Inductive and Deductive reasoning Learning Object #1.
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Transcript of 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
Inductive Reasoning #1
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 =
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 #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.