**This activity was developed by a
student or students at Mainland High School which is located in Daytona Beach, FL.
It is still a "work in progress" with editing and improvements yet to come.**

**The Student Council has asked you to organize a
single elimination bowling tournament as part of Winter Fun Week. Each team will consist
of four bowlers and there are 8 teams in the tournament. It will take about 25 minutes for
each round of the competition. Your job is to develop a playing schedule and a method to
record the progress of the competition.**

The 8 teams in the tournament are labeled Team A to Team H.

**Consider different ways you can determine the first
round of play**.

1. Suppose you begin with a team and have them play all of the other teams until they lose one game and are eliminated. Develop a schedule for this situation.

2. Explain why this method may not be fair to all of the teams in the tournament.

Suppose you decide to organize the competition based on the averages of each team. Team A is the team with the highest average and team H is the team with the lowest average. You will decide the pairing of opponents by randomly selecting their name out of a brown paper bag.

Write the following team names on squares and put them in a paper bag.

Team A | Team B | Team B | Team C | Team C | Team C | Team D |

Team D | Team D | Team D | Team E | Team E | Team E | Team E |

Team F | Team F | Team F | Team F | Team F | Team G | Team G |

Team G | Team G | Team G | Team G | Team G | Team H | Team H |

Team H | Team H | Team H | Team H | Team H | Team H |

There should be 34 squares of paper in the bag. The first team that you draw will have to play each team once. For example, if you select Team H from the bag and then Team E, These two teams will play the first round. The winner will play the team name that is drawn next from the bag. If you draw a team that has already been drawn, draw again.

3. Based on the names in the bag, predict how you think the first tournament will be organized.

Two pieces of paper are drawn from the bag without replacement. Find P(Team G, then Team C)by

4. First find P(Team G)

5. Then find P(Team C after G)

6. Then multiply to find P(Team G, then Team C)

7. Is the probability of P(Team G, then Team C) greater than P(Team C after G)? Explain.

8. Explain why the events in this situation are called dependent events.

9. Use the random method and draw names from the bag to set the opponents in Round 1 of the tournament. Write the schedule in the space provided.

10. How is the actual schedule similar or different to your prediction? Explain.

11. Would you consider this a fair schedule? Explain.

12. Suppose you begin Round 1 by pairing Team A with Team B, Team C with Team D, and so on. Make a list of this schedule.

13. Make a list of all of the possible winning outcomes in Round 1.

14. How many games will be played in Round 1?

15. How many teams will be eliminated in Round 1?

16. How many winners will there be in Round 1?

17. How many possible winning outcomes are there in Round 1?

18. How do you know that you have found all of the possible combinations of winners for Round 1? Explain.

19. Given all of the possible combinations of winning outcomes, what is the probability of any team winning in Round 1?

20. Choose one of the possible outcomes for Round 1 from your list in Exercise 12. Write it in the space provided.

21. How many games will be played in Round 2 ?

22. How many teams will be eliminated in Round 2 ?

23. How many possible outcomes are there in Round 2 ? List them in the space provided.

24. Using the Multiplication Principle of Counting, find the number of possible outcomes for Round 2 of the tournament.

Number of Choices |
Number of Outcomes |
Total Number of Possible Outcomes |

____________________ X | ____________________ = | ____________________ |

25. Choose one of the methods discussed here or choose one of your own and plan a schedule for the tournament. Include times, opponents, and round numbers. Then make a tree diagram to record the results for each round.

MathSummer Activity
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