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3D Shapes and Nets

Shape & Space · Year 1–Year 6

Count the faces on a net, then read off the edges and vertices.

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About the 3d shapes

A 3D shape on the left and its net on the right. Tap the faces on the net and the board counts them, and each one lights up on the shape beside it if it is a face you can actually see. Press Show under Numbers for the faces, edges and vertices.

Counting the faces of a solid means counting the ones you cannot see, which is the thing that makes it hard: a picture of a cube shows three faces and a cube has six. The net is where all six of them are, so that is where the counting happens, and the ones that light nothing up on the shape are the ones round the back.

Seven shapes: cube, cuboid, cylinder, cone, sphere, square-based pyramid and triangular prism. The cylinder's net is drawn with its rectangle as long as the circle is round, so a class measuring it finds the circumference rather than a tidy number somebody chose.

A sphere has no net, and the board says so rather than showing an empty space. It cannot be flattened without stretching it, which is why maps of the world are all wrong in one way or another.

The counts for the curved shapes follow the usual primary convention: a cylinder has three faces because the curved surface is counted as one, and a cone has two with an apex at the top. The board says which convention it is using, because it is an agreement rather than a fact and a class deserves to know which they have been given.

How to use it on your whiteboard

  1. 1Pick a shape on the toolbar. The shape and its net are drawn side by side.
  2. 2Tap the faces on the net one at a time. The board counts them as you go.
  3. 3Watch which faces light up on the shape: the ones that do not are round the back.
  4. 4Press Show under Numbers for the faces, edges and vertices.
  5. 5Press Hide under Net to take the net away and ask the class first. Tap Fullscreen to fill the board.

Questions

How many faces has a cylinder?
Three, on the convention primary schools use: two flat circles and the curved surface counted as a face. The board says so on screen, because it is an agreement about what to call a curved surface rather than something that can be proved.
Why count the faces on the net rather than on the shape?
Because a picture of a cube shows three of its six faces. Counting on the net is the only way a class can count all of them, and seeing which ones light up on the shape is how they work out where the other three went.
Why has the sphere got no net?
Because there is not one. A sphere cannot be flattened without stretching it, which is the same reason every flat map of the world distorts something. The board says so instead of leaving a gap.
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