Grade Level : 7-8

Materials : Liquid containers of different shapes, example cylindrical cups, spherical dishes, and cubic containers. Rulers to measure the length, width, height, and other dimensions such as radius and diameter of each object. Also, measuring cylinders to measure and verify the volume of liquid each container can hold, and work-sheets which would have the formula for volume calculations of each object.

Objective : To get each student to become familiar with the correct concept of volume as a measurable quantity and not just a theoretical expression. By finding the volume of any objects using both calculations and measurements, the students would then have the correct concept of volume.

Mathematical Concepts : Areas and Volumes.

NCTM Standards :
Standard 13 "Measurement"
Standard 9 "Algebra"
Standard 7 "Computation and Estimation"

Procedures : Distribute the materials to all the students in the class and ask them to compare any two different objects of the same apparent size.Then ask the students to guess which of the two containers would have a greater volume. After they have indicated which one,tell them to measure the inner dimensions of both containers which they have compared (e.g. length, width, height, radius and diameter), then use the given formula to calculate the volume of each container observed. Then for practical, tell them to fill both container with water and use the measuring cylinder to measure the volume held by each container. The theoretical and practical values must be approximately the same. After all the task have been completed, read the article below (A Chinese Derivation of the volume of a Sphere). This should now be interesting as it coincide with the lesson which has just been taught. Then for homework, ask them to solve the problems given on the worksheet.

References : Article taken from the journal "Mathematics Teachers" 1995, volume # 88.

Contributors : Major - Michael Dixon
Minor - Carol Marinas