1. Lesson 1-1: Patterns & Inductive Reasoning

2. Vocabulary Term Definition Own Words Inductive Reasoning Conjecture
Counterexample
Reasoning based on observed patterns.
A conclusion based on inductive reasoning.
An example that shows a conjecture is not true (false).
(Copy completed table in notes.)

3. 2, 3, 5 What will the next number be?
Conjecture: the next number is 8
CONGRATULATIONS!!!
You just used
inductive reasoning
based on what you
observed (saw).

4. We use inductive reasoning to find patterns
Find patterns from 2 main areas:
Numbers
See what is going on from one number to the next (add, subtract, multiply, divide?)
Shapes
How does the shape changed: turned? Added parts? removed parts?

5. Find the next 2 items in each pattern.
In-Class Examples
Find the next 2 items in each pattern.
5, 10, 20, 40,… 2) 80
160

6. 3) Assignment Practice 1-1
If you get a story problem see if you can draw a picture to help you find the pattern.

7. Were those conjectures correct?
Review our two examples from yesterday about the sunny days and 2, 3, 5.
Were those conjectures correct?
Conjectures are not always true (correct)
They are still conjectures though!
We prove a conjecture is not true by showing a counterexample
Sunny days counterexample: it will rain someday
2, 3, 5 counterexample: the next number could be 7 or 8
7 if your conjecture was prime numbers
8 if your conjecture was = 5, so = 8

8. Finding counterexamples:
Find numbers that fit the criteria but do not reach the correct result (conclusion)
Hint: throw the word “not” after the is
Example on page 7: find a counterexample.
25) The sum of two numbers is greater than either number.
Need to find two numbers whose sum is not greater than either number.
2 + 3 = 5; 5 > 2 and 5 > 3 … not 2 and 3
No positive numbers work!
Let one be negative: = 3; the sum, 3, is not greater than either number
Counterexample: -2 and 5