1. 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 =
2(4) + 8 =
Instances
Pattern
2(5) + 8 =
2(6) + 8 =

2. Constants
2(3) + 8 =
2(4) + 8 =
2(5) + 8 =
2(6) + 8 =
Variables
Which numbers are held fixed?
These are constants.
Which numbers change or vary?
These are variables.

3. Constants 2(3) + 8 = 3 + 3 + 8 2(4) + 8 = 4 + 4 + 8
2(5) + 8 =
2(6) + 8 =
Variables
The pattern above could be described using a variable.
2(x) + 8 = x + x + 8

4. 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
Miniature
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

5. 2 + 2 = 2 Some patterns may be true under some
instances but not always.
0 + 0 = 0
2 + 2 = 2 2 2 2
Does n + n = n always?
No, there are many values of n which prove
this statement false like n = 5.
= 5 . 2
Counterexample- an instance which shows that
a rule for a pattern is false.