Chapter 1 Lesson 2

1. Inductive Reasoning Chapter 1 Lesson 2

2. Inductive Reasoning • Reasoning based on patterns that you observe • Finding the next term in a sequence is a form of inductive reasoning

3. Conjecture • A conclusion that you reach based on inductive reasoning

4. Example of a conjectureMake a chart with the following information: • Count the number of ways 2 people shake hands • Count the number of ways 3 people shake hands • Count the number of ways 4 people shake hands • Count the number of ways 5 people shake hands • Make a conjecture about the number of ways 6 people shake hands People 2 3 4 5 6 Handshakes 1 3 6 10 ?

5. Make a conjecture • Finish the statement: The sum of any two odd numbers is ____________. • Begin by writing several examples: • What do you notice about each sum? • Answer: The sum of any 2 odd numbers is: • 1+1=2 • 1+3=4 • 3+5 = 8 • 5+7=14 • 7+9= 16 • 11+13 = 24 even

6. Make a conjecture • Complete the conjecture: The sum of the first 30 odd numbers is ____________________. • 1 = 1 • 1+3 = 4 • 1+3+5 = 9 • 1+3+5+7 = 16 • 1+3+5+7+9 = 25 • 1+3+5+7+9+11 = 36 • What do you notice about the pattern? • Conjecture: The sum of the first 30 odd numbers is 302.

7. Counterexamples • Just because a statement is true for several examples does not mean that it is true for all cases • If a conjecture is not always true, then it is considered false • To prove that a conjecture is false, you need ONE counterexample • Counterexample: an example that shows a conjecture is false.

8. Examples: • You can connect any three points to form a triangle. • Counterexample: three points on the same line • Any number and its absolute value are opposites

9. Show that the conjecture is false by providing a counterexample: • If the product of two numbers is even, then the numbers must be even. • If it is Monday, then there is school.

10. Assignment: Page 11 # 1 -19