Transcript Inductive Reasoning

What is a pattern?
“Like the color of my skin,
Or the day that I grow old,
My life is made of
patterns
That can scarcely be
controlled.”
- Paul Simon
1.1 Inductive Reasoning
Definition: Inductive reasoning is
making conjectures (predictions)
based on a pattern you observe.
Conjectures
What is the sum of the first n odd numbers?
1=1
1+3=4
1+3+5=9
1 + 3 + 5 + 7 = 16
1+3+5+…=?
1st n odds
Do you see a pattern?
Conjecture: The sum of the first n odd
numbers is n2
True or False?
All prime numbers are odd.
FALSE!
Counterexample:
2 is prime but it is even,
not odd.
True or False?
If you multiply two numbers and
you get an even number, then
the two numbers must both be
even.
FALSE!
Counterexample: 2 x 3 = 6.
6 is even, but 3 is odd.
Question
How do you show that a conjecture
is false?
Give a counterexample.
Vocabulary
1. Inductive reasoning
2. Conjecture
3. Counterexample
Practice Problems with Patterns
1. Think: Think about the answer. Try to do
it on your own, in your notes.
2. Pair: Compare answers with your
partner.
3. Square: Agree on the answer with your
group and write it on the white board.
4. Share: Hold up your group white board.
•
•
•
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Think: Think
about the
answer. Try to do
it on your own.
Pair: Compare
answers with
your partner.
Square: Agree
on the answer
with your group
and write it on
the white board.
Share: Hold up
your group white
board.
•
•
•
•
Think
Pair
Square
Share
Summaries
• Highlight 3 to 5 key words in your
notes.
• Write a summary using all 3, 4, or
5 key words.
• Summaries may be a part of your
notebook quiz!
1.1 Notes
Absent Students
1.1 Inductive Reasoning
Definition: Inductive reasoning is
making conjectures (predictions)
based on a pattern you observe.
Conjectures
What is the sum of the first n odd numbers?
1=1
1+3=4
1+3+5=9
1 + 3 + 5 + 7 = 16
1+3+5+…=?
1st n odds
Do you see a pattern?
Conjecture: The sum of the first n odd
numbers is n2
True or False?
All prime numbers are odd.
FALSE!
Counterexample:
2 is prime but it is even,
not odd.
Question
How do you show that a conjecture
is false?
Give a counterexample.