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2.1 Notes: Use Inductive Reasoning
Word
Conjecture
Definition
An ____________
statement based on
________________
Inductive Reasoning
Find a ___________ in ____________ cases and then write a
________________ for the _____________ case
______________ → ________________
Is a conjecture TRUE or FALSE?
TRUE
Counterexample
FALSE
Show it is true for _________
cases
Find _____
____________________
Sketch the next figure in the pattern.
Pattern
Next Figure
A __________ case for which the
conjecture is __________
Pattern
Next Figure
Describe a pattern in the numbers. Write the next number in the pattern.
Numbers
5, 10, 15, 20, …
80, 40, 20, 10, …
1, 4, 9, 16, 25, …
7, 3, -1, -5, -9, …
1, -2, 3, -4, 5, -6, …
+5 each
time
/2 each
time
Perfect
squares
-4 each
time
Increase #
by one &
switch sign
25
5
36
-13
7
Pattern
Next #
Complete the following table. Then complete the conjectures that follow.
Pair of odd #s
1,3
3,5
5,7
Sum of the #s
Average of #s
(Divide Sum by 2)
Conjectures:
4
2
8
4
7,9
9,11
12
6
16
20
8
10
The sum of any 2 consecutive odd integers is always Even (Multiple of 4)
The average of any 2 consecutive odd integers is
Even (# between odd #s)
Make and test a conjecture about the product of any two odd numbers.
Find a pattern using at least a few groups of small Write your conjecture
numbers.
1*3=3 The product of any two odd numbers is
3*5=15
7*1=7
5*9=45
Odd
Test your conjecture
using other numbers.
-9*3=-27
11*9=99
Numbers such as 3, 4, and 5 are called consecutive integers. Make and test a conjecture about the sum
of any three consecutive integers.
Find a pattern using at least a few groups of small Write your conjecture
Test your conjecture
numbers.
using other numbers.
The
sum
of
any
three
consecutive
3+4+5=12
10+11+12=33
integers is
1+2+3=6
6+7+8=21
4+5+6=15
-1+0+1=0
3*middle #
Show the conjecture is false by finding a counterexample.
Statement
Any 4-sided
The average of
We don’t have
polygon is a
any 2 even #s is
schools on
square
an even #
holidays
Counterexample
Statement
2&4
Desks are
arranged in a grid
like pattern
We have
school on
Halloween
The blinds are
always open in
Mrs. B’s room
The square of an
integer is a
positive integer
Counterexample The desks in this The blinds
room are going
were closed
in different
last night
directions
HOMEWORK pg 75 #1-27 odds and 32-34 all
𝟎𝟐 = 𝟎
It is only cloudy
when it rains
It was cloudy
yesterday
without rain
The square root
of a # is always
less than that #
√𝟏 = 𝟏
All odd #s are
prime
9
All triangles are
equiangular