geometry · Year 4 · AC9M4SP03
Rotational symmetry
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.
Sample questions
Imagine turning this shape through one full turn about its centre. How many times does it look exactly the same? (This is its order of rotational symmetry.)
- Turn it a little at a time through one full turn about its centre.
- It fits onto itself after every 90° turn: 90°, 180°, 270°, 360°.
- It fits 4 times in a full turn, so the order is 4.
Answer: 4
Imagine turning this shape through one full turn about its centre. How many times does it look exactly the same? (This is its order of rotational symmetry.)
- Turn it a little at a time through one full turn about its centre.
- It fits onto itself after every 120° turn: 120°, 240°, 360°.
- It fits 3 times in a full turn, so the order is 3.
Answer: 3
Imagine turning this shape through one full turn about its centre. How many times does it look exactly the same? (This is its order of rotational symmetry.)
- Turn it a little at a time through one full turn about its centre.
- It fits onto itself after every 180° turn: 180°, 360°.
- It fits 2 times in a full turn, so the order is 2.
Answer: 2