Cube Net Investigators

Overview

Students investigate which arrangements of six equal squares fold to make a cube. Working collaboratively, they test, record and justify their findings, building from prior learning about 2D shapes, 3D objects, faces, edges and vertices.

Learning intentions

• WALT identify the properties of a cube.
• WALT investigate and classify different cube nets.
• WALT explain why some arrangements of six squares fold into a cube and others do not.
• WALT record mathematical thinking clearly and use precise spatial language.

Success criteria

• I can describe a cube using faces, edges and vertices.
• I can make and test arrangements of six connected squares.
• I can decide whether an arrangement is a cube net and explain my reasoning.
• I can record more than one different cube net without counting rotations as new examples.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathsteasers: additional resources for advanced learners through open-ended investigation.
• Mathsteasers: alignment with relevant textbook content to provide seamless challenge and extension.
• Geometry learning in the New Zealand Curriculum: visualising, constructing and describing 2D and 3D shapes.

Lesson structure (50 minutes)

1. 0–5 min · Hook and notice. Teacher opens with the cube-net mystery hook and displays a picture of a cube beside six connected squares; ask, “If six squares have the right area, will they always fold into a cube?” Students make an individual prediction, then share one reason with a partner.

2. 5–12 min · Establish the mathematics. Teacher revises that a cube has six square faces, 12 edges and eight vertices, then demonstrates folding a simple net and introduces net, face, edge, vertex, overlap and rotation. Students handle a cube, identify its faces and edges, and explain what a net must do.

3. 12–17 min · Model the investigation. Teacher uses the 3D shape nets pack to show how a net is cut, folded and checked, modelling one successful and one unsuccessful arrangement without revealing all possible answers. Students predict what will happen when faces meet and identify possible problems such as overlap or an open side.

4. 17–32 min · Explore and test. Teacher places students in pairs, gives each pair square paper, scissors and the investigation worksheet, and reminds them that squares must be joined edge-to-edge. Students create, cut and fold different arrangements of six squares, testing each one and recording “cube net”, “not a cube net” and the reason. They should rotate or turn arrangements mentally before deciding whether a new arrangement is genuinely different.

5. 32–41 min · Organise and prove. Teacher pauses the class to ask, “How can we be confident we have found all the different nets?” and directs pairs to compare results, combine matching examples and agree on a checking strategy. Students arrange successful nets on a shared table or board, group rotations together, and use face positions and folding behaviour to justify their classifications.

6. 41–47 min · Share and challenge. Teacher uses the investigation discussion and challenge slides to display selected arrangements, including a near miss, and asks pairs to defend or revise their decisions. Students explain one successful net and one failed arrangement using “It works because…” or “It cannot work because…”. Advanced students investigate whether there are exactly 11 distinct cube nets and explain how rotations and reflections affect their count.

7. 47–50 min · Reflect and assess. Teacher returns to the plenary and exit-question slide and asks students to complete the final section of the cube nets investigation sheet: draw one cube net, state how they checked it, and answer, “Why are six squares necessary but not always sufficient?” Students share a final insight as they hand in their worksheets.

Resources

• the cube nets investigation slide deck
• the cube nets investigation sheet
• the 3D shape nets pack
• One solid cube or connecting-cube model per pair
• Equal-sized square paper or grid paper
• Scissors and glue or tape
• Pencils, coloured pens and a large recording area
• Six labelled trays or folders for tested arrangements

Assessment

• Listen for correct use of face, edge, vertex, net, overlap and rotation during partner discussion.
• Check each pair’s recorded decisions, especially whether reasons refer to folding, joined edges, overlap or missing faces rather than appearance alone.
• Use the final worksheet response to identify who can distinguish “six squares” from “a valid cube net” and who needs further concrete modelling.

Differentiation

• Support students who are working below expected level with a pre-cut set of six squares, a cube to handle, colour-coded faces and the sentence starters “This is a net because…” and “This is not a net because…”.
• Provide dyslexia-friendly worksheets and slides: clear sans-serif font, large diagrams, high contrast, short instructions, generous spacing and minimal text. Read instructions aloud and allow students to explain answers orally or draw rather than write extended explanations.
• Pair students deliberately so that one student can hold and fold while the other records; allow extra time for cutting and use teacher check-ins after the first two attempts.
• Extend advanced learners by asking them to develop a systematic method for proving they have found all distinct cube nets, classify nets by the position of the four-square strip, and explain why rotations do not create new nets.

Extension

• Ask students to design a “trap” arrangement of six squares that looks promising but cannot form a cube, then write a clue explaining the failure.
• Challenge students to label opposite faces on a successful net and predict which faces will meet when it is folded.