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Nets of Cubes and Pyramids: Which Fold, Which Complete

Maths · Stage 3
Year 5
Lesson Guide
Explanation
A net is the flat shape that folds up into a solid, with nothing left over and nothing overlapping. For a cube, always count the squares first: fewer than six cannot close it up, and more than six must overlap somewhere. Then look at the arrangement, because six squares is not enough by itself — a straight strip of six wraps round and its ends collide, and two columns of three leaves two faces doubled over and two gaps open.
Your Turn
How many squares must a cube net have? Check: exactly 6.
Watch Out
Six squares is necessary but not sufficient. A straight strip of six has the right count and still fails.
Explanation
The commonest cube net is a band of four squares with a cap above and a cap below. The band wraps right round the cube, so going along it, faces two apart end up opposite each other: the first is opposite the third, the second opposite the fourth. The two caps are opposite one another. The caps can sit above any column of the band and it still folds, which is part of why there are eleven different cube nets rather than one.
Your Turn
In a band of four labelled A, B, C, D, which face is opposite B? Check: D.
Watch Out
Faces that touch in the net are never opposite in the cube. Opposite means two apart round the band.
Explanation
A five-square net asks where the sixth goes. Find the band of four first; then the missing square is the second cap, and it has to be on the other side of the band from the first. It can sit below any of the four columns and the net still works. Putting it on the end of the band makes a strip of five, which collides when folded, and putting it beside the existing cap puts two caps on the same edge, which overlaps. So the question is always just: where does the second cap go?
Your Turn
A band of four has one cap above the second column. On which side must the last square go? Check: below the band.
Watch Out
Adding the sixth square to the end of the band makes a strip of five and fails. It must go on the opposite side.
Explanation
A pyramid's net is its base with one triangle standing on each side of that base — four triangles round a square, six round a hexagon. The number of pieces matches the number of faces, so a hexagonal pyramid's net has seven pieces. A prism's net looks quite different: two identical ends and a strip of rectangles joining them. Count the pieces and name the base, and the net tells you which solid it makes.
Your Turn
How many triangles are in the net of a hexagonal pyramid? Check: 6.
Watch Out
A net with a hexagon and six triangles is a pyramid. A net with two hexagons and six rectangles is a prism.
Explanation
Three habits cover every net question: count the pieces, find the band of four, and remember that two apart round the band means opposite. Six squares for a cube, a base plus one triangle per side for a pyramid, two ends and a strip for a prism. And if you can, trace one net onto paper and actually fold it — after doing that once you will see the band in every picture. Quiz and exercises now.
Your Turn
A net has two hexagons and six rectangles. What does it make? Check: a hexagonal prism.
Watch Out
Read whether the question wants the SOLID, the opposite FACE, or the missing PIECE. They need different work.
📌 Key Points — this lesson in a nutshell
  • A net is the flat shape that folds up to make a solid, with no overlaps and nothing missing.
  • A cube net needs six squares. There are eleven different ones, and the commonest is a band of four with a cap above and a cap below.
  • In a band of four, faces two apart end up opposite each other.
  • A pyramid net is its base with a triangle on each side of it — four triangles for a square base, six for a hexagon.
Step 1: Introduction
Step 1 of 5
Flat, then folded six squares, no overlaps → a cube A net folds up into the solid with nothing left over and nothing overlapping. Count the squares first: fewer than 6 cannot make a cube, and more than 6 must overlap. Then check the shape: six squares in a straight strip wrap round and the two ends collide. Two columns of three also fails — fold it and two faces land on top of each other while two gaps stay open.
The commonest cube net ABCDTU A, B, C and D wrap round the cube as a band; T caps the top and U the bottom. Going round the band, faces two apart are opposite: A is opposite C, and B is opposite D. The two caps are opposite each other: T is opposite U. The caps can sit above any column of the band and the net still folds — that is why there are eleven nets, not one. Opposite faces are never next to each other in the net.
Five squares — complete the net any of these four works the band already has 4 one cap is on; the other must go on the opposite side below any of the four Find the band of four first. Then the missing square is the second cap, on the other side of the band. Putting it beside the band instead makes a strip of five and one cap — fold that and two faces collide. Putting it next to the existing cap gives a band of four with two caps side by side on the same edge, which overlaps. So "which position completes the net?" is really "where does the second cap go?".
A base, with a triangle on every side square base → 4 triangles hexagonal base → 6 triangles the triangles meet at the apex A pyramid net is its base with one triangle on each side of the base. So the net of a hexagonal pyramid is a hexagon with six triangles round it: 7 pieces, matching its 7 faces. A prism net is different: two identical ends and a strip of rectangles between them. Count the pieces and name the base, and the net tells you the solid.
Reading the question How many squares in a cube net?6 Band A B C D — which is opposite A?C A hexagon with 6 triangles round it makes?a hexagonal pyramid Five squares in a band of 4 plus a cap — where does the sixth go?below the band Count the pieces · find the band of four · two apart is opposite. If you can, trace the net and fold it once. After that you will see it every time. Quiz and exercises now.
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