TechMathI - 2.1

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TechMathI - 2.1

  1. 1. INDUCTIVE REASONING We reason inductively when we reach a conclusion based on the observation of some pattern
  2. 2. 16 feet Rapunzel lives in a tower. Her window is 16 feet above the ground.
  3. 4. Rapunzel, Rapunzel let down thy hair!
  4. 5. It took exactly one second for the rabbit to land
  5. 6. The next night, the prince tries again.
  6. 8. Rapunzel, Rapunzel let down thy hair!
  7. 9. It took exactly one second for the rabbit to land
  8. 10. The next night, the prince tries again.
  9. 12. Rapunzel, Rapunzel let down thy hair!
  10. 13. It took exactly one second for the rabbit to land
  11. 14. The same thing happens every night for two weeks… finally...
  12. 16. Rapunzel, Rapunzel let down thy hair!
  13. 17. Yet again, it took exactly one second for the rabbit to fall the 16 feet from Rapunzel’s window!
  14. 18. Using my amazing powers of INDUCTIVE REASONING I conclude that a rabbit under the influence of gravity falls 16 feet in one second.
  15. 19. Finally becoming weary of Rapunzel and her rabbits, the prince decides to seek bunnies elsewhere
  16. 20. YE OLDE BUNNY INN
  17. 21. END OF TALE
  18. 22. Laws of science are derived using INDUCTIVE REASONING - they are conclusions drawn from the patterns we observe in nature Consider one more example of inductive reasoning
  19. 23. ? The sum of the first ten odd counting numbers
  20. 24. The sum of the first ten odd counting numbers Sum of the first 2 = 2x2 Sum of the first 3 = 3x3 Sum of the first 5 = 5x5 Sum of the first 4 = 4x4
  21. 25. The sum of the first ten odd counting numbers Sum of the first 2 = 2x2 Sum of the first 3 = 3x3 Sum of the first 5 = 5x5 Sum of the first 4 = 4x4 If you observe the pattern, and conclude that the sum of the first 10 odd counting numbers is 10x10 then you are using inductive reasoning!
  22. 26. Inductive reasoning does not always yield a true conclusion. Based on observation and experience, some ancient people concluded that the sun revolved about the earth.
  23. 27. <ul><li>Inductive Reasoning: </li></ul><ul><li>Observing Data </li></ul><ul><li>Recognizing Patterns </li></ul><ul><li>Making conclusions from your observations </li></ul>
  24. 28. Students in a science class are instructed to sprinkle salt into a Bunsen burner flame. Each time salt is sprinkled into the flame, the flame turns yellow. What assumption should the class make from their observations? The class decides that the salt always burns with a yellow flame.
  25. 29. An auto assembly plant can produce a maximum of 300 cars per day. A production line technician observes that during the first three hours of a production day the number of cars coming off the assembly line double each hour. Hours 1 2 3 4 … Cars 10 20 40 ? … Make a observation about the 4 th hour. What about the 10 th hour?
  26. 30. Use inductive reasoning to find the next two terms in each sequence of numbers. 1, 5, 9, … -12, -5, 2, …
  27. 31. Give a counter example to show that each statement is false. If a number is divisible by 2, then it is divisible by 4. If x + 1 > 0, then x is positive.
  28. 32. Homework Inductive Reasoning WS

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