Inductivereasoning and deductive 2013

GT Geometry Drill10/3/13

1. What are the next two terms in the sequence?

1, 4, 9, 16...

2. Write a counterexample for the following statement:

For any number m, 3m is odd.

Accept the two statements as given information. State the conclusion based on

the information.• 1. AB is longer than BC; BC is

longer than CD• 2. 12 is greater than integer M.

M is greater than 8• 3. 4x + 6 = 14, then x =?

Use inductive and deductive reasoning to identify patterns and make conjectures.

Find counterexamples to disprove conjectures.

Objectives

Find the next item in the pattern.

Example 1A: Identifying a Pattern

January, March, May, ...

The next month is July.

Alternating months of the year make up the pattern.

Find the next item in the pattern.

Example 1B: Identifying a Pattern

7, 14, 21, 28, …

The next multiple is 35.

Multiples of 7 make up the pattern.

Find the next item in the pattern.

Example 1C: Identifying a Pattern

In this pattern, the figure rotates 90° counter-clockwise each time.

The next figure is .

Check It Out! Example 1

Find the next item in the pattern 0.4, 0.04, 0.004, …

When reading the pattern from left to right, the next item in the pattern has one more zero after the decimal point.

The next item would have 3 zeros after the decimal point, or 0.0004.

When several examples form a pattern and you assume the pattern will continue, you are applying inductive reasoning. Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true. You may use inductive reasoning to draw a conclusion from a pattern. A statement you believe to be true based on inductive reasoning is called a conjecture.

Deductive reasoning is the process of using logic to draw conclusions from given facts, definitions, and properties.