1. 1-1 Patterns and Inductive Reasoning

2. Inductive Reasoning
When you use a pattern to find the next term in a sequence you’re using inductive reasoning.
The conclusion you’ve made about the next terms in the pattern are called a conjecture

3. Make a Conjecture
1. The price of overnight shipping was $8 in 2000, $9.50 in 2001, and $11 in Make a conjecture about the price in 2003.
2.Use inductive reasoning to make a conjecture about the sum of the cubes of the first 25 counting numbers

4. Are all conjectures true?
All Rivermont students live in Iowa.
The square of any number is greater than the original number.
You can connect any three points and form a triangle.

5. Find a counterexample Find a counterexample for these conjectures
A number is always greater than its reciprocal
If a number is divisible by 5, then it is divisible by 10

6. Other Examples
Where else do you use inductive reasoning, conjectures, and counterexamples. Talk with a partner and come up with some examples.

7. Ticket out of class
1. use inductive reasoning to make a conjecture about the next two numbers
3, -6, 18, -72, 360
2. Make a conjecture about the sum of the first 15 counting numbers
3. Show that this conjecture is false by providing a counterexample
The sum of 2 prime numbers is an even number