1 ­ Inductive Reasoning.notebook
December 02, 2011
Outcome 20.2­1 Demonstrate understanding of inductive and deductive reasoning
UNIT 1
Inductive and
Deductive
Reasoning
Level 2
Instructional
May 19­9:47 AM
Level 3
Independent
Level 4
Mastery
May 11­9:48 AM
If the first three colours in a sequence are red, orange, and yellow,
what colours might be found in the rest of the sequence? Explain.
Use reasoning to make predictions.
Pull
Pull
If the first three colours in a sequence are red, orange, and yellow,
what colours might be found in the rest of the sequence? Explain.
???
???
Apr 19­9:22 AM
Apr 19­9:22 AM
Georgia, a fabric artist, has been patterning with equilateral triangles.
Consider Georgia's conjecture about the following pattern:
Conjecture
I think Figure 10 in this
pattern will have 100
triangles, and all these
triangles will be congruent
to the triangle in Figure 1.
A testable expression that is
based on available evidence but
is not yet proved.
How did Georgia arrive at
this conjecture?
Apr 19­9:46 AM
Apr 19­9:29 AM
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1 ­ Inductive Reasoning.notebook
Inductive Reasoning
Drawing a general conclusion by observing
patterns and identifying properties in
specific examples.
December 02, 2011
Inductive Reasoning though is NOT proven beyond a shadow of a doubt. Unless you have observed EVERY possibility for the situation you are studying, you are unable to consider your conclusion a proof, it is only a theory.
In the investigation, how did Georgia use inductive reasoning to
develop her conjecture?
Apr 19­12:13 PM
Dec 2­1:57 PM
Example #2
Example #2
Complete the following:
Complete the following:
1 x 8 + 1 =
12 x 8 + 2 =
123 x 8 + 3 =
1234 x 8 + 4 =
1 x 8 + 1 =
12 x 8 + 2 =
123 x 8 + 3 =
1234 x 8 + 4 =
Does this continue?
May 19­9:57 AM
May 19­9:57 AM
Example #3
Example #3
The following shapes make a pattern:
The following shapes make a pattern:
May 19­9:59 AM
May 19­9:59 AM
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1 ­ Inductive Reasoning.notebook
Example #3
The following shapes make a pattern:
May 19­9:59 AM
How can you ensure you will win the game?
May 19­10:08 AM
Make a conjecture about the product of two odd integers.
December 02, 2011
Let's try a game. There are 20 stars on this page. One at a time, two players may remove 1 or 2 stars.
The person who removes the last star wins.
Discard Pile
May 19­10:06 AM
Make a conjecture about the product of two odd integers.
Apr 19­12:16 PM
Make a conjecture about the difference between consecutive perfect
squares.
Pull
Do you find the conjecture convincing? Why or why not?
Apr 19­12:16 PM
Apr 19­1:39 PM
3
1 ­ Inductive Reasoning.notebook
December 02, 2011
Make a conjecture about the difference between consecutive perfect
squares.
Key Idea
Inductive reasoning involves looking at specific examples. By observing
patterns and identifying properties in these examples, you may be able
to make a general conclusion, which you can state as a conjecture.
Need To Know
Is there more than one conjecture that could be made? How is it possible to
have two different conjectures about the same situation? Explain.
Apr 19­1:39 PM
*
*
A conjecture is based on evidence you have gathered
More support for a conjecture strengthens the conjecture,
but does not prove it.
Apr 19­1:41 PM
Assignment
Pages 12-14
#1-3, 6-11, 15,16
Dec 2­1:45 PM
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