California Middle School Mathematics Concepts and Skills: Course 2

Tell students you have a problem you want them to solve, but they will need some background information first. Ask them to watch Futures Channel Movie #5006 Water Tanks. Then ask this question: Suppose I have a water tank that is 20 feet in diameter and 10 feet high, and I want to build another one with twice the volume. What should the dimensions be?

Arrange students in small groups, and give each group three cans (two with the same diameter but different heights, and a third with the same height as one of the other two cans but roughly twice the diameter), a measuring cup, and a quantity of dry cereal. Tell students you want them to explore the relationship between volume of a can and its height, and the relationship between volume and diameter, record their data, and present their conclusions to the class.

Students should discover that the volume of a can increases proportionally with its height, but that doubling the diameter increases the volume by a factor of four.

Explain to students that in this chapter they are going to learn why that is true, as well as other aspects of circles and various three dimensional shapes.