Understand the idea.
Follow one face at a time
Choose one face to hold still while you imagine a net folding. Lift each neighbouring face around its shared edge, then follow the next face. Track the occupied positions so that no face is used twice.
With B as the front of this cube, A becomes left, C right, D back, E top and F bottom. Opposite faces lie across the solid; they do not share an edge.
Look for overlap and gaps
A valid net must place one face at each required position and join the remaining outside edges. If two panels arrive at the same position, they overlap rather than covering two different faces.
The pictured two-by-three block fails another check: four square panels meet at an interior grid corner. Only three square faces meet at a cube vertex. Without cutting those extra joins, the block cannot fold into the cube.
See the method in action.
Find an opposite face
Which face is opposite B?
Worked solution
- 1
Hold B in the front position.
Keeping one face fixed gives a reference for all the other folds.
- 2
Fold C around the edge beside B.
C becomes a side face adjacent to the fixed front.
- 3
Fold D around the next edge.
D moves from C to the back position, across the cube from B. Therefore D is opposite B.
D.
Test a proposed net
Six squares are laid in a straight row. Will they make a cube?
Worked solution
- 1
Wrap the first four squares around.
A straight strip can occupy the four positions of a band around a cube.
- 2
Continue folding the fifth and sixth.
Keeping the strip joins sends these panels into positions already covered by earlier squares.
- 3
Check the two ends.
No panel extends from the band to close either end. The row therefore cannot form a cube net.
No; panels overlap and the ends cannot both close.
Try it yourself.
Check your understanding
In the labelled net, what face is opposite E?
Show answer & reasoning
F.
With B held as the front, E folds to the top and F to the bottom. These close opposite ends, so F is opposite E.
Keep practising
6 worksheet questions · 9 marks
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 ↗