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Year 5 Maths 3D Objects, Volume & Capacity

Construct prisms & pyramids

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Theory

You can build a prism or pyramid from flat faces, from a net, or as a skeleton model of straws and joins. Each method uses a different count: faces, edges or vertices. This Year 5 maths page shows how to work out exactly what pieces you need.

A face is a flat surface. An edge is where two faces meet. A vertex (plural vertices) is a corner where edges meet.

Flat pieces: you need one piece for every face.

Skeleton model: you need one straw for every edge and one join (a ball of clay) for every vertex.

Net in one piece: some edges are already joined by folds. A net of \(F\) faces has \(F - 1\) folds, so the edges to tape \(=\) edges \(-\) (faces \(- 1\)).

Triangular prism A triangular prism drawn with hidden edges dashed: a triangle at the front and back joined by three rectangles. Its 6 vertices are marked with red dots.
Triangular prism: \(5\) faces, \(9\) edges, \(6\) vertices.
Square pyramid A square pyramid drawn with hidden edges dashed: a square base and four triangles meeting at the apex. Its 5 vertices are marked with red dots.
Square pyramid: \(5\) faces, \(8\) edges, \(5\) vertices.
Triangular pyramid A triangular pyramid drawn with one hidden edge dashed: four triangular faces. Its 4 vertices are marked with red dots.
Triangular pyramid: \(4\) faces, \(6\) edges, \(4\) vertices.

What to count for each way of building:

SolidFaces (pieces)Edges (straws)Vertices (joins)
Cube / rectangular prism\(6\)\(12\)\(8\)
Triangular prism\(5\)\(9\)\(6\)
Square pyramid\(5\)\(8\)\(5\)
Triangular pyramid\(4\)\(6\)\(4\)
\[ \text{edges to tape} = \text{edges} - (\text{faces} - 1) \]
edges to tape = edges −( faces −1)
Straws are edges, joins are vertices. Do not swap them: a skeleton cube needs 12 straws and 8 joins.
Cut, fold, then tape. Cut the net out first, fold along every line, then tape the edges that meet.

Working out the pieces

  1. Decide how the model is built: faces, skeleton or net.
  2. Count the matching feature: faces for flat pieces, edges for straws, vertices for joins.
  3. For a net, subtract the folds (faces minus one) from the edges to get the edges to tape.
  4. Multiply if several models are being built.
Example 1 — Flat pieces
Which flat pieces are needed for a triangular pyramid?
Solution

\(4\) triangles.

Example 2 — Skeleton
A skeleton triangular pyramid is built from straws and clay.
(i) How many straws?
(ii) How many balls of clay?
Solution

(i) \(6\) straws (edges)
(ii) \(4\) balls of clay (vertices)

Example 3 — Straws left over
Lee has \(20\) straws and builds one skeleton square pyramid. How many straws are left?
Solution
\(20 - 8\)\(=\)\(12\)
20−8=12

\(12\) straws are left over.

Example 4 — Tape a net
A net of a square pyramid is cut out in one piece and folded. How many edges must be taped?
Solution
\(5 - 1\)\(=\)\(4\ \text{folds}\)
\(8 - 4\)\(=\)\(4\ \text{edges}\)
8−(5−1)=4

\(4\) edges, one between each pair of neighbouring triangles.

Example 5 — Several models
A group builds \(3\) skeleton triangular prisms. How many joins do they need?
Solution
\(3 \times 6\)\(=\)\(18\)
3×6=18

\(18\) joins.

Example 6 — Which solid?
Jess has \(2\) squares and \(4\) rectangles that are all the same length. What can she build?
Solution

A square-ended rectangular prism (two square ends joined by four rectangles).

Example 7 — Steps in order
Put these steps in order: tape the edges, fold along the lines, cut out the net.
Solution

Cut out the net, fold along the lines, tape the edges.

Example 8 — Find the mistake
Rob says a skeleton square pyramid needs \(5\) straws and \(8\) joins. What went wrong?
Solution

He swapped them: \(8\) straws (edges) and \(5\) joins (vertices).

Common pitfalls

Swapping edges and vertices. Straws match edges; joins match vertices.
Taping every edge of a one-piece net. Edges along fold lines are already joined.
Wrong number of rectangles. A triangular prism needs 3 rectangles, one for each side of the triangle.
Forgetting the base. A square pyramid needs the square as well as 4 triangles.

Frequently asked questions

How many edges does a triangular prism have?

\(9\): three on each triangle and three joining them.

How many straws does a skeleton cube need?

\(12\), one for each edge.

What is a vertex?

A corner where edges meet.

Why do you tape fewer edges when folding a net?

Some edges are already joined by the folds. A net with \(F\) faces has \(F - 1\) folds.

What pieces make a square pyramid?

\(1\) square and \(4\) triangles.

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