Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 What is the order of rotational symmetry of an equilateral triangle?
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Order 3.
2 A shape has order 4. Write the smallest turn that brings it back, and the turn after two steps.
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90° and 180°.
3 What is 360 ÷ 6?
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60.
Level 2 · Core
4 What is the order of rotational symmetry of a rectangle that is not a square?
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A half turn and the full turn only: order 2.
5 A regular octagon is turned about its centre. Write its order, and the smallest turn in degrees.
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Order 8, and 360 ÷ 8 = 45°.
6 A square is turned 3 steps about its centre. How many degrees is that altogether?
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3 × 90 = 270°.
Level 3 · Challenge
7 Think about a parallelogram that is not a rectangle.1 It has no lines of symmetry.
2 Its order of rotational symmetry is 2.
3 Its order of rotational symmetry is 1.
Which statements are correct?
2 Its order of rotational symmetry is 2.
3 Its order of rotational symmetry is 1.
Which statements are correct?
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No fold matches (1 ✓), but a half turn does, so its order is 2, not 1 (2 ✓, 3 ✗). 1 and 2.
8 A shape has rotational symmetry of order 6. Write the smallest turn in degrees, and how many degrees it has turned after 4 steps.
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360 ÷ 6 = 60°, and 4 × 60 = 240°.
9 A shape first looks exactly the same after a turn of 72°. What is its order of rotational symmetry?
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5.