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Inductive and Deductive reasoning

Inductive and Deductive reasoning. Learning Object #1. Inductive Reasoning #1. What patterns do you notice?. Inductive Reasoning #1. What patterns hold?. Inductive Reasoning #1. Will this pattern continue forever? How do you know? 9 x 12 456. Inductive Reasoning #1.

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Inductive and Deductive reasoning

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  1. Inductive and Deductive reasoning Learning Object #1

  2. Inductive Reasoning #1 What patterns do you notice?

  3. Inductive Reasoning #1 What patterns hold?

  4. Inductive Reasoning #1 • Will this pattern continue forever? How do you know? 9 x 12 456

  5. Inductive Reasoning #1 Conjecture: The successive sums of the digits in any multiple of 9 will ultimately equal 9. Prove whether the statement above is true or false.

  6. Inductive Reasoning #2 • When do you have enough information to form a conjecture? • What comes next?

  7. Inductive Reasoning #2

  8. Inductive Reasoning #2

  9. Inductive Reasoning #2

  10. Inductive Reasoning #2 • Conjecture: • How would you prove your conjecture?

  11. Inductive Reasoning • The previous examples drew on your inductive reasoning skills. With a partner, discuss the concept of inductive reasoning. Together, create a one sentence description of Inductive reasoning.

  12. Critique the Statement Decisions can be made and actions taken based upon inductive reasoning

  13. Deductive Reasoning #1 At school, Kim, Terry, Robyn, and Dale all enjoy different subjects. • Terry likes Phys. Ed. and always carries gym clothes. • Neither Kim nor Dale particularly like Science class. • Neither Terry nor Kim like math although Kim gets good marks in Math. Can you match these people with their favourite subjects - Math, Science, Phys. Ed., and English? MathCatchers, January 2012, http://www.saskschools.ca/curr_content/mathcatch/index.html

  14. Deductive Reasoning #2 Assuming the statements true, what conclusions can be made? All oranges are fruitsAll fruits grow on treesTherefore, ___________________

  15. Deductive Reasoning #2 All men are mammals, John is a man, Therefore, ______________ All students love math, You are a student, Therefore, _______________

  16. Syllogisms – Valid or Not? All snakes are cold-blooded, All snails are cold-blooded, All snakes are snails. All rectangles are quadrilaterals, All squares are rectangles, All squares are rectangles.

  17. Syllogisms – Valid or Not? All students have pencils I do not have a pencil I am not a student All parallelograms are quadrilaterals All quadrilaterals are polygons All parallelograms are polygons

  18. Syllogisms – Valid or Not? 3 + 5 = 8 8 = 2 + 6 3 + 5 = 2 + 6 All triangles are polygons, A square is not a triangle, A square is not a polygon.

  19. Deductive #3 Conjecture: A number that is divisible by 6 is also divisible by both 2 and by 3. Necessary fact – If a number x is divisible by 2, it can be written as 2n.

  20. Inductive or Deductive? Known Fact: The cut-off date for the early-bird discount for camp registration is January 15. After that date, campers must pay full price. Known Fact: You are mailing your registration form in on January 23rd. Conclusion: You must pay full price.

  21. Inductive or Deductive? Observation: Lauren is seen purchasing a Koboo Touch. Observation: Lauren’s daughter loves to read and it is her birthday on the week-end. Conclusion: Lauren has purchased a Koboo for her daughter.

  22. Deductive Reasoning • With a partner, discuss the concept of deductive reasoning. Together, create a one sentence description of deductive reasoning.

  23. To Hand In Reflection: Which method of reasoning is more useful to the average person, inductive or deductive? * In your answer, you must completely describe the meaning of both inductive and deductive and highlight the differences between the two.

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