Introduction to Algebra
Contents
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