What is this lesson about

A Platonic solid is a regular convex object. The faces are regular polygons that are all the same

size. For example, a cube is a platonic solid. A cube is made up of six squares (regular quadrilat-

eral). They are named after Plato, although he did not discover them. Because each face is con-

gruent, platonic solids are used to manufacture dice. You can buy 4, 6, 8, 12 and 20 sided dice.

The Platonic solids are names by the number of sides they have. They all use the suffix ‘hedron’

4 sides: Tetrahedron

6 sides: Hexahedron (cube)

8 sides: Octahedron

12 sided: Dodechedron (Note this will not be made in this lesson)

20 sides: Icosahedron

Australian Curriculum Link

The grid above indicates that the lesson is designed to stimulate geometric problem solving

and reasoning. Specifically this lesson would fit the following content from the Australian

Curriculum. Yr 5 ACMMG111: Connect three-dimensional objects with their nets and other two-

dimensional representations.

Elaborations• identifying the shape and relative position of each face of a solid to determine the net of the

solid, including that of prisms and pyramids

• representing two-dimensional shapes such as photographs, sketches and images created by

digital technologies

Yr 6 ACMMG140: Construct simple prisms and pyramids

Elaborations

• constructing prisms and pyramids from nets, and skeletal models

Bring 2D to life with triqo

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triqo leskaart 04-w.indd 1 23-08-12 10:03

Introduction

Show the students some different dice, 4, 6, 8, 12 and 20 sided dice. Explain that these are the only fair dice that can be made. (Note that ten sided dice are close to being fair, but not perfectly fair.)Ask the students to explain why they think this is the case. (Essentially it is be-cause the objects are made from congruent (same size and same shape) faces.

Lesson

1. Provide the students with some Triqo pieces (they will need at least 20 triangles in order to make an icosahedron) and ask them to make nets for each of the platonic solids.

2. Check the nets by folding to make the associated Platonic Solid.

3. Use Google Sketch up to draw the Platonic Solids http://sketchup.google.com/3dwarehouse/cldetails?clid=483d177082448fb8ec39cc04ccdefbf38.

playing with triangles

Assessment

National tests such as the NAPLAN often contain pictures of 2D nets (the flat shape that may be folded to make a 3D object) and students are asked to visualize which net folds to make a solid. Students are also asked to identify the vertices faces and edges of 3D objects.

Which object has exactly twice as many edges as faces?

triqo leskaart 04-w.indd 2 23-08-12 10:03