Algebra Course

Lesson 1 • Patterns and Sequences

Identifies arithmetic and geometric patterns as precursors to functions. Students write rules for sequences and predict future terms.

Lesson 2 • Numbers, Operations, and Properties

Reviews integers, fractions, and decimals alongside arithmetic properties. Establishes the numerical fluency required for all symbolic work ahead.

Lesson 3 • The Coordinate Plane

Establishes the two-dimensional grid as a visual tool for algebra. Students plot points and identify quadrants to prepare for graphing equations.

Lesson 1 • Equations with Variables on Both Sides

Teaches collecting variable terms on one side before solving. Reinforces the balance model of equations through structured practice.

Lesson 2 • One-Step Equations

Applies inverse operations to isolate a variable in a single step. Connects arithmetic properties to formal equation-solving procedures.

Lesson 3 • Absolute Value Equations

Introduces absolute value as distance from zero and solves related equations. Students handle both cases and identify extraneous solutions.

Lesson 4 • Multi-Step Equations

Extends solving to equations requiring multiple inverse operations. Students learn to clear fractions and decimals before solving.

Lesson 1 • Solving One- and Multi-Step Inequalities

Applies inverse operations to inequalities, emphasizing the sign-flip rule. Mirrors the equation-solving sequence from Chapter 2.

Lesson 2 • Graphing Linear Inequalities in Two Variables

Extends single-variable inequalities to the coordinate plane using shading. Students identify boundary lines and test points to determine solution regions.

Lesson 3 • Compound Inequalities

Covers AND and OR compound inequalities and their solution sets. Students graph intersections and unions on number lines.

Lesson 4 • Absolute Value Inequalities

Translates absolute value inequalities into compound forms for solving. Connects to the absolute value equations introduced in Chapter 2.

Lesson 1 • Point-Slope and Standard Forms

Presents two additional linear equation forms and conversions between all three. Students choose the most efficient form for a given problem.

Lesson 2 • Slope-Intercept Form

Introduces y = mx + b as the standard form for graphing lines. Students graph lines and extract slope and intercept from equations.

Lesson 3 • Linear Models and Scatter Plots

Applies linear functions to real data using trend lines and scatter plots. Students interpret slope and intercept as meaningful quantities in context.

Lesson 4 • Parallel and Perpendicular Lines

Uses slope relationships to identify and write equations of parallel and perpendicular lines. Reinforces slope mastery in a geometric context.

Lesson 5 • Slope and Rate of Change

Defines slope as rise over run and as a rate of change. Students calculate slope from two points, tables, and graphs.

Lesson 1 • Substitution Method

Solves systems by substituting one equation's expression into the other. Builds on single-variable equation skills from Chapter 2.

Lesson 2 • Elimination Method

Adds or subtracts equations to eliminate one variable and solve. Students multiply equations by constants to create opposite coefficients.

Lesson 3 • Systems of Linear Inequalities

Extends graphing skills to find feasible regions for two or more inequalities. Connects to linear programming concepts in applied mathematics.

Lesson 4 • Graphing Systems of Equations

Finds solutions as intersection points of two lines on the coordinate plane. Students classify systems as consistent, inconsistent, or dependent.

Lesson 1 • Solving Equations by Factoring

Applies the zero-product property to solve polynomial equations. Connects factoring skills directly to finding roots of polynomial expressions.

Lesson 2 • Factoring Techniques

Covers GCF, grouping, trinomial, and special-pattern factoring systematically. Students develop a decision strategy for choosing the correct technique.

Lesson 3 • Adding and Subtracting Polynomials

Defines polynomial degree and standard form, then combines like terms. Extends expression simplification skills from Chapter 1.

Lesson 4 • Multiplying Polynomials

Applies the distributive property to multiply monomials, binomials, and polynomials. Students master FOIL and the general distribution method.

Lesson 1 • Complex and Imaginary Numbers

Introduces imaginary unit i and complex number arithmetic. Students solve quadratics with negative discriminants and express complex solutions.

Lesson 2 • Completing the Square

Transforms standard form to vertex form by completing the square. Builds algebraic manipulation skills needed for the quadratic formula derivation.

Lesson 3 • Quadratic Models and Applications

Applies quadratic functions to projectile motion, area, and optimization problems. Students interpret vertex and intercepts as meaningful real-world values.

Lesson 4 • The Quadratic Formula

Derives and applies the quadratic formula to solve any quadratic equation. Students use the discriminant to predict the number and type of solutions.

Lesson 1 • Multiplying and Dividing Rational Expressions

Extends fraction multiplication and division rules to polynomial expressions. Students factor completely before multiplying to simplify efficiently.

Lesson 2 • Solving Rational Equations

Clears denominators to convert rational equations into polynomial equations. Students identify and exclude extraneous solutions caused by domain restrictions.

Lesson 3 • Radical Expressions and Equations

Simplifies radicals using product and quotient rules, then solves radical equations. Students rationalize denominators and check for extraneous solutions.

Lesson 4 • Simplifying Rational Expressions

Factors numerators and denominators to cancel common factors. Identifies restrictions on the domain where the expression is undefined.