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Section 2- 1: Patterns and Inductive Reasoning

Section 2- 1: Patterns and Inductive Reasoning. Objectives: Use inductive reasoning to make conjectures. Vocabulary. Inductive Reasoning . Reasoning based on patterns you observe Assumes that a observed pattern will continue. Conjecture.

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Section 2- 1: Patterns and Inductive Reasoning

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  1. Section 2-1: Patterns and Inductive Reasoning • Objectives: • Use inductive reasoning to make conjectures Vocabulary Inductive Reasoning • Reasoning based on patterns you observe • Assumes that a observed pattern will continue Conjecture • Conclusion reached through inductive reasoning Counter Example • Example for which the conjecture is incorrect

  2. Use Inductive Reasoning to Find a Pattern What are the next two terms in the sequence: 3, 6, 12, 24, ___, ___ 96 48 Draw the next two figures in the pattern. Each circle has one more segment through the center to form equal parts.

  3. Do Now Making Conjectures Make a conjecture about the sum of the first 30 odd numbers. NOTE: Find the first few sums and look for a pattern. 1= 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7+ 9= 25 = 12 = 22 = 32 = 42 = 52 Notice that each sum is a perfect square and that the perfect squares form a pattern. Using inductive reasoning, you can conclude that the sum of the first 30 odd numbers is 302 or 900.

  4. Examine a Counterexample Find one counterexample to show that the conjecture below is false. “The sum of two numbers is always greater than either number.” Notice the statement does not specify if the numbers are positive or negative. Counterexample is: 5 + (-6) = -1

  5. Do Now Write the data in a table. Find a pattern. 2000 2001 2002 $8.00 $9.50 $11.00 Inductive Reasoning used in the Real-World The price of overnight shipping was $8.00 in 2000, $9.50 in 2001, and $11.00 in 2002. Make a conjecture about the price in 2003. Each year the price increased by $1.50. A possible conjecture is that the price in 2003 will increase by $1.50. If so, the price in 2003 would be $11.00 + $1.50 = $12.50.

  6. Do Now Inductive Reasoning used in the Real-World A skateboard shop finds that over a period of five consecutive months, sales of small-wheeled skateboards decreased. 1. Use inductive reasoning to make a conjecture about the number of skateboards the shop will sell in June. Approximately 43 skateboards will be sold in June. (Decrease of 4 per month) 2. Make a conjecture about the number of skateboards the shop will sell in July. Approximately 39 skateboards will be sold in June. 3. How confident would you be in using the graph to make a conjecture about the sales in December? Explain.

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