Unfolding Nets

Overview

In this second lesson of the five-lesson unit Shapes, Nets, Transformations, students connect familiar 3D solids with their 2D nets. They predict, construct and test nets, using spatial reasoning to explain how faces, edges and vertices join when a net folds.

Learning intentions

• We are learning to identify and match common 3D shapes with suitable nets.
• We are learning to explain how a net folds to make a solid.
• We are learning to use diagrams, models and words to communicate spatial reasoning.
• We are learning to check and revise a mathematical prediction.

Success criteria

• I can identify a cube, cuboid, triangular prism and square-based pyramid.
• I can match a 3D shape to a net that includes all its faces.
• I can explain how faces fold and join along adjacent edges.
• I can use arrows, labels, a model and words to show why a net works.

Curriculum links

• Mathematics and Statistics — spatial reasoning about 2D faces and 3D solids.
• Mathematics and Statistics — using mathematical representations, models and language to communicate thinking.
• Mathematics and Statistics — investigating, predicting, testing and explaining solutions.
• Mathsteasers — higher-order thinking and challenge through spatial problem solving for advanced learners.

Lesson structure (55 minutes)

1. 0–7 min · Hook and prediction. Display several nets, including one that will not form a solid, using the hook and net prediction slides; ask, “Which of these will fold successfully, and how do you know?” Students discuss with a partner, record a prediction on the net prediction and explanation sheet, and share reasons such as missing faces, overlapping faces or edges that cannot join.

2. 7–19 min · Teacher modelling. Use the next slides and solid models to cut and fold a cube net, naming faces, edges and vertices as they meet. Students watch, identify square faces and adjacent edges, and sketch arrows on their worksheet to show fold directions. Model a rectangular prism and triangular prism, emphasising that a net must contain every face and that the edges must join correctly; briefly show how a square-based pyramid has a square base and four triangular faces.

3. 19–23 min · Organise the investigation. Explain the group roles: reader/predictor, cutter, folder and recorder; roles may rotate. Distribute card, scissors, rulers, tape, coloured pencils and trays, together with the 3D shape nets pack and the investigation worksheet. Students study each pre-drawn net before cutting, name the solid they think it will make, and record “works” or “does not work” predictions.

4. 23–44 min · Collaborative investigation. Circulate as groups cut, fold and test nets for cubes, cuboids, triangular prisms and square-based pyramids. Students classify each net as “works” or “does not work”, checking whether all faces are present and whether edges meet without overlap; they annotate one successful net with arrows and write an explanation using words such as base, adjacent, fold, join and congruent. Photograph or collect annotated nets as evidence.

5. 44–49 min · Share and reason. Select two groups to compare a successful and unsuccessful net using the investigation discussion slides. Students explain what happened when the net folded, identify which faces became bases or sides, and respectfully challenge or improve another group’s reasoning.

6. 49–55 min · Plenary and checkpoint. Display the sentence frame on the plenary slides. Students complete on their worksheet: “This net makes a ___ because…” and add one feature needed for a net to work. Invite several responses, then collect worksheets or check them as students leave.

Resources

• the unfolding nets slide deck
• the net prediction and explanation sheet
• the 3D shape nets pack
• Card or light card
• Scissors and rulers
• Tape
• Cube, cuboid, triangular prism and square-based pyramid models
• Coloured pencils
• Trays for group materials

Assessment

• Listen to predictions during the hook and ask students to justify them before any cutting occurs.
• During group work, question students: “Which faces match?”, “Where is the base?”, “Which edges are adjacent?” and “What would happen if this face moved?”
• Check or photograph annotated nets and use the plenary response to assess whether students can identify the solid, describe folding and state a necessary feature of a successful net.

Differentiation

• Support students with nets showing fold lines, colour-matched faces, pre-cut shapes and a smaller selection of cube and cuboid nets. Provide sentence starters: “This face becomes the…”, “These edges join because…”, and “The net works because…”.
• Pair students strategically and provide physical solid models throughout the investigation. Allow students to explain orally before recording their ideas.
• For students ready for further challenge, ask them to design and test a different net for a cube or cuboid, then explain why it works. They may also investigate whether a cylinder net needs a rectangle and two circles.
• For EAL learners and students needing additional support, use the illustrated models, gestures for fold and join, repeated vocabulary, and labelled examples. Offer adult or peer scribing where writing would obscure spatial reasoning.