Download - Inductivereasoning and deductive 2013
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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.
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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 =?
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Use inductive and deductive reasoning to identify patterns and make conjectures.
Find counterexamples to disprove conjectures.
Objectives
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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.
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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.
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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 .
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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.
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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.
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Deductive reasoning is the process of using logic to draw conclusions from given facts, definitions, and properties.
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