1. 1.0.25, 1, 1 2.0, 3, 8 3.1, 3/2, 2 4.  1/2,  2,  3 1 Warm Up

2. What you will learn and why you will learn it How to find and describe patterns How to use inductive reasoning to make conjectures 2

3. 1.1 Patterns and Inductive Reasoning 3

4. Inductive Reasoning Watching weather patterns develop help forecasters… Predict weather.. They recognize and Describe patterns. They then try to make accurate predictions based on the patterns they discover. 4

5. Patterns & Inductive Reasoning In Geometry, we will Study many patterns… Some discovered by others…. Some we will discover… And use those patterns to make accurate predictions 5

6. VISUAL PATTERNS Can you predict and sketch the next figure in these patterns? 6

7. a.3 b/c you subtract 17-2, 15-3, …. b.16/27 b/c you divide by 3 each time 7

8. 8 Examples

9. Inductive Reasoning 1. Look for a pattern 2. Make a conjecture. A conjecture is an unproven statement (a “guess”) based on your observations. 3. Verify the conjecture. Either prove it is true through logical reasoning, or show that it is not true. 9

10. How do you know your conjecture is True or False? To prove a conjecture is TRUE, you need to prove it is ALWAYS true (not always so easy!) To prove a conjecture is FALSE, you need only provide a SINGLE counterexample. A counterexample is an example that shows a conjecture is false. 10

11. Decide if this conjecture is TRUE or FALSE. All people over 6 feet tall are good basketball players. This conjecture is false (there are plenty of counterexamples…) 11 Example 1

12. Example 2: Inductive Reasoning Each adult ticket costs $7 12

13. EXIT QUESTIONS 13 Patterns 1) Sketch the next figure in the pattern. 2) Describe the pattern and predict the next term 1, 4, 16, 64, …