**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**