In the summer of 2007, my wife Anne and I wrote an algebra book for the CK12 foundation. It is organized into 12 chapters and each chapter is split into 8 lessons. Each "lesson" typically covers 3 or 4 skills, and would take about 1 to 2 class periods to cover. The book is built around the NCTM standards for Algebra, and loosely mirrors the algebra-1 California State Standards. The book is available below. Each lesson has a number of worked examples and small number of homework problems. State standards for CA are stated at the start of each chapter, although often skills will be split between 2 or more chapters. It is the pre-edited version I post here - do not be surprised if you spot an error!
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Chapter 1: Expressions, Equations, and Functions |
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Lesson 1.1: Variable Expressions 1.1.1: Evaluate algebraic expressions. 1.1.2: Evaluate algebraic expressions with exponents. |
Lesson 1.2: Order of Operations 1.2.1: Evaluate algebraic expressions with grouping symbols. 1.2.2: Evaluate algebraic expressions with fraction bars. 1.2.3: Evaluate algebraic expressions with a graphing calculator. |
Lesson 1.3: Patterns and Expressions 1.3.1: Write an expression. 1.3.2: Use a verbal model to write an expression 1.3.3: Solve problems using expressions |
Lesson 1.4: Equations and Inequalities 1.4.1: Write equations and inequalities. 1.4.2: Check solutions to equations. 1.4.3: Check solutions to inequalities. 1.4.4: Solve real-world problems using an equation. |
Lesson 1.5: Functions as Rules 1.5.1: Identify the domain and range of a function. 1.5.2: Make a table for a function. 1.5.3: Write a function rule. 1.5.4: Represent a real-world situation with a function. |
Lesson 1.6: Functions as Graphs 1.6.1: Graph a function from a rule or table. 1.6.2: Write a function rule from a graph. 1.6.3: Analyze the graph of a real-world situation. 1.6.4: Determine whether a relation is a function. |
Lesson 1.7: Problem-Solving Plan 1.7.1: Read and understand a given problem situation. 1.7.2: Make a plan to solve the problem. 1.7.3: Solve the problem and check the results. 1.7.4: Compare alternative approaches to solving the problem. 1.7.5: Solve real-world problems using a plan. |
Lesson 1.8: Problem-Solving Strategies: Make a Table; Look for a Pattern 1.8.1: Read and understand given problem situations. 1.8.2: Develop and use the strategy: Make a Table. 1.8.3: Develop and use the strategy: Look for a Pattern. 1.8.4: Plan and compare alternative approaches to solving problems. 1.8.5: Solve real-world problems using selected strategies as part of a plan.
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Chapter 2: Properties of Real Numbers |
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Lesson 2.1: Integers & Rational Numbers 2.1.1: Graph and compare integers. 2.1.2: Classify rational numbers. 2.1.3: Order rational numbers. 2.1.4: Find opposites of numbers. 2.1.5: Find absolute values. |
Lesson 2.2: Addition of Rational Numbers 2.2.1: Add using a number line. 2.2.2: Add rational numbers 2.2.3: Identify and apply properties of addition. 2.2.4: Solve real-world problems using addition. |
Lesson 2.3: Subtraction of Rational Numbers 2.3.1: Find additive inverses. 2.3.2: Subtract rational numbers. 2.3.3: Evaluate change using a variable expression. |
Lesson 2.4: Multiplication of Rational Numbers 2.4.1: Multiply by –1. 2.4.2: Multiply rational numbers. 2.4.3: Identify and apply properties of multiplication. 2.4.4: Solve real-world problems using multiplication. |
Lesson 2.5: The Distributive Property 2.5.1: Apply the distributive property. 2.5.2: Identify parts of an expression. 2.5.3: Solve real-world problems using the distributive property. |
Lesson 2.6: Division of Rational Numbers 2.6.1: Find multiplicative inverses 2.6.2: Divide rational numbers. 2.6.3: Solve real-world problems using division. |
Lesson 2.7: Square Roots and Real Numbers 2.7.1: Find square roots. 2.7.2: Approximate square roots. 2.7.3: Identify irrational numbers. 2.7.4 Classify real numbers. 2.7.5: Graph and order real numbers. |
Lesson 2.8: Problem-Solving Strategies: Guess and Check; Work Backward 2.8.1: Read and understand given problem situations. 2.8.2: Develop and use the strategy: Guess and Check. 2.8.3: Develop and use the strategy: Work Backward. 2.8.4: Plan and compare alternative approaches to solving problems. 2.8.5: Solve real-world problems using selected strategies as part of a plan. |
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Chapter 3: Linear Equations |
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Lesson 3.1: One-Step Equations 3.1.1: Solve an equation using addition. 3.1.2: Solve an equation using subtraction. 3.1.3: Solve an equation using multiplication. 3.1.4: Solve an equation using division. 3.1.5 Solve real-world problems using equations |
Lesson 3.2: Two-Step Equations 3.2.1: Solve a two-step equation. 3.2.2: Solve a two-step equation by combining like terms. 3.2.3: Solve real-world problems using two-step equations. |
Lesson 3.3: Multi-Step Equations 3.3.1: Solve a multi-step equation by combining like terms. 3.3.2: Solve a multi-step equation using the distributive property. 3.3.3: Solve real-world problems using multi-step equations. |
Lesson 3.4: Equations with Variables on Both Sides 3.4.1: Solve an equation with variables on both sides. 3.4.2: Solve an equation with grouping symbols. 3.4.3: Solve real-world problems using equations with variables on both sides. |
Lesson 3.5: Ratios and Proportions 3.5.1: Write a ratio. 3.5.2: Write and solve a proportion. 3.5.3: Solve proportions using cross products. 3.5.4: Solve real-world problems using proportions. |
Lesson 3.6: Scale and Indirect Measurement 3.6.1: Use scale on a map. 3.6.2: Solve problems using scale drawings. 3.6.3: Use similar figures to measure indirectly |
Lesson 3.7: Percent Problems 3.7.1: Find a percent of a number. 3.7.2: Use the percent equation. 3.7.3: Find percent of change. 3.7.3: Solve real-world problems using percents. |
Lesson 3.8: Problem Solving Strategies: Use a Formula 3.8.1: Read and understand given problem situations. 3.8.2: Develop and apply the strategy: Use a Formula 3.8.3 Plan and compare alternative approaches to solving problems. 3.8.4: Solve real-world problems using selected strategies as part of a plan. |
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Chapter 4: Graphing Linear Equations and Functions |
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Chapter 5: Writing Linear Equations |
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Chapter 6: Linear Inequalities and Absolute Value; Introduction to Probability |
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Chapter 7: Systems of Equations and Inequalities; Counting Methods |
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