Symmetry

• Recognise line (reflective) symmetry in shapes and patterns.
• Identify a line of symmetry and complete a symmetrical figure.
• Understand rotational symmetry and describe its order.
• Create a symmetrical design and explain the symmetry in it.

Start from the mirror-line idea with folding and paint blots, then move to finding lines of symmetry in given shapes. Common misconceptions to watch for: assuming every shape has exactly one line of symmetry, and confusing "how many lines of symmetry" with "order of rotational symmetry". For rotational symmetry, count matching positions in a full turn (including the return to start = order).

Symmetry is one of the first places children meet the idea of a transformation. Reflective (line) symmetry: a shape maps onto itself across a mirror line; a shape can have more than one line of symmetry (a square has four). Rotational symmetry: a shape looks the same more than once as it turns through a full circle; its order is the number of matching positions in one full turn (a square has rotational symmetry of order 4). Symmetry appears everywhere — in leaves, snowflakes and faces, and in art and design from tiling to logos — which makes it an ideal bridge between maths and art.

line of symmetry

a mirror line where one half of a shape matches the other

reflection

a flip of a shape across a line

rotational symmetry

when a shape looks the same more than once as it turns through a full circle

order of symmetry

how many times a shape matches itself in one full turn

1. Which capital letters have a line of symmetry?
2. Can a shape have more than one line of symmetry?
3. Where do you see symmetry in nature?

• Fold and paint blots to make symmetrical butterflies.
• Find the order of rotational symmetry of a starfish, a snowflake and a car wheel.
• Design a logo that has two lines of symmetry.

• NRICH maths resources
• BBC Bitesize