PSLE Mathematics Learning Guide · Guide 12
Return to the PSLE Learning Guide · Explore the Mathematics Learning Hub
A net is a flat arrangement of faces that can be folded to form a three-dimensional solid. The challenge is not merely recognising a familiar cross-shaped picture. A learner must preserve which faces touch, which edges meet, which faces become opposite, and whether folding creates overlap or leaves a gap.
This guide develops a spatial habit: name the solid, count and classify its faces, track shared edges, choose one face as an anchor, imagine neighbouring faces folding around it, and reject arrangements that force two faces into the same position.
The current MOE Primary Mathematics syllabus updated October 2025 includes 2D representations and nets of common 3D solids within the primary curriculum before PSLE, including cubes, cuboids, prisms and pyramids. The SEAB 2026 PSLE examination-format page links the current Mathematics syllabus. All examples below are original eduKate teaching material.
A net is a connected surface map
Imagine cutting selected edges of a cardboard box and opening the faces flat without tearing the faces apart. The result is a net.
A valid net must contain exactly the faces of the solid and must allow them to fold into the correct positions without impossible overlap.
For a cube, all six faces are congruent squares. For a cuboid, the six faces form three pairs of matching rectangles. A prism has two congruent parallel end faces joined by rectangular side faces. A pyramid has one base and triangular side faces meeting at an apex.
Count faces before judging the arrangement
A cube net needs six squares. Five squares cannot form a closed cube. Seven squares contain an extra face.
A cuboid needs six rectangular faces, but their dimensions must match the solid: opposite faces occur in equal pairs.
A triangular prism has two triangular ends and three rectangular side faces. A square-based pyramid has one square base and four triangular side faces.
Face count is a necessary check, but not sufficient. Six squares can still be arranged in a way that does not fold into a cube.
Adjacency matters more than page orientation
Two faces joined along an edge in the net will remain adjacent after folding. But faces that look far apart on paper can become neighbours, while faces that appear near each other without sharing an edge may not touch at all.
Rotate the paper mentally or physically if helpful. A valid net remains valid after rotation. “Top”, “left” and “right” on the page are temporary viewing positions, not permanent face names.
Anchor one face and fold its neighbours first
For a cube net, choose one square as the base. Squares sharing its four edges can fold upward to become side faces. A remaining square attached to one of those side faces may fold over to become the top.
This anchor strategy reduces the problem from “imagine the whole cube at once” to a sequence of local folds.
If two different squares would both fold into the top position, the net is invalid because two faces cannot occupy the same place.
Track opposite faces through folding
In a cube, every face has one opposite face that does not share an edge with it.
When a net is folded, two squares separated by a chain of side faces may become opposite. This is a common question type because opposite-face relationships are not always obvious in the flat net.
One strategy is to anchor a base, label the four side faces in order around it, then identify the remaining face as the top. The top and base are opposite.
Not every six-square arrangement is a cube net
Suppose four squares lie in a straight row, with one square attached above the second and another attached below the second. This arrangement can be tested by anchoring one of the middle squares and folding systematically.
Another arrangement may have too many squares clustered around one hinge so that two faces collide when folded. Rather than memorising all cube-net silhouettes, learn to test the folding constraints.
Cuboid nets preserve three pairs of equal faces
A cuboid of dimensions 2 cm × 3 cm × 5 cm has:
- two 2 × 3 faces,
- two 2 × 5 faces,
- two 3 × 5 faces.
A proposed net with the wrong face dimensions cannot form that cuboid even if it has six rectangles.
When one 2 × 3 face is chosen as the base, the four side faces around it must have edge lengths that match the base edges they attach to.
Prism nets have two matching ends
A triangular prism has two congruent triangles and three rectangles. When folded, the triangles become parallel end faces and the rectangles wrap around them.
The widths of the rectangles must match the corresponding side lengths of the triangular ends. If the triangle is scalene, the three side-face widths need not be equal.
This is a useful reminder that a prism is defined by its repeated cross-section, not by having only rectangular faces.
Pyramid nets bring side faces to one apex
A square-based pyramid has one square base and four triangular faces. Each triangle attaches to one side of the square in a common simple net, and their free vertices meet at the apex when folded.
Other valid arrangements may place some triangles attached to other triangles, but the final adjacency must still allow all side faces to meet correctly without overlap.
2D representations are not nets
A perspective drawing of a cube on paper is a 2D representation of a 3D solid. It shows visible edges and depth cues, but it is not a net because its faces are not laid flat for folding.
Similarly, a top view, front view or side view records the appearance from one direction. These views can help identify a solid, but they do not show the complete connected surface in the way a net does.
A drawing can contain hidden faces or edges
In a perspective cuboid drawing, some edges may be hidden behind visible faces. A learner should not count only what is visible on the page when asked for the solid’s total faces or edges.
A cube always has 6 faces, 12 edges and 8 vertices, regardless of viewing angle.
