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Use Inductive Reasoning Lesson 4.2 Page 197

Enhance your ability to describe patterns using inductive reasoning and form logical arguments with deductive reasoning. Practice forming conjectures from observations and utilizing facts, definitions, and logic laws. Improve skills in recognizing patterns, writing conjectures, and constructing logical arguments.

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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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