1. 2.1 Inductive Reasoning and Conjecturing
OBJ: To make conjectures based on inductive reasoning

2. Definitions An unproven statement that is based on observation
*Conjecture:
Inductive Reasoning:
Conjecture based on several observations
Counter Example:
One Example that proves a conjecture false

3. Make and test a conjecture
Make and test a conjecture about the sum of any 3 consecutive integers
= 69
1+2+3 = 6
= 33
5+6+7= 18
Do you notice any patterns? Does it work for
all numbers? Can you find an example
to prove it false?
3 times the middle number is always the sum.

4. Is Mr. Chandler Psychic? Pick any 3 digit #? Ex 123
Make a different 3 digit # using the same digits. Ex 213
Find the positive difference between the 2 numbers (use a calculator…you look foolish if your math is incorrect)
Circle one of the digits, (not zero-it’s already a circle)
Tell Mr. Chandler the digits you didn’t circle and he will tell you the one that you did circle
Make a conjecture about how he is doing it and test it.

5. Example
For pts A, B, C, and D, AB = 5, BC = 10, CD = 8, and AD = 12. Make a conjecture and draw a figure to illustrate your conjecture.
Conjecture: the points make a 4-sided figure

6. Your Turn:
Given pts P, Q, and R are collinear, make a conjecture based on the given information
Conjecture: Q is between P and R.

7. Example:
Given that pts P, Q, and R are collinear, a conjecture was made that Q is between P and R. Determine if the conjecture is True or False. Explain your answer.
False, P R Q

8. Homework Put this in your agenda
Pg 75 3 – 11 odd, 12 – 19, 21 – 27 odd, 30, 36