Table of Contents

From the book: Introduction to Algebra

Introduction to Algebra


Introduction: How to Use this Book 1

Lessons 1-3: Beginning Algebra by Solving for Area 2

How Much Land does a Man Need, Tolstoy 3

Pakhom’s Claim to Land 8

Lesson Activities: Perimeter and Area of Pakhom’s Land 10

Lesson 4: Magic Triangles 13

Lesson 5: Interest 14

Lesson 6: The Circle’s Area and Circumference 17

Lesson Activity: Proof of the Circle’s Area 18

Lesson Activities: Area Formulas 21

Lesson 7: Distance Problems Outdoors 22

Lesson Activities: Distance Problems 23

Lesson 8: Ratios and Cross Multiplying 25

The Attack on the Castle Rathskeller (A Story on Ratios) 26

Lesson 9: Exponents, Powers, and Scientific Notation 29

The King and the Chessboard (A Story on Exponents) 29

Lesson Activities: Four Processes, Scientific Notation, and Powers 31

Kepler’s Third Law of Planetary Motion: Application 32

Microscopic Numbers 33

Lesson 10: Positive and Negative Numbers 34

Leonardo Fibonacci and Negative Numbers (A Story) 34

Lesson Activities: Bookkeeping with a Florentine Merchant 36

Lesson Activities: Temperature Differences (Subtracting Negatives) 37

Lesson Activities: Multiplication and Division with Negatives 38

Lesson 11: Combining Like Terms, Unwrapping, Distributive Law and Equations 39

Lesson 12: Principles in Solving Linear Equations 42

Solving Linear Equations 43

Practical Applications with Linear Equations 44

Lesson 13: Cartesian Coordinates 45

Lesson Activity: Exploring the Sea of Many Islands with Coordinates 45

Lesson 14: Graphing Symmetrical Linear Equations 47

Slope, Rise and Run 49

Lesson Activity: Charting the Falling Comet 50

Lesson Activities: Charting from Port to Port with Linear Equations 51

Lesson 15: The Algebra of the Pythagorean Theorem 52

Lesson Activities: Practical Applications of the Pythagorean Theorem 53

Lesson 16: The Second Degree Equations of Circles and Curves 55