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 to be turned in to your child’s teacher, instead it is an opportunity for you to work together to solve a mathematical problem. This Month’s Family Mathematics Problems are about scheduling and playing sports. We hope you will enjoy working together to solve these problems.
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.
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From June 2002
 Solutions
  
Grades 4, 5, 6, 7, 8
Grade 6, 7, 8
Grades 7 and 8


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

Schedules Galore
There are ten teams and each team must play each of the other nine teams. However when team A plays team B, it is the same as team B playing team A. So, 10 teams x 9 games — 2 (eliminate duplicates) = 45 games need to be scheduled.

Family Mathematics Problem Solving: Grade 6, 7, 8

Tournament Time
Since this is a double-elimination tournament, each team must lose two games to be eliminated, so there are two brackets. Once a team loses a game it goes into the second bracket. Click here to see the chart.
Family Mathematics Problem Solving: Grades 7 and 8

Winning Percentages
This problem is a good one to do either algebraically or with a chart. Starting with the first situation, the Breakers have won 4 out of 8 games and want to win 75%.
wins:
4
5
6
7
8
9
10
11
12
played
8
9
10
11
12
13
14
15
16
Twelve out of sixteen is 75%, to get this they had to win 8 in a row. You could continue the chart to find that they would need to win 12 in a row to get to 80%. Making a similar chart, you would find that when they started out with 3 out of 6 wins, that they need to win 6 games in a row to achieve 75% and 9 games in a row for 80%.

Algebraically, (4 + x)/(8 + x) = 3/4
4(4 + x) = 3(8 + x)
16 + 4x = 24 + 3 x
16 + x = 24
x = 8, the number of games they must win to have a 75% record.


Other Problem Solving Sources:
http://mathforum.org/pow/
http://www.figurethis.org/index40.htm
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