We can use this simple exercise to make students aware of the many avenues they may explore to solve problems. Children love to manipulate their world, to build and create. We can apply this natural ability and tendency to manipulate to the geometry class by providing exercises that will make sense of the 3-dimensional figures we use in finding volume.

If we secure the apex of the tetrahedron and provide more toothpicks to build a full tetrahedron, (a small bit of modeling clay at each apex will do the trick) students can feel the strength of this collection of triangles. Man has determined that the triangle is the most stable system. Triangular braces are used to strengthen bridges, buildings, shelves, and a host of other constructions. Many students may argue that a square base or cubic system is more secure. An interesting exercise is to give half the students toothpicks and clay with instructions to build a 3-dimensional system using squares (a cubic system) while the remaining students construct a 3-dimensional system with triangles (a tetrahedral system). The system constructed with triangles will be stronger and more stable than the cubic system.