2.1 Patterns/Inductive Reasoning

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Presentation transcript:

2.1 Patterns/Inductive Reasoning

2.1 Patterns/Inductive Reasoning

Vocabulary: Inductive Reasoning Conjecture Pattern Counterexample 2.1 Patterns/Inductive Reasoning

Provide the solutions! 2.1 Patterns/Inductive Reasoning

Now try to explain the patterns in words! Are you understanding? Now try to explain the patterns in words! 2.1 Patterns/Inductive Reasoning

Try it! 2.1 Patterns/Inductive Reasoning

Try it! 2.1 Patterns/Inductive Reasoning

2.1 Patterns/Inductive Reasoning

2.1 Patterns/Inductive Reasoning

2.1 Patterns/Inductive Reasoning

2.1 Patterns/Inductive Reasoning

Did you get it? The following questions are designed to help you determine if you understood today’s lesson. Be sure to talk to Mr. Torres if you missed more than you got right and you do not understand why the answers you had were wrong. 2.1 Patterns/Inductive Reasoning

1. Find a counterexample to show that the conjecture is false 1. Find a counterexample to show that the conjecture is false. Conjecture: The product of two positive numbers is greater than the sum of the two numbers. 3 and 5 2 and 2 A counterexample exists, but it is not shown above. There is no counterexample. The conjecture is true. Non-Response Grid 2.1 Patterns/Inductive Reasoning

2. Based on the pattern, what are the next two terms of the sequence 33, 972 39, 45 162, 972 33, 39 Non-Response Grid 2.1 Patterns/Inductive Reasoning

3. Based on the pattern, what is the next figure in the sequence? Non-Response Grid 2.1 Patterns/Inductive Reasoning

4. Based on the pattern, make a conjecture about the sum of the first 20 positive even numbers. = 1*2 2 + 4 6 2*3 2 + 4 + 6 12 3*4 2 + 4 + 6 + 8 20 4*5 2 + 4 + 6 + 8 + 10 30 5*6 The sum is 20*21 The sum is 19*20 The sum is 21*22 The sum is 20*20 Non-Response Grid 2.1 Patterns/Inductive Reasoning

39 words per minute 29 words per minute 35 words per minute 5. Alfred is practicing typing. The first time he tested himself, he could type 23 words per minute. After practicing for a week, he could type 26 words per minute. After two weeks he could type 29 words per minute. Based on this pattern, predict how fast Alfred will be able to type after 4 weeks of practice. 39 words per minute 29 words per minute 35 words per minute 32 words per minute Non-Response Grid 2.1 Patterns/Inductive Reasoning

Assignment 2-1 p.85 #6-36 even 2.1 Patterns/Inductive Reasoning