8.29.2013 Inductive Reasoning.

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Presentation transcript:

8.29.2013 Inductive Reasoning

Using the rule, find the first 5 terms in the sequence. Do Now Using the rule, find the first 5 terms in the sequence. n2 (-n)2 -n2

Objective Students will identify the next term in a pattern using inductive reasoning. Agenda Quiz Overview (10) class Inductive Reasoning (20) group

Inductive Reasoning – the process of observing data, recognizing patterns, and making generalizations about those patterns.

Conjecture– a generalization made using inductive reasoning

To prove a conjecture true, you must prove that it is true in all cases. To prove a conjecture is false, you must prove it false in only one case.

Give a counter example to the following conjecture: The difference of two positive numbers is always a positive number.

Do you think it is easier to prove a conjecture is true or false?

Write a sequence. When I say switch, have your neighbor try to figure it out.

Write a conjecture (true or false) Write a conjecture (true or false). When I say switch, have your neighbor prove it true or false.

Goldbach’s Conjecture: Every even number greater than two can be written as the sum of two primes. Select an even number from 50-100 and show that Goldbach’s conjecture is true.

Turn and Talk Did you prove his conjecture Turn and Talk Did you prove his conjecture? No, you showed it true only for your number.

Exit Ticket What is the next term in the sequence? 1, -2, 3, -4, _____ A, b, C, d, ____