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Suppose you are the director of the soccer league for the City Park Summer Programs.  In this league, each team plays every other team once before the playoffs, so the number of games to be scheduled (not including playoff games) depends upon how many teams are allowed in the league.  Your immediate task is to investigate how many games would be played altogether, based on the number of teams in the league.  For example, in a league with two teams, only one game would be played.  How about a league with three teams? Four teams?

1.  To get a feel for the numbers involved, do some calculations.  It will be helpful for you to record your findings in a table.  It may also be helpful to think of ways to draw diagrams to model the situation.

2.  Make a graph by plotting the data points from your table.  Does it make sense to connect the points together?  Why or why not?

3.  What type of relationship do you think there is between the number of teams and the number of games played?

4.  How can you use the table and graph to obtain more data points without doing the types if calculations you did in #1?

5.  If there are n  teams in the league, find a formula for the number of games needed.  Explain how you found this formular.

6.  Use your formula to calculate the number of teams that can be in the league if the maximum number of games you can schedule is 120.  Can you find this same information in the table and/ or graph?  If not, can you use the table or graph to predict the answer?