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

Front

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.

Front

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.

Front

What is a counterexample?

Back

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

Front

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.

Tags

CCSS.HSF.BF.A.2

Front

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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CCSS.3.OA.D.9

Front

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

Back

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

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CCSS.3.OA.D.9

Front

What does it mean for two angles to be supplementary?

Back

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

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CCSS.7.G.B.5

Front

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°).

Tags

CCSS.7.G.B.5

Front

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

Back

Multiply the previous number by -2.

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CCSS.HSF.BF.A.2

Front

What is the difference between inductive and deductive reasoning?

Back

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

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CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1