Family Mathematics Problem Solving
Sponsored by
The Somerville Mathematics Fund

The Family Mathematics problems are written for adults and children to work on together. They are not meant as another homework, instead it is an opportunity for you to work together to solve a mathematical problem. This Month’s Family Mathematics Problems are are about scheduling and playing sports.. We hope you will enjoy working together to solve these problems. A link for the solutions is listed below. Enjoy.
Spring is here and it is time for warm weather outside team sports.
The problems are written so that fourth and fifth graders can solve the first problem, six graders the first two problems, and seventh and eight graders can solve all the problems.
The Somerville Mathematics Fund was founded in 2000 to celebrate and encourage mathematics achievement in the city of Somerville. We offer scholarships to students and grants to teachers.
For more information, call 617-666-0666 (evenings)
or e-mail voolich@aol.com

From June 2002    


Family Mathematics Problem Solving: Grades 4, 5, 6, 7, 8

Schedules Galore
Last weekend when there was registration for soccer teams at the park league, so many players showed up that the recreation department decided to have more youth soccer teams this year. However, that means not only more coaches, equipment, field time, but they need a whole new schedule. There are ten teams and every team must play each of the other teams once. How many games will they need to schedule?

Family Mathematics Problem Solving: Grade 6,7, 8

Tournament Time
At the end of the season, there will be a double-elimination tournament. Every team will play one other team in the first round. After that round, each team who won their first game will play another winning team for their second game, and so forth until there is only one team left. After the first round, each team that loses one game will play another team that lost one game, and will keep playing as long as they keep on winning. Once a team has lost two games, they are out of the tournament. For the league championship, the team that won all of its games will play the team that won all but one game. However, this is a double-elimination tournament, so in order to be eliminated, one must lose two games. So when the final two teams meet, if the team that already lost one game wins that game, then they play again for the championship. What is the minimum and maximum number of games that need to be scheduled for this tournament? What is the fewest number of games that that a team must win to be the league champion?
Family Mathematics Problem Solving: Grades 7 and 8

Winning Percentages
The Breakers have won four of their first eight games. They really want to have a better season and would love to win 75% of their games. How many games must they win in a row (no losing games), in order to win exactly 75%? What if they decide they would really like to win exactly 80% of their games, can they do it?
What if they decide after winning three of their first six games to improve their winning percentage, how many games must they win in a row to win 75%? 80%