Strategies and Principles

1. Strategies and Principles

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. Inductive and Deductive Reasoning 1.2 • Understand the difference between inductive and deductive reasoning

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. Inductive Reasoning 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. • 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.

6. Inductive Reasoning

7. Incorrect Inductive Reasoning • Example:

8. Incorrect Inductive Reasoning • Example: Conjecture (incorrect): the number of regions is given by 2n–1 (n = # of points).

9. Deductive Reasoning • Examples of deductive reasoning: • Mathematical proofs • Step-by-step mathematical solutions • Using scientific laws to make predictions

10. Explaining a Number Trick by using Deductive Reasoning • Pick a number from 1 to 9 • Multiply that number by 2 • Add 5 to the number you got in step 2 • Multiply the number you obtained in step 3 by 50.

11. Explaining a Number Trick by using Deductive Reasoning If you have already had your birthday this year, add 1764, if you haven’t, add 1763 Subtract the four-digit year that you were born. I can tell you what number you started with and how old you are!