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
Lesson
Set out your lesson
“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.”
Bring to the table
- Unit cubes or squared paper nets
- Pencil for recording
Extra for the adult
Worked example. A 2 by 3 by 4 cuboid has volume 24 unit cubes.
Optional challenge. For Symmetry of 3-D solids, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Symmetry of 3-D solids, not mastery.
Share and support
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Practice this concept
Start practiceSymmetry of 3-D solids practice
Practice key ideas from Symmetry of 3-D solids.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
BBC Bitesize · Practice link — not the full lesson
KS3 Maths
Before you open · source notes
KS3 Maths supports Symmetry of 3-D solids. An adult previews and guides; this is a learning page, not a scored quiz.
Free educational page, no sign-in required for the tested path.
Before you openAsk the learner one fact they learned and one question they still have.
Opening this link does not save learning or assess mastery.
Source, access and review notes
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.
Unknown — link only
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