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2.1 Inductive Reasoning and Conjecture

2.1 Inductive Reasoning and Conjecture. Objectives. Make conjectures based on inductive reasoning Find counterexamples. Making Conjectures. Conjecture – an educated guess Inductive Reasoning – using observations to make a conjecture. × 2. × 3. × 4. × 5.

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2.1 Inductive Reasoning and Conjecture

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  1. 2.1 Inductive Reasoning and Conjecture

  2. Objectives • Make conjectures based on inductive reasoning • Find counterexamples

  3. Making Conjectures • Conjecture– an educated guess • Inductive Reasoning – using observations to make a conjecture

  4. ×2 ×3 ×4 ×5 Conjecture: The next number will be multiplied by 6. So, it will be or 1440. Example 1: Make a conjecture about the next number based on the pattern. 2, 4, 12, 48, 240 Find a pattern: 2 4 12 48 240 The numbers are multiplied by 2, 3, 4, and 5. Answer: 1440

  5. Make a conjecture about the next number based on the pattern. Answer: The next number will be Your Turn:

  6. For points L,M,and N,and,make a conjecture and draw a figure to illustrate your conjecture. Example 2: Conjecture:L, M, and N are collinear.

  7. ACE is a right triangle with Make a conjecture and draw a figure to illustrate your conjecture. Your Turn:

  8. Counterexamples • Providing evidence a conjecture false is a counterexample.

  9. Example 3: UNEMPLOYMENT Based on the table showing unemployment rates for various cities in Kansas, find a counterexample for the following statement. The unemployment rate is highest in the cities with the most people. Source: Labor Market Information Services–Kansas Department of Human Resources

  10. Your Turn Find the counterexample: The greater the population of a state, the lower the number of drivers per 1000 residents.

  11. Assignment • Geo WB, pgs. 20-22

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