Download Inductive Reasoning and Patterns

Welcome to Geometry
Objective: Use inductive reasoning to
make conjectures, use inductive
reasoning in number/picture patterns
Problem
Mrs. Magers has given her Geometry
class a pop quiz every Tuesday for
the past 3 weeks. On Monday
afternoon, Natalie told Imari to go
home and study her Geometry notes.
Why?
Inductive Reasoning
and Patterns
 Inductive Reasoning is reasoning
based on observed patterns. (We
assume the observed pattern will continue.
This may or may not be true.)
 A conjecture is a conclusion reached
through inductive reasoning.
(Remember, the conjecture seems likely, but
it is unproven)
 A single counter-example is enough to
disprove a conjecture.
 Example
Conjecture: The difference of two integers is less
than either integer.
6-4 = 2
10-7 =3
Can you find a counterexample?
8-(-15) = 23
Given the pattern _____, -6, 12, _____, 48, …
 a. Fill in the missing numbers.
 b. Determine the next two numbers in this
sequence.
 c. Describe how you determined what
numbers completed the sequence. Be sure
to explain your reasoning.
 d. Are there any other numbers that would
complete this sequence? Explain your
reasoning.
Ex: Find the next two terms and indicate the
process for generating the next term.
49
64
1) 1, 4, 9, 16, 25, 36, ___,
___
127
255
2) 1, 3, 7, 15, 31, 63, ___,
___
3) What figure comes next?
Closure
 Inductive reasoning
 Conjecture
 Counterexample
homework
 p.6-8 #12-30, 34-37, 43