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0.25, 1, 1 0, 3, 8 1, 3/2, 2 1/2, 2, 3

Warm Up. 0.25, 1, 1 0, 3, 8 1, 3/2, 2 1/2, 2, 3. What you will learn and why you will learn it. How to find and describe patterns How to use inductive reasoning to make conjectures. 1.1 Patterns and Inductive Reasoning. Inductive Reasoning.

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0.25, 1, 1 0, 3, 8 1, 3/2, 2 1/2, 2, 3

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  1. Warm Up 0.25, 1, 1 0, 3, 8 1, 3/2, 2 1/2, 2, 3

  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

  3. 1.1 Patterns and Inductive Reasoning

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

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

  6. Visual Patterns Can you predict and sketch the next figure in these patterns?

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

  8. Examples

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

  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.

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

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

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

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