Using Fermi Questions to Teach Math Concepts: Water Balloon Fun

From "Math Forum” (http://mathforum.org)

Purpose: To encourage multiple approaches, emphasize process rather than “the answer,” and promote nontraditional problem-solving strategies. Fermi questions receive their name from Enrico Fermi, an Italian physicist known for his participation in the Los Alamos atomic bomb project and the development of quantum theory

Materials: Paper or poster board, a large quantity of balloons, a supply of running water, the approval of a very understanding principal and of very supportive parents!

Procedure:

1. What could be more fun for middle school students than water balloons? Pose the question to the class: How many water balloons does it take to fill the school gymnasium, auditorium, classroom, and so on?
   
   
2. Have students, working in groups of two or three, build a cubic foot container using paper or poster board.
   
   
3. Have students approximate the volume of a water balloon.
   
   
4. Have students approximate how many water balloons are needed to fill their cubic foot container.
   
   
5. Have students investigate measure, or approximate the volume of the room to be filled with water balloons.
   
   
6. Have students determine, based on approximations in steps 1—4, the approximate number of water balloons that would be needed to fill the room or gym.
   
   
7. Then for the real fun.. . let students test out their approximations. Allow students to fill their cubic foot container with water balloons. Have students keep a record of how many water balloons they place in the container. Allowing for varying amounts of water in balloons, calculate the “average number of balloons” per cubic foot of water.