Strategies and Principles

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Section 1.2, Slide 1

Problem Solving1

Strategies and Principles



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)



Inductive and Deductive Reasoning

1.2

• Understand the difference between inductive and deductive reasoning

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)


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.


Inductive Reasoning


Incorrect Inductive Reasoning

• Example:


Incorrect Inductive Reasoning

• Example:

Conjecture (incorrect): the number of regions is given by 2n–1 (n = # of points).


Deductive Reasoning

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


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.


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!

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Strategies and Principles