Mrs. Kim's Inductive reasoning, conjectures, and counterexamples

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What is inductive reasoning?

Back

Inductive reasoning is a method of reasoning in which a general conclusion is drawn from specific examples or patterns. It involves observing patterns and making conjectures based on those observations.

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What is a conjecture?

Back

A conjecture is a statement or proposition that is believed to be true based on observations but has not yet been proven.

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What is a counterexample?

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A counterexample is an example that disproves a conjecture or statement. It shows that the statement is not universally true.

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How do you identify a pattern in a sequence of numbers?

Back

To identify a pattern, look for consistent differences or ratios between consecutive numbers. This can involve addition, subtraction, multiplication, or division.

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What is the next number in the sequence: 12, 17, 22, 27, ___?

Back

32 (the pattern is adding 5 each time).

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What is the next number in the sequence: 23, 33, ___, 53, ___?

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43, 63 (the pattern is adding 10 each time).

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What does it mean for two angles to be supplementary?

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Two angles are supplementary if their measures add up to 180 degrees.

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Provide a counterexample to the claim: 'If two angles are supplementary, then they are not congruent.'

Back

90° and 90° (both angles are congruent and add up to 180°).

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What is the conjecture about the sequence: –2, 4, –8, 16, –32, ...?

Back

Multiply the previous number by -2.

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What is the difference between inductive and deductive reasoning?

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Inductive reasoning involves making generalizations based on specific observations, while deductive reasoning involves applying general principles to reach specific conclusions.