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

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.

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

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

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 + 5 = 5 . 2 Counterexample- an instance which shows that a rule for a pattern is false.