1.1 Patterns and Inductive Reasoning
August 19, 2009
1­1 Patterns and Inductive Reasoning
Objective
Use inductive reasoning to make conjectures.
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1.1 Patterns and Inductive Reasoning
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1.1 Patterns and Inductive Reasoning
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Which do you think describes the square of any odd number?
It is odd.
Correct
Incorrect
HOW DO YOU KNOW?
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1.1 Patterns and Inductive Reasoning
August 19, 2009
Reasoning based on patterns that you observe is called
INDUCTIVE REASONING.
Find a pattern for this sequence.
Find the next two terms in the sequence.
3 6 12 24...
48 96
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1.1 Patterns and Inductive Reasoning
August 19, 2009
A conclusion you reach using inductive reasoning is called a
CONJECTURE.
Make a conjecture about the sum of the first 30 odd numbers.
Step 1: Find the first few sums.
Step 3: Make a conclusion.
1 = 1 + 3 =
1 + 3 + 5 =
1 + 3 + 5 + 7 =
The sum of the first 30
odd numbers is
302 or 900.
Step 2: Find a pattern.
1 = 1 = 12 1 + 3 = 4 = 22
1 + 3 + 5 = 9 = 32
1 + 3 + 5 + 7 = 16 = 42
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1.1 Patterns and Inductive Reasoning
August 19, 2009
Not all conjectures turn out to be true!
You can prove that a conjecture is false by
finding one COUNTEREXAMPLE.
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1.1 Patterns and Inductive Reasoning
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Find a counterexample that makes these conjectures false:
The square of any number is greater than the original number.
Any number and its absolute value are opposites.
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1.1 Patterns and Inductive Reasoning
August 19, 2009
HOMEWORK
p. 6 # 1­6, 17­18, 19­22, 25­26, 51, 52
CHALLENGE #54
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