The idea, step by step
Follow one face at a time
Choose a face to hold still. Imagine its neighbours folding upward along shared edges. Continue around the shape, keeping track of faces already in place.
In our labelled cube net, hold B as the front. A folds to the left, C to the right, D to the back, E above and F below. Opposite pairs are A/C, B/D and E/F.
Look for overlap and gaps
A valid net covers each face of the solid exactly once. All outside edges must meet matching edges after folding. An arrangement can have the right number of panels and still fail.
The two-by-three block of squares is not a cube net. Around its interior grid corners, four panels meet; trying to fold them as a cube forces overlap instead of the three faces that meet at a cube corner.
A common trap
Two faces that are separated on the flat page must be opposite on the solid.
Instead: Their folded positions matter. Trace the fold; flat distance alone does not decide opposition.
See the thinking
Find an opposite face
Which face is opposite B?
- Keep B fixed and fold A and C into side faces.
- D folds from C around to the back, opposite the fixed face B.
Test a proposed net
Six squares are laid in a straight row. Will they make a cube?
- The first four squares can wrap around four side positions.
- Continuing the straight strip puts later squares into positions already covered. There are no separate panels to close both ends.
Check your understanding
In the labelled net, what face is opposite E?
Show answer
F.
E closes one end and F closes the other.
Your turn
6 questions · 9 marks · Work at your own pace.
Read the questions online
- Which face is opposite A?1 mark
- Which face is opposite B?1 mark
- If E becomes the top, which face is the bottom?1 mark
- Can A and C share an edge on the folded cube? Explain.2 marks
- Is this two-by-three arrangement a cube net? Explain.2 marks
- Why does checking only the number of faces not prove a net is valid?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Which face is opposite A?1 mark
A and C fold to the left and right of B.
C. - Which face is opposite B?1 mark
D folds around from C to the back.
D. - If E becomes the top, which face is the bottom?1 mark
E and F are opposite end faces.
F. - Can A and C share an edge on the folded cube? Explain.2 marks
They are opposite faces, so they do not meet along an edge.
No. - Is this two-by-three arrangement a cube net? Explain.2 marks
The arrangement forces overlapping faces when folded; four panels meet at an interior grid corner instead of the cube's three.
No. - Why does checking only the number of faces not prove a net is valid?2 marks
A valid net must both supply the correct faces and arrange them so every face closes correctly.
The panels may overlap or leave gaps when folded.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Connect objects and two-dimensional nets; construct and explain spatial relationships.
Official curriculum source ↗