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

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.

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

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

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

32 (the pattern is adding 5 each time).

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

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

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

Multiply the previous number by -2.

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