Activities for Students: The Volume of a Pyramid: Low-Tech and High-Tech Approaches

Abstract

This lesson came about spontaneously during a geometry unit on volume. I had used the lesson shown here in activity sheet 1, in which students use cubic blocks to rediscover the formulas for volumes of right prisms, that is, V = Bh and V = lwh. This lesson was a simple review for my tenth-grade class, and they completed it easily before the end of the period. With the wooden cubes still on their desks, most of them used the remaining time to build towers and other objects. I noticed that many students piled the cubes into bumpy pyramidal shapes. Because the next day's lesson involved studying the volume of pyramids, I wondered whether these bumpy shapes could be useful for discovering the volume of a real pyramid with smooth sides. Students could compare the volumes of these “pyramids of cubes” with the volumes of corresponding right prisms and perhaps discover the ratio 1/3 to obtain the formula for the volume of a pyramid, V = (1/3)Bh. As it turns out, the ratio of 1/3 does not become evident right away. To my students' delight, we found that using a spreadsheet is an excellent way to investigate this problem. My geometry classes had not used spreadsheets before, and the students enjoyed the experience of using the efficiency of technology to compare hundreds— and even thousands—of shapes with ease.