Essential Question: How do we use inductive reasoning?

Essential Question:How do we use inductive reasoning? 09 September 2013

Vocabulary Please define the following vocabulary words in the Reference section of your binder.

Inductive reasoning: Make a prediction based on patterns or examples

Conjecture: A conclusion you reach using inductive reasoning

Counterexample: An example for which your conjecture is not true

Postulate An accepted statement of fact

Theorem A conjecture that is proven

Notes Please follow along and copy the following examples into the Notes section of your binder, using Cornell Notes

1 Consider the following situation… At step 1, there is 1 segment. Example 1

3 At step 2, there are now 3 segments Example 1

7 Step 3: 7 segments… Example 1

15 Example 1

31 Example 1

63 +32 +4 +8 +16 +2 What is the pattern?

3, 6, 9, 12, 15, Example 2 18, 21

-2 -2 -2 -2 -2 5, 3, 1, -1, Example 3 -5 -3,

2+3= 1+2= 3+5= Example 4 1,2,3, 5, 8

Example 5 How can you represent the “nth” step? 2n

Example 6 Step 1: Look for the difference in each step; multiply by n Step 2: Add or subtract to make the pattern true 3n 3n+_ 3n+1 +3 +3 +3 +3

Essential Question: How do we use inductive reasoning?