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Use Inductive Reasoning Lesson 4.2 Page 197

Use Inductive Reasoning Lesson 4.2 Page 197. Apply Deductive Reasoning Lesson 4.4 Page 211. Lesson 4.2. *The goal is to be able to describe patterns and use inductive reasoning. Vocabulary : A conjecture is an unproven statement that is based on observations.

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Use Inductive Reasoning Lesson 4.2 Page 197

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  1. Use Inductive ReasoningLesson 4.2Page 197 Apply Deductive Reasoning Lesson 4.4 Page 211

  2. Lesson 4.2 *The goal is to be able to describe patterns and use inductive reasoning. Vocabulary: • A conjecture is an unproven statement that is based on observations. • You use inductive reasoning when you find a pattern in specific cases and then write a conjecture for the general case.

  3. Example Describe a pattern in the numbers. Write the next number in the pattern. Solution: Add consecutive integers to each term, starting with 2; 24.

  4. Lesson 4.4 *The goal of this lesson is to use deductive reasoning to form a logical argument. Vocabulary: • Deductive reasoning uses facts, definitions, accepted properties, and the laws of logic to form a logical argument. • Law of Detachment: If the hypothesis of a true conditional statement is true, then the conclusion is also true.

  5. Law of Syllogism: If hypothesis p, then conclusion q. If hypothesis q, then conclusion r. If hypothesis p, then conclusion r.

  6. Example #1 Decide whether inductive or deductive reasoning is used to reach the conclusion. Explain your reasoning. You diet for 3 weeks and lose 3 pounds. You conclude that you can lose 20 more pounds in the next 20 weeks. Solution: Inductive; the conclusion is a conjecture based on your specific results from the first 3 weeks.

  7. Example #2 You use the rise of 8.1 and the run of 2.7 between two points on a line in the coordinate plane to conclude that the slope of the line is 3. Solution: Deductive; you calculated the actual slope using the slope formula.

  8. Homework Assignment: From Lesson 4.2 Page 199 # 5 – 13 From Lesson 4.4 Page 213 # 1 – 9

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