Introduction

The transparent Power Solids™ set includes 12 plastic three-dimensional shapes that allow for hands-on study of volume. Power Solids can be integrated easily with daily math lessons for introducing, teaching, and reviewing math concepts effectively. They allow students to make concrete connections between geometric shapes and their associated formulas for volume, and to observe volumetric relationships between the geometric shapes as well.

Most shapes in this set are variations of a prism or a pyramid, both of which are polyhedrons. Polyhedrons are solid figures with flat sides, or faces. Faces may meet at a point, called a vertex, or at a line, called an edge. A prism has two congruent bases; the remaining faces are rectangles. A pyramid has one base and the remaining faces are triangles.

Three shapes in this set have curved faces rather than flat ones; the cylinder, cone, and sphere. Technically, they are not polyhedrons. Even so, a cylinder can be thought of as a circular prism: a figure with congruent circular bases and a single, rectangular face. A cone can be thought of as a pyramid with a circular base and a face that is a wedge. A sphere is a unique shape with no parallel to prisms or pyramids.

At the outset, learning formulas for the volume of more than a dozen geometric shapes may seem daunting to your students. Formulas become much easier to remember when students recognize that only the method for calculating the area of a base changes from formula to formula; the other variables are calculated the same way, regardless of shape.

Getting Started With Power Solids™

Allow students to become familiar with the manipulatives before beginning directed activities. You may want to explore prisms and pyramids on separate days. Encourage students to handle, observe, and discuss the Power Solids. Ask them to write down their observations as they make the following comparisons: How are the shapes similar? (All shapes have the same height. They are all three-dimensional. They all have empty spaces inside them.) How are the different? (Some have flat sides; some have curved sides. Some are box- shaped; some are round, and some are triangle-shaped.) Where have students seen these shapes in the world around them? (Great Pyramids of Egypt, traffic pylons, film canisters, soccer balls, pieces of chalk, boxes, lipstick tubes, and so on.)

Introduce and identify the following terms: face, edge, vertex or corner, and base. Mention to students that the base of each Power Solid can be identified by the hole in the face.