1.1 Patterns and Inductive Reasoning Goal 1: Find and describe patterns. Goal 2: Use inductive reasoning to make real-life conjectures.

Inductive Reasoning Inductive reasoning is a process consisting of three stages Look for a Pattern Make a conjecture Verify the conjecture Begin an example on white board: p. 6/ 11

1. Look for a pattern In this stage we look at several examples. Use diagrams, tables, and pictures to discover a pattern. Ask students to look at the example to see if they notice a pattern.

2. Make a Conjecture A conjecture is an unproven statement that is based on observations. An educated guess based on previous knowledge. Ask students to state what they think

3. Verify the Conjecture After you make a conjecture, you use logical reasoning to verify the conjecture is true in all cases. If a conjecture is false, there exist a counterexample to the conjecture. All you need is ONE case where the conjecture is not true, then the conjecture is false. That “ONE case” is called a Counterexample Verify by doing a couple examples

Counterexample A Counterexample is an example that shows a conjecture is false. Ex. Here is an example of a conjecture about birds. “All birds fly.” Is this a true of false statement? If false, give an example of a bird that doesn’t fly.

Conjectures Not every conjecture is known to be true or false. If a conjecture cannot be proven true or false they are called unproven or undecided conjectures.

Describe a pattern in the sequence of numbers 1) 2, 6, 18, 54, ____ 2) 0, 1, 4, 9, ____

Describe a pattern in the sequence of images