Algebra 1
The gateway to all higher mathematics. Master variables, equations, functions, and graphing: the language every math and science course speaks.
12 units and 67 lessons, for Grade 8 to Grade 9. Free on Slate.
Unit 1: Foundations of Algebra
Establish the language and properties of algebra before solving equations.
Unit 2: Solving Linear Equations
Develop systematic, proof-like techniques for isolating unknowns.
- One-Step Equations (30 min)
- Two-Step Equations (30 min)
- Multi-Step Equations (35 min)
- Equations with Variables on Both Sides (35 min)
- Literal Equations and Formulas (25 min)
- Linear Equation Word Problems (40 min)
Unit 3: Linear Inequalities & Absolute Value
Extend equation-solving techniques to inequalities and introduce absolute value.
- Solving and Graphing One-Variable Inequalities (35 min)
- Compound Inequalities (30 min)
- Absolute Value Equations (30 min)
- Absolute Value Inequalities (35 min)
- Inequality Word Problems (35 min)
Unit 4: Functions & Relations
Understand functions as the mathematical objects that drive all of algebra and beyond.
- Relations and Functions (25 min)
- Function Notation (30 min)
- Domain and Range (30 min)
- Identifying Functions from Graphs, Tables, and Equations (25 min)
- Linear vs. Nonlinear Functions (25 min)
Unit 5: Linear Functions
Master every representation of a line and understand what each reveals.
- Slope: Definition and Calculation (30 min)
- Slope-Intercept Form: y = mx + b (30 min)
- Point-Slope Form (25 min)
- Standard Form: Ax + By = C (30 min)
- Writing Equations of Lines (30 min)
- Parallel and Perpendicular Lines (30 min)
- Scatter Plots and Lines of Best Fit (30 min)
- Linear Function Applications (30 min)
Unit 6: Systems of Equations & Inequalities
Solve problems with two unknowns using three methods and understand when each is most efficient.
- Introduction to Systems of Equations (25 min)
- Solving Systems by Graphing (30 min)
- Solving Systems by Substitution (30 min)
- Solving Systems by Elimination (30 min)
- Special Cases: No Solution and Infinitely Many Solutions (25 min)
- Systems of Equations Word Problems (30 min)
- Graphing Systems of Inequalities (30 min)
Unit 7: Exponents & Exponential Functions
Unlock the power of repeated multiplication and model explosive growth and decay.
- Laws of Exponents (30 min)
- Zero and Negative Exponents (30 min)
- Scientific Notation (30 min)
- Exponential Growth and Decay (35 min)
- Comparing Linear and Exponential Growth (35 min)
- Exponential Function Applications (35 min)
Unit 8: Polynomials
Build and manipulate the algebraic objects that power all advanced mathematics.
- Introduction to Polynomials (30 min)
- Adding and Subtracting Polynomials (30 min)
- Multiplying Polynomials (30 min)
- Special Products (30 min)
- Introduction to Factoring: GCF (30 min)
Unit 9: Factoring Polynomials
Learn the full toolkit for factoring, essential for solving quadratic equations.
- Factoring Trinomials: Leading Coefficient 1 (30 min)
- Factoring Trinomials: Leading Coefficient ≠ 1 (35 min)
- Factoring Special Cases (35 min)
- Factoring Completely (30 min)
- Solving Quadratic Equations by Factoring (35 min)
Unit 10: Quadratic Functions
Explore the most important nonlinear function class in all of algebra.
- Introduction to Quadratic Functions (30 min)
- Vertex, Axis of Symmetry, and Parabola Graphing (30 min)
- Solving Quadratic Equations by Square Roots (30 min)
- Completing the Square (35 min)
- The Quadratic Formula (35 min)
- The Discriminant (30 min)
- Quadratic Function Applications (35 min)
Unit 11: Radical Expressions & Equations
Work fluently with square roots and introduce the connection to rational exponents.
- Simplifying Square Roots (30 min)
- Operations with Radical Expressions (30 min)
- Solving Radical Equations (35 min)
- The Pythagorean Theorem (35 min)
Unit 12: Data Analysis & Statistics
Analyze real data, interpret graphical displays, and make sound statistical arguments.
- Measures of Center and Spread (35 min)
- Two-Way Frequency Tables (30 min)
- Interpreting Data Displays (35 min)
- Correlation vs. Causation (30 min)