PATTERNS AND INDUCTIVE REASONING

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Presentation transcript:

PATTERNS AND INDUCTIVE REASONING LESSON 1.1 PATTERNS AND INDUCTIVE REASONING

Objectives To find and describe patterns. To use inductive reasoning to make conjectures.

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

Describing a visual pattern: Sketch the next figure in the pattern. Describe the pattern.

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

Describe a pattern in the sequence of numbers. Predict the next number. -3 Subtracting 2 from previous number. 1) 5, 3, 1, -1, . . . 2) 1, -4, 9, -16, . 3) 25 These are perfect squares with alternating signs. 1 The denominators are being multiplied by 2. 16

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

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 _____. 8 a2 - b2

Show the conjecture is false by finding a counterexample. Conjecture: All odd numbers are prime. 9