Objective To recognize patterns and to use variables to describe patterns.

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Objective- To recognize patterns and to use
variables to describe patterns.
Pattern- a general idea for which there Are many
examples or instances.
2(3) 8 3 3 8
2(4) 8 4 4 8
Instances
Pattern
2(5) 8 5 5 8
2(6) 8 6 6 8
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Constants
2(3) 8 3 3 8
2(4) 8 4 4 8
2(5) 8 5 5 8
2(6) 8 6 6 8
Variables
Which numbers are held fixed?
These are constants.
Which numbers change or vary?
These are variables.
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Constants
2(3) 8 3 3 8
2(4) 8 4 4 8
2(5) 8 5 5 8
2(6) 8 6 6 8
Variables
The pattern above could be described using a
variable.
2(x) 8 x x 8
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Sometimes it is necessary to use more than one
variable to describe a pattern.
Adults are charged more than children for
certain activities.
Activity A Adult fee C Child fee
Movie 7 4 Boat Ride 10
4 Miniature 4
2.50 Golf
T Total Cost 2(7) 3(4) 2(10)
3(4) 2(4) 3(2.50)
Find the cost of each for a family of 2 adults
and 3 children?
Write an equation for the total cost in terms of
A and C.
T 2A 3C
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Some patterns may be true under some instances
but not always.
2
0 0 0 2 2 2
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Does n n n always?
No, there are many values of n which prove this
statement false like n 5.
5 5 5 .
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Counterexample- an instance which shows that a
rule for a pattern is false.