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 Problem is in honor of Pi Day, March 14th. Even if you do not solve the problems below, be sure to wish everyone who is with you that day at 1:59 "Happy Pi Day!" We hope you will enjoy working together to solve these problems. 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,
Grade 6
Grades 7 and 8


Family Mathematics Problem Solving: Grades 4 and 5

Hunting for Pi
After finding and measuring lots of circles, you should have discovered that the Circumference divided by the Diameter of any circle is just a little bigger than 3. This number which is a little bigger than three is called Pi (). This works for small circles that you can pick up and measure, and would even work for a really big circle such as the equator of the earth (which you can not pick up and measure!).

Family Mathematics Problem Solving: Grade 6

The Mathematics Club Celebrates Pi Day with Pizza!
The Mathematics Club can order 10 different pizzas with one topping each. If you start listing two topping pizzas, it is best to do it systematically. Imagine we have 10 toppings to choose from A, B, C, D, E, F, G, H, I, and J. First list the toppings with A: A+B, A+C, A+D, A+E, A+F, A+G, A+H, A+I, A+J (9 pairs). Then list the toppings with B (don’t include B+A, it is the same as A+B): B+C, B+D, B+E, B+F, B+G, B+H, B+I, B+J (8 pairs). Keep listing the possible combinations until you get to I+J. Look at the pattern of the totals: 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45. That gives us a total of 10 plus 45, 55 ways the Mathematics Club can have either one or two toppings on a pizza. So, it would take them 55 years before they repeated their Pizza Pi Day party order.
Family Mathematics Problem Solving: Grades 7 and 8

Oh, the Challenges of Ordering Pizza!
The area of the 12 inch pizza is 6 x 6 x pi, divide that answer by 6 to find the area of one slice of 12 inch pizza. Rounded off, the area of the piece of pizza is 18.4 square inches. The area of the 10 inch pizza is 5 x 5 x pi, approximately 78.5 square inches. If you divide 78.5 by 18.4 you get approximately 4. So the Mathematics Club should have “Have it Your Way House of Pizza” cut each 10 inch pizza into 4 pieces.
Use the information you calculated above: the 12 inch pizza is cut into 6 pieces and the 10 inch pizza should be cut into 4 pieces.
In order to order exactly 28 pieces of cheese pizza, you need to figure out how many groups of 6 plus some number of groups of 4 that total 28. If you use an organize list, starting with groups of 6, and compute the number of 4’s needed to reach 28, you will find:
1 x 6 = 6; (28 - 6)/4 = 22/4
2 x 6 = 12; (28 - 12)/4 = 16/4 = 4
So if the Mathematics Club should buy two 12 inch cheese pizzas (12 pieces) and four 10 inch cheese pizzas (16 pieces), they will have 28 pieces of cheese pizza.
For the 14 slices of pepperoni pizza:
1 x 6 = 6; (14-6)/4 = 8/4 = 2.
The Mathematics Club needs to buy one 12 inch pepperoni pizza and two 10 inch pepperoni pizzas to go with their cheese pizzas.
 


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