### Module 2: Patterns and Counting

by Valerie A. DeBellis and Joseph G. Rosenstein

Chapter 5: Number patterns

- The Handshake Problem
- Triangular and Square Numbers
- Extending Sequences of Numbers
- Recursive Number Patterns

(Introduction to Fibonacci Numbers)

Chapter 6: Systematic Listing and Counting

- How Many Triangles? (The Addition Rule)
- How Many Outfits? (The Multiplication Rule)
- How Many Orders? (Permutations)
- How Many Words? (Combinations)
- The Choose Numbers

Chapter 7: Pascal's Triangle

- Introduction to Pascal's Triangle
- Patterns in Pascal's Triangle
- Pascal's Triangle as a Graph
- The Choose Numbers in Pascal's Triangle

Chapter 8: Number Patterns Revisited

- Classifying Number Sequences (Linear, Quadratic, Exponential)
- The Technique of Finite Differences
- Fast Growing Sequences (Doubling, Tower of Hanoi)
- Fibonacci Numbers