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
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.
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
Visual Patterns Can you predict and sketch the next figure in these patterns?
3 b/c you subtract 17-2, 15-3, …. 16/27 b/c you divide by 3 each time
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.
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.
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.
Example 2: Inductive Reasoning • Each adult ticket costs $7
Exit Questions Patterns 1) Sketch the next figure in the pattern. 2) Describe the pattern and predict the next term 1, 4, 16, 64, …