Main Goals for Chapter 1

• To become familiar with different approaches to problem solving
• To use inductive reasoning to understand number patterns
• To explore Pascal's triangle

Section 1.1 Solving Problems by Inductive Reasoning. Key Ideas: inductive reasoning, deductive reasoning, solving problems.  Sample exercises (pages 7-9): 3, 5, 9, 11, 15, 17, 19, 21, 23, 25, 31, 33, 37, 43, 57

Section 1.2 An Application of Inductive Reasoning: Number Patterns.  Key Ideas: successive differences, sum 1+2+...+n, triangular numbers.  Sample exercises (pages 16-19): 3, 5, 7, 11, 13, 15, 21, 23, 29, 31, 33, 35

Section 1.3 Strategies for Problem Solving.  Key Ideas: Polya's 4 steps, different problem solving strategies.  Sample Exercises (pages 25-31): 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 31, 33, 35, 37, 47, 51, 53, 55, 59, 63, 65 (There are many problems from this section- they are all different and the idea is not to memorize examples but to develop problem-solving skills, so pick the ones that you think are more interesting)

Pascal's Triangle.  Key Ideas: Where the numbers in the triangle come from, some patterns (see notes for more details and sample exercises)

Chapter 1 Slides

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last updated September 21, 2011