1. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 1.2, Slide 1 Problem Solving 1 Strategies and Principles

2. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 1.2, Slide 2 Inductive and Deductive Reasoning 1.2 Understand how inductive reasoning leads to making conjectures Give examples of correct and incorrect inductive reasoning (continued on next slide)

3. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 1.2, Slide 3 Inductive and Deductive Reasoning 1.2 Understand the difference between inductive and deductive reasoning

4. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 1.2, Slide 4 Inductive Reasoning Example: Consider the numbers 72, 963, 10,854, and 7,236,261, which are all divisible by 9. Add the digits in each number and make a conjecture based on the pattern. (solution on next slide)

5. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 1.2, Slide 5 Inductive Reasoning Example: Consider the numbers 72, 963, 10,854, and 7,236,261, which are all divisible by 9. Add the digits in each number and make a conjecture based on the pattern. 7 + 2 = 9 9 + 6 + 3 = 18 1 + 0 + 8 + 5 + 4 = 18 7 + 2 + 3 + 6 + 2 + 6 + 1 = 27 A number is divisible by 9 if the sum of its digits is divisible by 9.

6. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 1.2, Slide 6 Inductive Reasoning

7. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 1.2, Slide 7 Incorrect Inductive Reasoning Example:

8. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 1.2, Slide 8 Incorrect Inductive Reasoning Example: Conjecture (incorrect): the number of regions is given by 2 n–1 ( n = # of points).

9. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 1.2, Slide 9 Deductive Reasoning Examples of deductive reasoning: –Mathematical proofs –Step-by-step mathematical solutions –Using scientific laws to make predictions

10. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 1.2, Slide 10 Explaining a Number Trick by using Deductive Reasoning 1.Pick a number from 1 to 9 2.Multiply that number by 2 3.Add 5 to the number you got in step 2 4.Multiply the number you obtained in step 3 by 50.

11. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 1.2, Slide 11 Explaining a Number Trick by using Deductive Reasoning 5.If you have already had your birthday this year, add 1765, if you haven’t, add 1764 6.Subtract the four-digit year that you were born. 7.I can tell you what number you started with and how old you are!