A shape has rotational symmetry if it looks exactly the same after turning part of the way round its centre. The order of rotational symmetry is how many times it fits onto itself in one full turn. Count the fits during the turn, including the final one when it is back at the start, but do not count the start as well. A square fits after 90°, 180°, 270° and 360°, so its order is 4. A shape that only fits at the end of the full turn has order 1. With coloured patterns, the colours must match too, not just the outline.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- rotational symmetry
- looking the same after a turn of less than a full turn
- order
- how many times a shape fits onto itself in one full turn
Worked examples
What is the order of rotational symmetry of a square?
- 1.It fits after 90°, 180°, 270° and 360°.
- 2.That is 4 fits in one full turn.
= 4
What is the order of rotational symmetry of a parallelogram?
- 1.It fits after a half turn (180°) and after a full turn (360°).
- 2.It has no lines of symmetry, but it still has 2 fits.
= 2
What is the order of rotational symmetry of a regular hexagon with alternate triangles shaded?
- 1.The colours must match: it fits every 120°.
- 2.120°, 240°, 360°: 3 fits.
= 3
For parents
Method: Trace the shape, pin the centre with a pencil and turn the tracing, counting each fit.
What to say: Turn it slowly. Does it look the same yet? How many times does that happen before a full turn?
Common mistakes:
- Gives the number of sides as the order of rotational symmetry.
- Confuses rotational symmetry with line symmetry and gives the number of fold lines.
- Says a shape with no rotational symmetry has order 0, forgetting it always fits once, after a full turn.
- Counts the starting position and the end of the full turn as two separate fits, giving one too many.
- Only tests whether the shape looks the same upside down, giving 2 if it does and 1 if it does not.