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LESSON 1.1

PATTERNS AND INDUCTIVE REASONING

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ObjectivesTo find and describe patterns.

To use inductive reasoning to make conjectures.

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Vocabulary A__________________ is an

unproven statement that is based on observations.

______________________________is a process that involves looking for patterns and making conjectures.

A ___________________________is an example that shows a conjecture is false.

conjecture

Inductive Reasoning

counterexample

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Describing a visual pattern: Sketch the next figure in the

pattern. Describe the pattern.

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Sketch the next figure in the pattern. Describe the pattern.

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Describe a pattern in the sequence of numbers. Predict the

next number. 1) 5, 3, 1, -1, . . .

2) 1, -4, 9, -16, .

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-3 Subtracting 2 from previous number.

25 These are perfect squares with alternating signs.

1 The denominators are being multiplied by 2.

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See if you can use the patterns to make a prediction… Describe the pattern in the sequence of

numbers. Predict the next number. 2. 1, 2, 6, 24, . . . multiply by consecutive numbers 120 3. 0, 3, 8, 15, 24, . . . add 3, then, 5, then 7, . . . 35

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Complete the conjecture. (list specific examples and look for a pattern.)

Conjecture: The product of two consecutive even integers is divisible by _____.

Conjecture: For any two numbers a and b, the product of (a +b) and (a - b) is always equal to _____.

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a2 - b2

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Show the conjecture is false by finding a counterexample.

Conjecture: All odd numbers are prime.

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