1. 2-1 Patterns and Inductive Reasoning
Objective:
Use inductive reasoning to make conjectures

2. Reasoning based on patterns you observe. Conjecture
Inductive Reasoning
Reasoning based on patterns you observe.
Conjecture
A conclusion you reach using inductive reasoning.
Example
A scientist dips a platinum wire into a solution containing salt (sodium chloride), passes the wire over a flame, and observes that it produces an orange-yellow flame.
She does this with many other solutions that contain salt, finding that they all produce an orange-yellow flame.
Conjecture
If a solution contains sodium chloride, then in a flame test it produces an orange-yellow flame.

3. Example 2:
Consider the sequence
2, 4, 7, 11, . . .
Make a conjecture about the rule for generating the sequence.
Then find the next three terms.
Conjecture:
You always add the next counting number to get the next term.

4. Patterns about 1st, 3rd, and 5th shape.
Half shaded circles, with the circle rotating a quarter turn counter clockwise from previous circle.
Patterns about 2nd, 4th, and 6th shape.
Polygons with consecutive odd numbered sides and a triangular pattern of dots, solid dot on top two hollow dots on bottom.
Draw next two shapes.

5. Find one counterexample to prove a conjecture is false.
An example that shows that a conjecture is incorrect.
Find one counterexample to prove a conjecture is false.
If the name of a month starts with the letter J, it is a summer month.
Counterexample: January starts with the letter J and it is a winter month.

6. What is a counterexample for each conjecture?
If a flower is red, it is a rose.
When you multiply a number by 3, the product is divisible by 6.
p. 85: 7-23 odd, odd