Hands-On Maths: The Platonic Solids (Using a Model)

In this course, you’ll learn all about Platonic Solids, and you’ll do it by making a model. This is easy since I supply you with PDF worksheets so you can cut out the outlines, and then put the model together with sticky tape.

Having seen how the Platonic Solids inscribe inside one another, we will then calculate and compare their volumes and surface areas. There is also a downloadable worksheet for this.

The Platonic Solids often come up in Maths tests and problems, and having a good understanding of them, means you will recognize them and find solutions quickly. They are also a thing of wonder and beauty.

There are only five, and they have been known about since the time of Plato in ancient Greece, or even longer. They were often seen as being key to understanding nature, be that the makeup of the world around us, of the orbits of the planets, or whatever. Nevertheless, this is a Maths course, and I’ll show you how interesting mathematically they are.

What you’ll learn:

  • The names of the 5 Platonic Solids
  • The history of the Platonic Solids
  • A Definition and comparison to the Archimedean Solids
  • Why there are only 5 Platonic Solids
  • Making a paper model of Platonic Solids(which fit inside one another)
  • The nets of the Platonic Solids
  • Vertices, edges, sides and Euler’s formula
  • Volumes of Platonic Solids (a comparison)
  • Duality in Platonic Solids
  • Surface Areas of Platonic Solids (a comparison)

Pre-requisites for the course:

Students need to be able to handle square roots in formulas, and to enter square roots in a calculator for more complicated formulas. These kind of problems are usually taught at the Lower Secondary Level.

Also, for the model, you’ll need to print out the nets, cut them out with scissors and put them together with sticky tape. There is also a 2 page worksheet to print out. (It can be printed back to back in black and white)

 Jon Molomby

Jon Molomby

I have taught Mathematics both at the Upper and Lower Secondary levels, and I believe they should be taught differently. While Upper Secondary is all about preparing for important exams at the end of Year 12, lower secondary should be about understanding concepts, and the best way to do this is to learn in a fun, hands-on way. The courses presented here in my Hands-on Maths series are mostly for Lower Secondary Level.

I’ve had a lot of success using hands-on materials … like geoboards, paper models , compass and straight edge, (for Geometry), and blocks and dice (for Probability) teaching Lower Secondary Maths. The understanding gained through hands-on activities is deep and permanent, and not easily forgotten like many formulas. Once these concepts are well understood, a strong base is created for later studies at the Upper Secondary level, and beyond. There is undoubtedly a strong link between what is done with the hands, and the mind’s understanding. There is also a strong link between this and the memory … retaining what is learnt.

My courses here are free, and I am proud to be one of the community of teachers who provide online education at no cost to the student. Even if you do not take any of my courses … good luck with your Maths !

Estimated Time: 6 hours

Difficulty: Intermediate

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The Platonic Solids
 Jon Molomby
Jon Molomby