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MathematicsGeometryAges 7–12

2-D shapes (age 8+)

Identify lines of symmetry in 2-D shapes presented in different orientations; recognise line-symmetric figures and draw lines of symmetry

Lesson

Set out your lesson

Test mirror symmetry rather than merely count corners.

Before teaching

Activity

Ask the learner to explain one prerequisite idea before starting. If uncertain, revisit it; graph order is not learner readiness.

Policy

Check readiness rather than assuming source graph order establishes attainment.

Printer, credit, and teaching notes
Instructions

Use the supplied symmetry SVGs or trace them on scrap paper. Folding is optional; screen rotation must not change the answer.

No Printer

Use the supplied stage cards on screen or scrap paper; adult key stays separate.

Materials are ready in each step. Use them on screen or print just the current step. Put teaching examples aside before the learner tries.

Next: Show

Adult extras
What this lesson covers and its limits

These are bounded opportunities, not learner attainment. Partial and blocked source requirements remain so.

  • partial: Identify lines of symmetry in 2-D shapes presented in different orientations; recognise line-symmetric figures and draw lines of symmetry

    Bounded objective: Test mirror symmetry rather than merely count corners. Finite set; independent drawing/visual access requires delivered SVG. Exact taught figures later repeated are application, not fresh discovery.

  • partial: Find all lines of symmetry in a rectangle, square, and equilateral triangle

    Rectangle/square/equilateral mirror lines taught with actual outlines; discovery not independent.

  • partial: Determine whether a given shape has a line of symmetry when rotated

    Rotated rectangle outline tests preservation under rotation.

  • partial: Identify which shapes in a set have exactly one line of symmetry

    One-line isosceles example only; not a broad fresh set.

  • partial: Determine how many lines of symmetry a regular hexagon has

    Regular hexagon outline invites six mirror lines.

  • partial: Draw all lines of symmetry for a given figure

    Tracing/drawing lines available; nonvisual description changes evidence mode.

  • partial: Identify which figures from a set are not line-symmetric

    Non-rhombus slanted parallelogram supplies a non-symmetric example only.

  • partial: If {{name}} is given a picture of a butterfly or a star shape, can they draw the line (or lines) where you could fold it exactly in half so both sides match?

    Try offers new-visual-application for the bounded objective; it does not establish every part of the source assessment. Finite set; independent drawing/visual access requires delivered SVG. Exact taught figures later repeated are application, not fresh discovery.

  • Finite set; independent drawing/visual access requires delivered SVG. Exact taught figures later repeated are application, not fresh discovery.

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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.

Learning resources

Extra practice links — they do not replace Gakuva’s teaching approach.

Illustrative Mathematics · Practice link — not the full lesson

Finding Lines of Symmetry

Open practice (new tab)
Before you open · source notes

Shapes are checked for lines of symmetry by folding or matching halves. Emphasise reflection lines, not every rotation symmetry.

Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.

Before you open

Ask the learner to find one line of symmetry on a shape and explain the matching halves.

Opening this link does not save learning or assess mastery.

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 2026-11-11 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. “Finding Lines of Symmetry.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.

CC BY-NC-SA 4.0 — link only

Check understanding

  • Find all lines of symmetry in a rectangle, a square, an equilateral triangle and a regular hexagon
  • Decide whether shapes shown in different orientations are line-symmetric, identifying those with exactly one line of symmetry and those with none
  • Draw all lines of symmetry on a given figure
“If your child is given a picture of a butterfly or a star shape, can they draw the line (or lines) where you could fold it exactly in half so both sides match?”

Curriculum record

Type
Conceptual
Subject
Mathematics
Domain
Geometry
Age range
Ages 7–12

Standards

acara-v9:AC9M4SP03acara-v9:AC9M5SP03ccss-math:4.G.3the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G2-E1.1the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G4-E1.1the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G6-E1.1uk-nc-2013:Ma/KS2/Y4/GPS/3