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Rotational Symmetry Worksheet

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Rotational Symmetry Worksheet

A local makers’ market is choosing a badge design. Use rotational symmetry to test patterns and create a design that looks the same after a turn. A full turn is 360°. Unless stated otherwise, count the starting position when finding the order.

Spot the turning pattern

A shape has rotational symmetry if it matches its original outline during a turn of less than 360°. Its order is the number of matching positions in one full turn. The smallest angle that maps it onto itself is 360° ÷ order.

1.A badge turns around one fixed point. What is this point called?

Centre of rotation
Line of symmetry
Vertex
Perimeter

2.A square badge is turned around its centre. What is its order of rotational symmetry?

3.A regular hexagon on a stall sign is turned by its smallest matching angle. Find the angle.

4.Which design has rotational symmetry of order 3?

An equilateral triangle
A rectangle that is not a square
The capital letter F
An isosceles triangle that is not equilateral

Work it out

Use order = 360° ÷ smallest angle of rotation. Regular polygons have the same rotational order as their number of sides.

5.A rectangular flag design (not a square) is rotated around its centre. State its order and smallest angle of rotation.

6.A regular octagonal market token has 8 equal sides. How many matching positions does it have in one full turn, and what is its smallest matching angle?

7.True or false: A circle has rotational symmetry for every angle of rotation around its centre.

TrueFalse

8.A badge has rotational order 5. Fill in the smallest angle that maps it onto itself: 360° ÷ 5 = .

9.A designer says the capital letter P has rotational symmetry of order 2. Explain why the claim is incorrect.

Create a market badge

Plan a shape or repeated motif, then check that it matches after a 120° turn. A clear design can be a simple three-bladed pinwheel or three identical shapes spaced evenly around a centre.

10.Draw a badge design with rotational order 3. Mark the fixed point around which it turns and explain how you know the design matches during a full turn.

Draw your order-3 design here. Mark its centre.