1 LESSON 1.1 PATTERNS AND INDUCTIVE REASONING

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

3 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

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

5

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

7 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 , 3, 8, 15, 24,... add 3, then, 5, then 7,... 35

8 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 a 2 - b 2

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