Inductive and Deductive reasoning

Learning Object #1

Inductive Reasoning #1

What patterns do you notice?1 x 9 = 9 6 x 9 = 542 x 9 = 18 7 x 9 = 633 x 9 = 27 8 x 9 = 724 x 9 = 36 9 x 9 = 815 x 9 = 45 9 x 10 = 90

Inductive Reasoning #1What patterns hold?

1 x 9 = 9 9 x 11 = 992 x 9 = 18 9 x 12 =3 x 9 = 27 9 x 13 =4 x 9 = 36 9 x 14 =5 x 9 = 45 9 x 15 =6 x 9 = 54 9 x 16 =7 x 9 = 63 9 x 17 =8 x 9 = 72 9 x 18 =9 x 9 = 81 9 x 19 =9 x 10 = 90

9 x 20 =

Inductive Reasoning #1

O Will this pattern continue forever? How do you know?

9 x 12 456

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

Inductive Reasoning #2

Inductive Reasoning #2

Inductive Reasoning #2

O Conjecture:

O How would you prove your conjecture?

Inductive ReasoningO 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, http://www.saskschools.ca/curr_content/mathcatch/index.html

Deductive Reasoning #2

Assuming the statements true, what conclusions can be made?

All oranges are fruitsAll fruits grow on treesTherefore, ___________________

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 pencilsI do not have a pencilI am not a student

All parallelograms are quadrilateralsAll quadrilaterals are polygonsAll parallelograms are polygons

Syllogisms – Valid or Not?

3 + 5 = 88 = 2 + 63 + 5 = 2 + 6

All triangles are polygons,A square is not a triangle,A square is not a polygon.

Deductive #3Conjecture: 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 23rd.

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 ReasoningO With a partner, discuss the concept

of deductive reasoning. Together, create a one sentence description of deductive reasoning.

To Hand InReflection: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.