Mathematics K–6 · Years 5–6

Which nets fold into a cube

Measurement and space

PracticalLow risk

The idea

A net is a flat arrangement of faces that folds into an object, and only some arrangements of six squares fold into a cube.

What you need

2 cm grid card, scissors and sticky tape
a set of 20 cards each showing a different arrangement of six joined squares (including all 11 cube nets and 9 that are not)
a cardboard box (a tissue box) to unfold
a cube to compare with

How to do it

Cut along the edges of the tissue box until it lies flat in one piece. Draw its net and count the faces.
Predict for each of the 20 cards whether it folds into a cube. Sort them into yes and no piles.
Cut each arrangement from grid card and fold it. Move any card whose prediction was wrong and say why it failed (two squares land on the same face, or a face is left open).
Take a net that works, label the square that will be the base, and predict which square will be the top before folding. Fold and check.
Draw two nets for a square pyramid and test them by folding.

What you should see

Exactly 11 of the arrangements of six squares fold into a cube and the other 9 do not; a row of five or six squares fails because the fifth square lands on the first, and a 2 by 3 rectangle of squares fails because faces overlap while one side stays open. Faces opposite each other on a cube are the squares separated by one square in a straight line of the net. The tissue box unfolds to six rectangles joined in a cross or a row with flaps.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

Any six squares joined together fold into a cube.
A net of a cube must be a cross shape.

Safety card

Low riskLearners carry it out

Hazards

scissors

Controls

rounded-tip scissors

Note

No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA3-3DS-01 MAO-WM-01
Australian Curriculum v9AC9M5SP01

Sources

The pages the author read to write this activity.

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