Shape Investigators

Overview

Students investigate and describe three-dimensional shapes using precise geometric language. They build on prior understanding of two-dimensional shapes by identifying faces, edges and vertices, then justify how these properties distinguish prisms, pyramids and other 3D objects.

Learning intentions

• WALT identify and name the faces, edges and vertices of 3D shapes.
• WALT describe the properties of common 3D shapes accurately.
• WALT use models, diagrams and mathematical language to explain our thinking.
• WALT classify 3D shapes by noticing similarities and differences.

Success criteria

• I can identify faces, edges and vertices on a 3D model.
• I can record the number and type of faces, edges and vertices.
• I can explain how the properties of two 3D shapes are alike or different.
• I can use the words face, edge, vertex, prism and pyramid correctly.

Curriculum links

• Mathematics and Statistics — Geometry: describing, classifying and comparing 3D shapes by their properties.
• Mathematics and Statistics — Spatial reasoning: visualising and representing objects from different viewpoints.
• Mathsteasers: using higher-order thinking questions to challenge advanced learners and deepen understanding.
• Mathematical communication and problem-solving: explaining, justifying and testing geometric ideas.

Lesson structure (60 minutes)

1. 0–5 min · Hook and notice. Teacher displays a cube, cuboid, triangular prism and square-based pyramid, then opens the hook and learning intention slides and asks, “Which shape has the most edges, and how could we prove it?” Students make an individual prediction, then share what they notice with a partner.

2. 5–15 min · Direct teaching. Teacher uses physical models and the key vocabulary and demonstration slides to define a face as a flat surface, an edge as where two faces meet, and a vertex as a corner where edges meet. Teacher models tracing one cube systematically, counting each feature once, and clarifies that the plural of vertex is vertices. Students handle a model, point to and name each feature, and sketch and label one shape.

3. 15–30 min · Investigate in groups. Teacher places students in four groups of three or four and distributes models and the 3D shape properties investigation sheet. Students rotate through the models, recording each shape’s name, number of faces, edges and vertices, and the shape of its faces. They must agree on a counting method and mark features on the model or diagram to avoid double-counting.

4. 30–42 min · Classify and justify. Teacher returns to the investigation and classification slides and asks groups to sort the models into categories, without giving category names initially. Students decide how to group the shapes, then explain their rule using a sentence such as, “We grouped these together because…” Teacher introduces or reinforces prism and pyramid, explaining that a prism has matching, parallel bases while a pyramid has one base and triangular faces meeting at one vertex.

5. 42–52 min · Reasoning challenge. Teacher presents the prompts on the reasoning challenge slides: “A shape has 6 vertices, 9 edges and 5 faces. What might it be?” and “Can two different 3D shapes have the same number of vertices?” Students work in pairs, use models or drawings to test possibilities, and record a convincing explanation on the worksheet. Invite several pairs to compare methods rather than only answers.

6. 52–60 min · Plenary and exit check. Teacher displays the plenary and exit-question slide and asks students to complete the final section of the worksheet: draw and label a 3D shape, state its numbers of faces, edges and vertices, and explain one way it differs from another shape studied. Students share one precise sentence before handing in their work.

Resources

• the 3D shapes investigation slide deck
• the 3D shape properties investigation sheet
• Physical models of cubes, cuboids, triangular prisms, rectangular prisms, cylinders, cones and pyramids
• One mixed set of models per group
• Mini-whiteboards and pens
• Pencils, rulers and coloured pens
• Large paper or a board space for group classification

Assessment

• During modelling, ask students to point to a face, edge and vertex on the same object; note whether they can distinguish the terms.
• Check group recording for systematic counting and accurate use of “faces”, “edges” and “vertices”. Question students who count inconsistently: “Where have you started, and how will you know you have counted every feature?”
• Use the final drawing and explanation as an exit assessment. Look for a recognisable 3D shape, correct property counts and a valid comparison.

Differentiation

• Support learners with larger, tactile models, coloured tape or stickers marking one face, edge and vertex, and a vocabulary bank with labelled diagrams. Pair students strategically and provide the sentence frames “It has ___ faces…” and “These shapes are similar because…”.
• Allow students who find recording difficult to give oral explanations while a partner or teacher records key information. Use partially completed tables and pre-drawn shapes where needed.
• For learners ready for challenge, ask them to investigate whether the number of faces, edges and vertices follows a pattern across prisms and pyramids, and to justify their observations with several examples.
• Support EAL learners by pre-teaching vocabulary with gestures and real objects, checking understanding through pointing and drawing, and accepting labelled diagrams before requiring full written explanations.