Inductive and Deductive reasoning Learning Object #1

Inductive and Deductive reasoning

Learning Object #1

Inductive Reasoning #1

What patterns do you notice?

1 x 9 = 9 6 x 9 = 54

2 x 9 = 18 7 x 9 = 63

3 x 9 = 27 8 x 9 = 72

4 x 9 = 36 9 x 9 = 81

5 x 9 = 45 9 x 10 = 90


What patterns hold?1 x 9 = 9 9 x 11 = 99

2 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 =


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

9 x 12 456


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.


O When do you have enough information to form a conjecture?

O What comes next?





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


Assuming the statements true, what conclusions can be made?

All oranges are fruitsAll fruits grow on treesTherefore, ___________________


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.


All students have pencilsI do not have a pencilI am not a student

All parallelograms are quadrilateralsAll quadrilaterals are polygonsAll parallelograms are polygons


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 #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 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 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.

Documents

Inductive and Deductive reasoning Learning Object #1