This week I am starting to explore platonic solids with my grade 8 students. The key question that I want them to answer is “Why are there only five platonic solids?” (For a brief explanation, see the MathsIsFun website. For a more detailed explanation, read this entry from The University of Utah.)

I want this to be a true exploration activity, and as such, I will give my students limited information. I will not volunteer this information, but I will give it only after they determine the right questions to ask.

First, the students will be given nets of the platonic solids so that they can build them and use them in their exploration. I will be giving them the copy from the learner.org interactives.

They will also get scissors and a handout with the regular polygons. They may cut out the polygons and use them as manipulatives. There are eight copies of each polygon, from three-sided to eight-sided figures.

I have also created a Notebook file for the Smartboard. This will be open for the students to come and explore with, as well. It is not fancy. On one side of the page are the platonic solids for the students to see. On the other side of the page are the regular polygons, set up as infinite clones. In the middle of the page is a play area. Students can thus pull out copies of the polygons, turn them around, and see how they fit together. (The polygons were created from the tools in the program, and the platonic solid images were taken from Wikipedia. If you click on each image on the second page of the file, you will be taken to the home site for that image. )

Platonic Solids Notebook File (Unfortunately, this is what the Notebook file looks like as a PDF. WordPress will not allow me to upload the Notebook file. Help anyone?)

Should students get frustrated, I will begin to lead them through the following thought process:

- Consider the regular polygons. Starting with the triangle, what is the measure of each interior angle? Continue for the rest of the polygons.
- What do you notice about the sum of the interior angles of the polygons, as you go from three-sided figures up to eight-sided figures?
- Which of these polygons are able to tessellate? Why are they able to tessellate?
- Which of these would be able to be constructed into a polyhedron? Why wouldn’t all of the regular polygons be able to be constructed into a polyhedron?

They can then go play on the Learner.org website.

The final task will be for them to submit an explanation as to why there are only five platonic solids. I will accept written work or digital work – students can choose which method suits them best.

Have a great week.