Inductive and Deductive reasoning Learning Object #1.

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Presentation transcript:

Inductive and Deductive reasoning Learning Object #1

Inductive Reasoning #1 What patterns do you notice? 1 x 9 = 96 x 9 = 54 2 x 9 = 187 x 9 = 63 3 x 9 = 278 x 9 = 72 4 x 9 = 369 x 9 = 81 5 x 9 = 459 x 10 = 90

Inductive Reasoning #1 What patterns hold? 1 x 9 = 99 x 11 = 99 2 x 9 = 189 x 12 = 3 x 9 = 279 x 13 = 4 x 9 = 369 x 14 = 5 x 9 = 459 x 15 = 6 x 9 = 549 x 16 = 7 x 9 = 639 x 17 = 8 x 9 = 729 x 18 = 9 x 9 = 819 x 19 = 9 x 10 = 909 x 20 =

Inductive Reasoning #1 O Will this pattern continue forever? How do you know? 9 x

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.

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

Inductive Reasoning #2

O Conjecture: O How would you prove your conjecture?

Inductive Reasoning O 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.

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

Deductive Reasoning #1 At school, Kim, Terry, Robyn, and Dale all enjoy different subjects. O Terry likes Phys. Ed. and always carries gym clothes. O Neither Kim nor Dale particularly like Science class. O 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,

Deductive Reasoning #2 Assuming the statements true, what conclusions can be made? All oranges are fruits All fruits grow on trees Therefore, ___________________

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

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.

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

Syllogisms – Valid or Not? = 8 8 = = All triangles are polygons, A square is not a triangle, A square is not a polygon.

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.

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 23 rd. Conclusion: You must pay full price.

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.

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

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.