Rotational symmetry
Recognise rotational symmetry in shapes and designs, state how many times a shape matches itself in a full turn, and create patterns with line and rotational symmetry, including by rotating a motif in dynamic geometry software
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Rotational symmetry 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: Paper shapes or a ruler and pencil; Shape name cards. Adult traces or shows one shape and names a property (sides/angles). Child identifies three shapes or measures one simple property and records it. Done: three correct shape/property responses. Stop after the fresh check; keep optional challenge for another day.
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Start practiceRotational symmetry practice
Practice key ideas from Rotational symmetry.
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Learning resources
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Illustrative Mathematics · Practice link — not the full lesson
Lines of symmetry for triangles
Before you open · source notes
Triangle symmetry lines support early symmetry reasoning before full rotational tests. Not every transformation on a grid.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk how many lines of symmetry a given triangle has and show them.
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Source, access and review notes
Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.
Illustrative Mathematics. “Lines of symmetry for triangles.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.
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Check understanding
- Turn a square tracing and show it fits onto itself 4 times in a full turn
- Identify which of a pinwheel, a heart and an equilateral triangle have rotational symmetry
- Use dynamic geometry software to rotate a motif by quarter turns about a point to create a design with rotational symmetry of order 4
“If your child turns a pinwheel or a square tile, can they notice it looks exactly the same after part of a turn — and count how many times that happens in one full turn?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Geometry
- Age range
- Ages 9–12
Standards