2. Inductive Reasoning  Reasoning based on patterns you observe

3. Inductive Reasoning  Look at specific examples
Inductive Reasoning  Look at specific examples.  Recognize patterns, which you assume will continue.  Use the examples to find a general rule.

4.  We call the general rule a. conjecture
 We call the general rule a conjecture We use inductive reasoning all the time in everyday life.

5. Often conjectures are true, and they help us get on the right track,
Often conjectures are true, and they help us get on the right track, BUT …

6. The conjectures you find through inductive reasoning aren’t necessarily always true.  You found them by assuming the pattern would continue, which you can’t always say for sure it will.

8. Counterexample  A single example that. shows a general rule
Counterexample  A single example that shows a general rule doesn’t always work.  Even though a rule might work in most cases, you can’t say it’s “true” if there is even one counterexample.

10. What could be a counter-example to “They always cancel school when it snows.”

11. One possibility … The snow could have started after school started and come too fast, so they couldn’t cancel.

12. Another possibility … It could be snowing somewhere else, but not here.

13. Third possibility … It could be Christmas vacation, so there’s no school anyway.

14. Unless you can find an example for every possible case, you can’t actually prove a conjecture is true with inductive reasoning (but you often can find out all you need to know for practical purposes).

15. REMEMBER  inductive reasoning  conjecture  counterexample