

A.CED: Creating Equations

3.1: Create equations that describe numbers or relationships.

A.CED.1: Apply and extend previous understanding to create equations and inequalities in one variable and use them to solve problems.

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

A.CED.2: Apply and extend previous understanding to 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
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form
Solving Equations on the Number Line
Standard Form of a Line
Using Algebraic Equations

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)

A.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

A.REI: Reasoning with Equations and Inequalities

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

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

4.2: Solve equations and inequalities in one variable.

A.REI.2: Apply and extend previous understanding to solve equations, inequalities, and compound inequalities in one variable, including literal equations and inequalities.

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

A.REI.3: Solve equations in one variable and give examples showing how extraneous solutions may arise.

A.REI.3a: Solve rational, absolute value and square root equations.

Absolute Value Equations and Inequalities
Radical Functions

A.REI.4: Solve radical and rational exponent equations and inequalities in one variable, and give examples showing how extraneous solutions may arise.

Radical Functions

A.REI.5: Solve quadratic equations and inequalities.

A.REI.5a: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives no real solutions.

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

A.REI.5b: Solve quadratic equations with complex solutions written in the form a ± bi for real numbers a and b.

Points in the Complex Plane
Roots of a Quadratic

A.REI.5c: Use the method of completing the square to transform and solve any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions.

Roots of a Quadratic

4.3: Solve systems of equations.

A.REI.6: Analyze and solve pairs of simultaneous linear equations.

A.REI.6a: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

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)

A.REI.6c: Solve real-world and mathematical problems leading to two 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)

A.REI.7: Represent a system of linear equations as a single matrix equation and solve (incorporating 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.

A.REI.8: 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

A.REI.9: Solve an equation f(x) = g(x) by graphing y = f(x) and y = g(x) and finding the x-value of the intersection point. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

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

A.REI.10: 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: 9/24/2019

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