1.1 Introduction to Problem Solving: Outlines Polya’s four-step process for solving problems and presents several problem solving strategies through worked examples. Subsections: Making a Drawing; Guessing and Checking; Making a Table; Using a Model; Working Backward. One-page Math Activity: The Peg Jumping Puzzle.
1.2 Patterns and Problem Solving: Introduces two more common problem solving strategies, presents number patterns including arithmetic, geometric, and patterns from nature, and discusses inductive reasoning. Subsections: Patterns in Nature; Number Patterns; Inductive Reasoning; Problem-Solving Application. One-page Math Activity: Pattern Block Sequences
1.3 Problem Solving with Algebra: Provides conceptual foundations for algebra through the use of the balance beam model to illustrate equations and inequalities and their solutions. Subsections: Variables and Equations; Solving Equations; Solving Inequalities; Using Algebra for Problem Solving; Problem Solving Application. One-page Math Activity: Extending Tile Patterns
The Tower Puzzle is based on the "Tower of Brahma" legend that predicted the world would vanish after 64 disks are transferred from tower to tower according to certain rules. You are challenged to transfer 15 disks, but you may wish to generalize your solution to 64 disks to solve the time required in ancient legend.