Module 2: Patterns and Counting

by Valerie A. DeBellis and Joseph G. Rosenstein

Chapter 5: Number patterns

  1. The Handshake Problem
  2. Triangular and Square Numbers
  3. Extending Sequences of Numbers
  4. Recursive Number Patterns
    (Introduction to Fibonacci Numbers)

Chapter 6: Systematic Listing and Counting

  1. How Many Triangles? (The Addition Rule)
  2. How Many Outfits? (The Multiplication Rule)
  3. How Many Orders? (Permutations)
  4. How Many Words? (Combinations)
  5. The Choose Numbers

Chapter 7: Pascal's Triangle

  1. Introduction to Pascal's Triangle
  2. Patterns in Pascal's Triangle
  3. Pascal's Triangle as a Graph
  4. The Choose Numbers in Pascal's Triangle

Chapter 8: Number Patterns Revisited

  1. Classifying Number Sequences (Linear, Quadratic, Exponential)
  2. The Technique of Finite Differences
  3. Fast Growing Sequences (Doubling, Tower of Hanoi)
  4. Fibonacci Numbers