Shape and space · Ages 11–12
Rotational symmetry worksheet
Part of: Line and rotational symmetry
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Rotational symmetry worksheet
Shape and space · Ages 11–12
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.A regular polygon has 5 sides. Turn it a whole turn (360°) about its centre. How many times does it match its starting position?
Answer:
2.Turn this shape a whole turn (360°) about its centre. How many times does it match its starting position?
Answer:
3.A regular polygon has 11 sides. Turn it a whole turn (360°) about its centre. How many times does it match its starting position?
Answer:
4.A regular polygon has 3 sides. Turn it a whole turn (360°) about its centre. How many times does it match its starting position?
Answer:
5.A regular polygon has 6 sides. Turn it a whole turn (360°) about its centre. How many times does it match its starting position?
Answer:
6.What is the smallest turn about its centre, in degrees, that makes this shape match itself?
Answer:
7.A regular polygon has 15 sides. What is the smallest turn about its centre, in degrees, that makes it match itself?
Answer:
8.A regular polygon has 20 sides. What is the smallest turn about its centre, in degrees, that makes it match itself?
Answer:
9.A regular polygon has 8 sides. What is the smallest turn about its centre, in degrees, that makes it match itself?
Answer:
Part B: Choose, or true or false (2 marks each)
10.This shape has rotational symmetry.
True or false?
Answer:
11.Which shape has rotational symmetry?
- A
- B
- C
- D
Choose the right picture
Answer:
12.The top-left pattern is turned 90° at a time about the centre to finish a shape with rotational symmetry. Which picture is right?
- A
- B
- C
- D
Choose the right picture
Answer:
Part C: Word problems (4 marks each)
13.A fan has 3 identical, evenly spread blades. While the blades turn 2 whole turns, how many times do they look exactly as they did at the start (counting the end)?
Working:
Answer:
14.A logo first matches itself after a turn of 45° about its centre. How many times does it match in a whole turn (360°)?
Working:
Answer:
15.A windmill has 6 identical sails spread evenly round its centre. What is the smallest turn, in degrees, after which it looks the same as before?
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16.A fan has 6 identical, evenly spread blades. While the blades turn 4 whole turns, how many times do they look exactly as they did at the start (counting the end)?
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17.A windmill has 12 identical sails spread evenly round its centre. What is the smallest turn, in degrees, after which it looks the same as before?
Working:
Answer:
18.A fan has 5 identical, evenly spread blades. While the blades turn 2 whole turns, how many times do they look exactly as they did at the start (counting the end)?
Working:
Answer:
Show the answers and working
Rotational symmetry worksheet: Answers and working
Part A: Working out and filling in
1. 5 times
Every side of a regular polygon is the same. Each time a side turns into the next one's place, it matches.
A regular polygon's sides are all equal, so it matches every 360° ÷ 5: 5 times in a whole turn.
2. 2 times
Imagine turning it slowly and count each time it looks the same, until one whole turn is done.
It matches every 360° ÷ 2: 2 times in a whole turn.
3. 11 times
Every side of a regular polygon is the same. Each time a side turns into the next one's place, it matches.
A regular polygon's sides are all equal, so it matches every 360° ÷ 11: 11 times in a whole turn.
4. 3 times
Every side of a regular polygon is the same. Each time a side turns into the next one's place, it matches.
A regular polygon's sides are all equal, so it matches every 360° ÷ 3: 3 times in a whole turn.
5. 6 times
Every side of a regular polygon is the same. Each time a side turns into the next one's place, it matches.
A regular polygon's sides are all equal, so it matches every 360° ÷ 6: 6 times in a whole turn.
6. 180°
First count how many times it matches in a whole turn, then divide 360° by that.
It matches 2 times in a whole turn: 360 ÷ 2 = 180°.
7. 24°
A regular polygon with 15 sides matches itself how many times in a whole turn?
It matches 15 times in a whole turn: 360 ÷ 15 = 24°.
8. 18°
A regular polygon with 20 sides matches itself how many times in a whole turn?
It matches 20 times in a whole turn: 360 ÷ 20 = 18°.
9. 45°
A regular polygon with 8 sides matches itself how many times in a whole turn?
It matches 8 times in a whole turn: 360 ÷ 8 = 45°.
Part B: Choose, or true or false
10. True
Before a whole turn (360°), is there any moment when it looks exactly the same?
It has rotational symmetry only if it matches before a whole turn; this one matches 2 times in one turn.
11. A
Imagine turning each shape: which one matches itself before a whole turn?
Only it matches itself before a whole turn.
12. C
The top-left pattern turned 90° goes to the top right, then the bottom right. Check each corner of each picture.
Draw it after each 90° turn: all four corners come from the same pattern, turned.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 6 times
In one whole turn, how many times do the blades look as they did at the start?
3 matches a turn, so 2 turns make 3 × 2 = 6.
14. 8 times
It matches every 45°. How many lots of 45° are there in 360°?
It matches every 45°: 360 ÷ 45 = 8.
15. 60°
With 6 evenly spread sails, how many times does it match in a whole turn? Divide 360° by that.
6 evenly spread sails match 6 times in a whole turn: 360 ÷ 6 = 60°.
16. 24 times
In one whole turn, how many times do the blades look as they did at the start?
6 matches a turn, so 4 turns make 6 × 4 = 24.
17. 30°
With 12 evenly spread sails, how many times does it match in a whole turn? Divide 360° by that.
12 evenly spread sails match 12 times in a whole turn: 360 ÷ 12 = 30°.
18. 10 times
In one whole turn, how many times do the blades look as they did at the start?
5 matches a turn, so 2 turns make 5 × 2 = 10.
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