Construct prisms & pyramids
Theory
A solid can be built from flat faces, from a net folded in one piece, or as a skeleton of straws and joins. Each way uses a different count: one piece per face, one straw per edge, one join per vertex. This Year 6 maths page shows how to plan the materials for any prism or pyramid, including pentagonal and hexagonal ones.
Flat faces: one piece of card for every face. A prism needs its \(2\) end shapes and one rectangle for each side of the end. A pyramid needs its base and one triangle for each side of the base.
Skeleton model: one straw for every edge and one join (clay or a connector) for every vertex.
Net in one piece: the faces are already joined along the fold lines. A net with \(F\) faces has \(F - 1\) folds, so edges to tape = edges − (faces − 1).
Order of work for a net: cut out, fold along every line, then tape the edges that meet.
What to count:
| Build with | Count | Pentagonal prism | Hexagonal pyramid |
|---|---|---|---|
| Flat pieces | faces | \(7\) | \(7\) |
| Straws | edges | \(15\) | \(12\) |
| Joins | vertices | \(10\) | \(7\) |
Planning a model
- Choose the way of building: faces, net or skeleton.
- Count faces, edges or vertices of the solid.
- For a net, subtract the folds (faces minus one) from the edges.
- For several models, multiply.
| \(2 + 5\) | \(=\) | \(7\) |
\(2\) pentagons and \(5\) rectangles: \(7\) pieces.
\(1\) hexagon and \(6\) triangles.
(i) How many straws?
(ii) How many joins?
| \(2 \times 6\) | \(=\) | \(12\) |
| \(6 + 1\) | \(=\) | \(7\) |
(i) \(12\) straws
(ii) \(7\) joins
| \(25 - 2 \times 9\) | \(=\) | \(7\) |
\(7\) straws.
| \(7 - 1\) | \(=\) | \(6\) |
| \(15 - 6\) | \(=\) | \(9\) |
\(9\) edges.
| \(4 \times 8\) | \(=\) | \(32\) |
| \(4 \times 12\) | \(=\) | \(48\) |
\(32\) joins and \(48\) straws.
A pentagonal pyramid with \(6\) faces.
A pyramid has only one base. It needs \(1\) pentagon and \(5\) triangles.
Common pitfalls
Frequently asked questions
How many straws does a skeleton pentagonal prism need?
\(15\), one for each edge.
How many joins does a hexagonal pyramid need?
\(7\), one for each vertex.
Why are fewer edges taped on a net?
The folds already join \(F - 1\) pairs of faces.
What pieces make a hexagonal prism?
\(2\) hexagons and \(6\) rectangles.
In what order do you make a solid from a net?
Cut it out, fold along every line, then tape the edges that meet.