Net Detectives

Overview

Students explore how two-dimensional faces combine to form three-dimensional objects. They begin with a quick mathematical game, then identify and match common 3D shapes with their nets before colouring the correct pairs and, if time allows, cutting and assembling a net.

Learning intentions

• WALT identify common 3D shapes from their 2D faces.
• WALT recognise which 2D shapes make a net for a 3D object.
• WALT use mathematical language to describe faces, edges and vertices.
• WALT explain how a net folds to make a 3D shape.

Success criteria

• I can name a 3D shape from its faces.
• I can match a 3D shape to its correct net.
• I can explain why a net will or will not fold into a particular shape.
• I can use the words face, edge, vertex, square, rectangle, triangle and circle correctly.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking and challenge through non-routine mathematical questions.
• Mathematics and Statistics — Mathsteasers: additional resources for advanced learners.
• Mathematics and Statistics — Mathsteasers alignment: connecting representations and building on relevant mathematical learning.
• Geometry learning in the refreshed New Zealand curriculum: recognising, describing and representing 2D and 3D shapes and their properties.

Lesson structure (40 minutes)

1. 0–3 min · Roll and settle. Teacher takes the roll while displaying the opening shape question: “Which 3D shape could be made from these faces?” Students silently sketch or name a possible shape as they enter and place their books ready.

2. 3–13 min · Quick maths game — Shape Detective. Teacher shows one clue at a time from the Shape Detective game slides: number of faces, shape of faces, or whether faces are equal; students work in four groups of four to identify the mystery 3D shape, holding up or writing their answer and explaining their reasoning. Award a point for a correct answer and an additional point for a clear explanation. Use cubes, cuboids, cylinders, cones and pyramids, adapting the clues to the class.

3. 13–19 min · Explicit teaching — From faces to nets. Teacher displays the nets teaching slides and models that a net is a flat arrangement of 2D shapes that folds to make a 3D object; demonstrate a cube net and discuss faces, edges and vertices. Students identify the 2D shapes in sample nets and predict which 3D object each could form.

4. 19–23 min · Guided check. Teacher displays three possible nets, including one that will not fold correctly, and asks: “How do you know?” Students discuss with a partner, then share evidence using the sentence frame, “I think this net makes a ___ because it has ___ faces shaped like ___.”

5. 23–34 min · Independent matching activity. Teacher distributes the 3D shape and net matching worksheet and checks that students understand the colour-matching instruction. Students identify each 3D shape, find its matching net, colour both the same colour, and label selected faces, edges or vertices. Teacher circulates, asking, “Which faces meet when the net folds?” and “What evidence rules out that net?”

6. 34–38 min · Optional cut-and-assemble. If most students have completed the matching task, teacher directs students to cut out one suitable net from the cut-and-assemble net page and fold it carefully to make a 3D object. Students test whether the faces meet correctly, using tabs or tape as needed; students who need more time explain the folding sequence orally instead.

7. 38–40 min · Plenary and exit check. Teacher returns to the final reflection slide and asks students to complete the prompt: “A net is useful because…” Students share one discovery, then answer on a small piece of paper: “Name a 3D shape with two triangular faces and explain what other faces it has.” Collect responses as students leave.

Resources

• the shape investigation slide deck
• the 3D shape and net matching worksheet
• 3D shape models: cube, cuboid, cylinder, cone and pyramid
• Whiteboard and markers
• Coloured pencils or crayons
• Scissors
• Glue sticks or sticky tape
• Four group answer boards or mini-whiteboards
• Optional pre-cut nets and paper for students who need support

Assessment

• During the game, listen for accurate identification of shapes and reasoning based on faces, not guesses based only on appearance.
• During the matching task, check whether students count and compare faces and can explain why a net belongs to a particular 3D shape.
• Use the final response to identify students who can connect the number and shape of faces with a 3D object. Photograph or retain completed worksheets for follow-up grouping.

Differentiation

• Support students with real 3D models, pre-cut nets and a reference display showing cube, cuboid, cylinder, cone and pyramid. Allow students to trace or point to faces before naming them.
• Provide sentence starters: “I can see ___ faces”; “This net matches because…”; and “When it folds, ___ meets ___.”
• Pair students strategically and read worksheet instructions aloud. Accept oral explanations, labelled drawings or pointing for students with writing or language needs.
• Challenge confident students to find or sketch a different valid net for a cube, or explain why a tempting arrangement will not make a closed solid. Encourage precise use of face, edge and vertex.