Geometry Notes 1.1 Patterns and Inductive Reasoning

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Presentation transcript:

Geometry Notes 1.1 Patterns and Inductive Reasoning Mr. Belanger

Inductive Reasoning I am COOL, Reasoning based on patterns you observe. I am COOL, I am COOL, I am COOL, What do you observe???

Examples 3, 6, 12, 24, ….. 80, 40, 20, 10, ….. What do you notice? Next number is previous times 2. 80, 40, 20, 10, ….. Previous number divided by 2. Next shape?? Triangle.

Conjecture 1, 4, 16, 64, …. conjecture Conclusion you reach using inductive reasoning. (Not thinking and figuring it out, but the actual written answer) 1, 4, 16, 64, …. Multiplying previous number by 4. conjecture

Counterexample The sky is blue! Example that proves a conjecture false (untrue) The sky is blue! Counterexample – raining outside (sky is gray) conjecture You only need to provide ONE counterexample to disprove a conjecture.

Examples 1) The square of any number is greater than the original. counters

Examples 2) The product of two positive numbers is greater than both numbers.