Mathematics K–6 · Years 3–4
Fold and mirror: lines of symmetry and turning symmetry
Measurement and space
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The idea
A shape has a line of symmetry when folding along it makes the halves match exactly, and it has turning symmetry when it fits its own outline before a full turn.
What you need
- a small plastic mirror per pair
- paper squares, rectangles, equilateral triangles, circles and a scalene triangle, cut ready
- tracing paper and a pin
- a sheet of capital letters printed large
How to do it
- Fold the square so the halves match exactly. Open it, fold a different way, and keep going until no new fold matches. Count the fold lines and draw them.
- Repeat for the rectangle, the equilateral triangle and the scalene triangle. Try the circle and say why you cannot finish counting.
- Stand the mirror on a shape along each fold line and check that the reflection completes the shape. Then stand it where there is no fold line and see what changes.
- Trace the square onto tracing paper, pin it at the centre and turn it. Count how many times it fits its outline in one full turn. Repeat for the rectangle and the equilateral triangle.
- Sort the capital letters into those with a vertical line of symmetry, a horizontal line, both, or none.
What you should see
The square has 4 lines of symmetry, the rectangle 2, the equilateral triangle 3, the scalene triangle 0, and the circle has a line through the centre in every direction so the count never ends. The mirror on a line of symmetry shows the whole shape; off the line it shows a different shape. The square fits its outline 4 times in a full turn, the rectangle 2 and the equilateral triangle 3. Letters such as A, M and T have a vertical line, B, C and E a horizontal line, H, I, O and X both, and F, G and J none.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Every shape has at least one line of symmetry.
- A rectangle has 4 lines of symmetry like a square, including its diagonals.
Safety card
Hazards
- pin
- mirror edges
Controls
- plastic mirrors with rounded edges; an adult places the pin
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA2-2DS-01MA2-2DS-02MAO-WM-01
- Australian Curriculum v9AC9M4SP03
Sources
The pages the author read to write this activity.