Main worked workshop: twelve original net and solid tasks
Problem 1: cube face count
How many square faces must a cube net contain?
Answer: 6.
Problem 2: cuboid face pairs
A cuboid measures 2 cm × 4 cm × 7 cm. List its face-size pairs.
Answer: two 2×4, two 2×7 and two 4×7 rectangles.
Problem 3: triangular prism
What faces appear in a triangular-prism net?
Answer: two congruent triangles and three rectangles.
Problem 4: square pyramid
What faces appear in a square-based pyramid net?
Answer: one square and four triangles.
Problem 5: insufficient cube net
A connected arrangement contains five squares. Can it form a closed cube?
Answer: No; a cube has six faces.
Problem 6: extra cube face
A connected arrangement contains seven congruent squares. Can all seven become faces of one cube?
Answer: No; a cube has only six faces.
Problem 7: base and top
In a valid cube net, choose one face as the base. After four adjacent faces fold up around it, what role must the final face play?
Answer: It closes the cube as the face opposite the base.
Problem 8: collision test
Two different squares in a proposed cube net would both fold into the position opposite the chosen base. Is the net valid?
Answer: No; the faces would overlap.
Problem 9: cuboid mismatch
A 2×3×5 cuboid proposal contains three 2×3 rectangles and only one 3×5 rectangle. Can it be the correct net?
Answer: No; the face pairs do not match the cuboid.
Problem 10: prism end faces
Why must the two end faces of a prism be congruent?
Answer: A prism has a constant cross-section; the two parallel ends have the same shape and size.
Problem 11: perspective versus net
A drawing shows a cube with three visible faces. Is it necessarily a net?
Answer: No. It is a 2D representation unless the faces are laid flat and connected for folding.
Problem 12: rotate the page
If a valid cube net is rotated 90° on the page, does it become invalid?
Answer: No. Rotation changes viewing orientation, not adjacency.
Edge matching is a strong cuboid test
When two rectangles share an edge in a cuboid net, the lengths of the touching edges must be equal. A 5 cm edge cannot be glued to a 3 cm edge without distortion.
For labelled nets, trace the lengths around the proposed folds. This converts a visual puzzle into a measurement-and-adjacency problem.
Colour-coding can reduce working-memory load
During practice, colour opposite or matching face pairs in the same colour. For a cuboid, mark the two length×width faces alike, the two length×height faces alike and the two width×height faces alike.
For a cube, label faces A–F and track which become opposite after folding. The labels make the spatial transformation easier to discuss and check.
Use a paper model during learning, then remove it for transfer
Cutting and folding paper nets can build spatial understanding. But the final goal is to reason from the diagram without always needing a physical model.
A useful progression is: fold one model, predict another before folding, check the prediction physically, then attempt a new net without folding.
Independent transfer check
- How many faces, edges and vertices does a cube have?
- How many rectangles are in a triangular-prism net?
- How many triangular side faces does a square-based pyramid have?
- A cuboid is 3×4×6 cm. List its three pairs of face dimensions.
- Why is face count alone not enough to prove that six squares form a cube net?
- What does it mean if two faces would fold into the same location?
- Explain why rotating a net on the page does not change its validity.
- Explain the difference between a perspective drawing and a net.
Independent-check answers
1. 6 faces, 12 edges, 8 vertices.
2. 3 rectangles.
3. 4 triangles.
4. two 3×4, two 3×6, two 4×6 rectangles.
5. Their arrangement may cause overlap or fail to close correctly.
6. The net is invalid because faces cannot occupy the same final position.
7. Rotation preserves every shared edge and adjacency relationship.
8. A perspective drawing depicts a 3D solid on a flat page; a net is the connected set of faces laid flat so they can fold into the solid.
Parent and tutor guide
Do not begin by asking a child to memorise all valid cube nets. Give one net, choose a base, and ask where each neighbour will go. Use face labels and a real paper model when necessary.
If cuboid nets fail, check face dimensions before spatial reasoning. If a learner counts only visible edges in a 3D drawing, return to the fixed structural counts of the solid.
After physical folding succeeds, remove the model and use a rotated or differently arranged example to test transfer.
The learner’s final card
What solid must form? Does the net contain exactly the right faces? Which edges are joined? Which faces become neighbours or opposites? Will any faces overlap when folded?
Continue through the PSLE Mathematics Learning Guide
Use Guide 9: Dividing Fractions, Guide 10: Algebraic Expressions, and Guide 11: Simple Linear Equations.
Return to the PSLE Learning Guide.
Sources and boundaries
Official references: SEAB 2026 PSLE formats and MOE Primary Mathematics syllabus, updated October 2025.
Teaching boundary: All examples are original eduKate teaching material. The guide treats nets and 2D/3D representation as cumulative primary Mathematics knowledge relevant to PSLE preparation; it does not claim every item is newly introduced only in Primary 6.