Students will bring with them the collection of solids from a previous lesson

During this lesson the students will:

Students should notice that the number of edges is always the largest.  Ask them to think why this is.  Challenge students to think if they can use two of the categories to predict the third category such as:

Using the smartboard technology the teacher will bring up NCTM's Illumination Site for geometric solids

The teacher will demonstrate how the figure can be changed to different figures by clicking on the NEW SHAPE button. 

After students have viewed the different shapes that can be viewed the teacher to should start with the tetrahedron and turn the figure so students can view the tetrahedron from different angles.  Ask the students to record the number of faces, edges and vertices for this solid.  Continue with the cube, octahedron, dodecahedron, icosahedron, and the irregular polyhedron. 

This site will offer the students the opportunity to view some of the Platonic Solids and see if the number of faces, edges, and vertices follow the same pattern as the solids they have brought with them to class.  For the dodecahedron and icosahedron the teacher may want to only count the faces and vertices and then use the pattern to determine the number of edges.  Is it still true that the number of edges is always largest?  Do all other patterns still hold true?

The students should have determined that the number of Faces + the number of Vertices = the number of Edges +2 or any arrangement of these terms. 

Material developed from National Council of Teachers of Mathematics Illuminations Site.