geometry notes 1.1 patterns and inductive reasoning mr. belanger
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Geometry Notes1.1 Patterns and Inductive Reasoning
Mr. Belanger
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Inductive ReasoningInductive Reasoning
Reasoning based on patterns you observe.
I am COOL, I am COOL, I am COOL,
What do you observe???
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ExamplesExamples
3, 6, 12, 24, ….. What do you notice?
Next number is previous times 2.
80, 40, 20, 10, ….. Previous number divided by 2.
Next shape?? Triangle.
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ConjectureConjecture
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
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CounterexampleCounterexampleExample that proves a conjecture false (untrue)
The sky is blue!
conjecture
Counterexample – raining outside (sky is gray)
You only need to provide ONE counterexample to disprove a conjecture.
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ExamplesExamples1) The square of any number is greater than the original.
648
10010
42
2
2
2
0625.25.
11
00
2
2
2
counters
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ExamplesExamples
2) The product of two positive numbers is greater than both numbers.
60106
48124
632
5.135.
221