1. Patterns, Inductive Reasoning & Conjecture

2. Inductive Reasoning Inductive reasoning is reasoning that is based on patterns you observe.

4. You Try!

5. Conjecture A conclusion you reach using inductive reasoning.

7. You Try! What conjecture can you make about the twenty-first term in R, W, B, R, W, B,... ?

9. You Try! What conjecture can you make about the first 30 odd numbers?

11. Counterexamples Not all conjectures will turn out to be true, you should always test your conjecture, to prove a conjecture false you only need to find one counterexample. Counterexample is an example that shows a conjecture is incorrect.

13. You Try! Write a counterexample for each conjecture. –If a flower is red it is a rose. –One and only one plane exists through any three points –When you multiply a number by three the product is divisible by six.