Transcript Inductive Reasoning

Inductive Reasoning
Geometry
Week 1 of 9
Unit 1: Logic & Reasoning
8/31 & 9/1
Standards & Vocabulary
Standard 1.0
Students demonstrate understanding by
identifying and giving examples of undefined
terms, axioms, theorems, and inductive and
deductive reasoning.
Standard 3.0
Students construct and judge the validity of a
logical argument and give counterexamples to
disprove a statement.
Vocabulary
Inductive Reasoning
Conjecture
Counterexample
Inductive Reasoning – “Bottom Up”
4. Theory
ALL shirts at this
store are 20% off.
3. Tentative
Hypothesis
It seems like shirts are
20% off at this store.
2. Pattern
Another shirt is on sale,
from $30 to $24. That is
also 20% off.
1. Observation
A shirt is on sale. It was
$20, but after 20% off,
is only $16.
What Comes Next? - Inductive Reasoning
Description: In groups of 2 to 4, create your
own patterns using action, rhythm,
letters/words, numbers or pictures. The
class has to guess what is to come next in
the pattern.
Example: (Hey, Ho, Hey, Ho, __)
(5, 10, 15, 20, _ , _ , _)
Purpose: This activity is used to determine
that students already use inductive
reasoning.
Vocabulary Defined
Inductive Reasoning –
reasoning that
is based on continuing patterns you
observe
[Induce – to determine, based on a number
of particular facts]
Conjecture –
a conclusion you reach using
inductive reasoning (seem likely, but
unproven)
Counterexample –
an example for which
the conjecture is incorrect. It only takes
one counterexample to prove the
conjecture incorrect.
More Practice…
 Find a Pattern For Each Sequence.
3, 6, 12, 24,…
1, 2, 4, 7, 11, 16, 22,…
AL, AK, AZ, AR,…
Derek, Kobe, Ron,…
Red, Orange, Yellow, Green,…
Counterexamples
X=X·X
X=0
0=
X=1
1=
However…
X=2
2≠
X=3
3≠
…and so on…
0·0
1·1
True
True
2·2
3·3
False
False
More Counterexamples
Find a counterexample for
each conjecture:
a) The square of any number is
greater than the original
number.
b) You can connect any three
points to form a triangle.