2.1 Inductive Reasoning and Conjecturing

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Presentation transcript:

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

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

Make and test a conjecture Make and test a conjecture about the sum of any 3 consecutive integers 22+23+24= 69 1+2+3 = 6 10+11+12 = 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.

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.

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

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.

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

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