Symmetry of 3-D solids
Identify and describe the symmetry of prisms, pyramids and cylinders by examining the actual solid — turning a model, using a mirror or imagining a cut: find planes of reflective symmetry (a plane that cuts the solid into two mirror-image halves) and axes of rotational symmetry with their order (how many times the solid fits onto itself in one full turn), and use these with faces, edges and vertices to describe and classify solids; recognise that a solid's name does not fix its symmetry (a right regular square pyramid has 4 planes through its apex and a 4-fold axis, while an irregular pyramid may have none) and that an ideal right circular cylinder has infinitely many planes containing its axis, a plane across its middle, and rotational symmetry for every angle about its axis
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Symmetry of 3-D solids means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Unit cubes or squared paper nets; Pencil for recording. 1. Say the goal of Symmetry of 3-D solids in plain words once. 2. Adult builds a 2×3×4 cuboid and counts 24 unit cubes. 3. Child builds or sketches three cuboids/nets and records length×width×height. 4. Fresh check: one fresh L×W×H volume. Record and stop. Done: three correct volume or net records. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
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BBC Bitesize · Practice link — not the full lesson
KS3 Maths
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KS3 Maths supports Symmetry of 3-D solids. An adult previews and guides; this is a learning page, not a scored quiz.
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Before you openAsk the learner one fact they learned and one question they still have.
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Public BBC Bitesize page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
BBC Bitesize. “KS3 Maths.” External page; Gakuva does not copy, host, embed, or redistribute materials.
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Check understanding
- For a supplied simple model (for example, a right prism with an equilateral-triangle base), test several proposed planes with a mirror or a slicing diagram, decide which are planes of symmetry, and explain how each one cuts the solid into mirror-image halves (this prism has 3 planes along its length and 1 plane across its middle)
- Turn a model to find an axis of rotational symmetry and its order (for example, the axis through the apex and the centre of the base of a right regular square pyramid has order 4), and explain how an axis of rotation differs from a plane of symmetry
- Compare two solids with the same name but different shapes (such as a right regular square pyramid and an irregular pyramid) and explain why their symmetry differs, and describe why an ideal right circular cylinder has infinitely many planes of symmetry containing its axis and fits onto itself after any turn about that axis
“If your child holds a model of a tent-shaped prism or a square-based pyramid, can they show where it could be cut into two mirror-image halves and how many times it looks the same as they turn it around — without assuming every pyramid works the same way?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Geometry
- Age range
- Ages 12–13
Standards