Inductive reasoning, conjectures, & 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.

Front

Define a conjecture in the context of mathematics.

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 by showing that it is not always true.

Front

How can you prove a conjecture is false?

Back

You can prove a conjecture is false by providing a counterexample.

Front

What is the relationship between supplementary angles?

Back

Supplementary angles are two angles whose measures add up to 180 degrees.

Front

Give an example of two supplementary angles that are congruent.

Back

90 degrees and 90 degrees are supplementary angles that are also congruent.

Front

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

Back

The next two numbers are 32 and 37.

Front

What pattern do you observe in the sequence: 12, 17, 22, 27?

Back

The pattern is that each number increases by 5.

Front

How do you make a conjecture about a sequence?

Back

To make a conjecture about a sequence, analyze the pattern of the numbers and predict the next number(s) based on that pattern.

Front

What is the next item in the sequence: -4, -1, 2, 5, 8?

Back

The next item is 11, as you add 3 to the previous number.