2.1 Patterns and Inductive Reasoning

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What is a counterexample?

Back

A counterexample is an example that disproves a statement or conjecture.

Tags

CCSS.HSS.CP.A.5

CCSS.HSS.CP.A.3

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What does it mean for a number to be divisible by another number?

Back

A number A is divisible by a number B if there exists an integer C such that A = B * C.

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CCSS.5.OA.B.3

Front

Provide an example of a number that is divisible by 2 but not by 4.

Back

An example is 2, since 2 is divisible by 2 but not by 4.

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CCSS.3.OA.D.9

Front

What is a conjecture in mathematics?

Back

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

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CCSS.6.SP.A.3

Front

What is the sum of two even numbers?

Back

The sum of two even numbers is always even.

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CCSS.3.OA.D.9

Front

What is the product of two odd numbers?

Back

The product of two odd numbers is always odd.

Tags

CCSS.3.OA.D.9

Front

What is a linear pair of angles?

Back

A linear pair of angles are two adjacent angles whose non-common sides form a straight line.

Tags

CCSS.7.G.B.5

Front

Back

They are supplementary angles.

Tags

CCSS.7.G.B.5

Front

What is an example of a false conjecture?

Back

The conjecture 'The sum of two odd numbers is even' is false; it is actually odd.

Front

What is inductive reasoning?

Back

Inductive reasoning is a method of reasoning in which a general conclusion is drawn from specific examples.

Tags

CCSS.HSS.IC.B.3