Shape and space · Ages 8–9
Colouring a map worksheet
Part of: Parallel lines, quadrilaterals and triangles
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Colouring a map worksheet
Shape and space · Ages 8–9
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 flag is split into 5 stripes from left to right, and neighbouring stripes must be different colours. What is the fewest colours needed?
Answer:
2.8 houses stand in a row, and neighbouring houses must be painted different colours. What is the fewest colours needed?
Answer:
3.A flag is split into 7 stripes from left to right, and neighbouring stripes must be different colours. What is the fewest colours needed?
Answer:
4.9 houses stand in a row, and neighbouring houses must be painted different colours. What is the fewest colours needed?
Answer:
5.A flag is split into 11 stripes from left to right, and neighbouring stripes must be different colours. What is the fewest colours needed?
Answer:
6.4 houses stand in a row, and neighbouring houses must be painted different colours. What is the fewest colours needed?
Answer:
7.A flag is split into 9 stripes from left to right, and neighbouring stripes must be different colours. What is the fewest colours needed?
Answer:
8.12 houses stand in a row, and neighbouring houses must be painted different colours. What is the fewest colours needed?
Answer:
9.A flag is split into 3 stripes from left to right, and neighbouring stripes must be different colours. What is the fewest colours needed?
Answer:
10.5 houses stand in a row, and neighbouring houses must be painted different colours. What is the fewest colours needed?
Answer:
11.The outer regions of this map make a ring, and the middle region touches every one of them. Neighbouring regions need different colours. What is the fewest colours needed?
Answer:
12.The regions of this map make a ring round a lake, which isn't coloured. Neighbouring regions need different colours. What is the fewest colours needed?
Answer:
Part B: Word problems (4 marks each)
13.A cloth of squares has 3 rows and 2 columns. Squares sharing an edge must be different colours; touching at a corner doesn't count. What is the fewest colours needed?
Working:
Answer:
14.A park has 12 flower beds in a ring, and a round bed in the middle next to every one of them. Neighbouring beds need different colours. What is the fewest colours needed?
Working:
Answer:
15.A park has 11 flower beds in a ring, each next to the two beside it. Neighbouring beds need flowers of different colours. What is the fewest colours needed?
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16.A cloth of squares has 8 rows and 8 columns. Squares sharing an edge must be different colours; touching at a corner doesn't count. What is the fewest colours needed?
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17.A park has 3 flower beds in a ring, and a round bed in the middle next to every one of them. Neighbouring beds need different colours. What is the fewest colours needed?
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18.A park has 10 flower beds in a ring, each next to the two beside it. Neighbouring beds need flowers of different colours. What is the fewest colours needed?
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Answer:
Show the answers and working
Colouring a map worksheet: Answers and working
Part A: Working out and filling in
1. 2 colours
Start from the left, switching colour each time. Can you keep taking turns with just two?
In a row, two colours taking turns are enough: red, blue, red, blue… for all 5, so 2 is the fewest.
2. 2 colours
Start colouring from the first house, switching colour each time. Can you keep taking turns with just two?
In a row, two colours taking turns are enough: red, blue, red, blue… for all 8.
3. 2 colours
Start from the left, switching colour each time. Can you keep taking turns with just two?
In a row, two colours taking turns are enough: red, blue, red, blue… for all 7, so 2 is the fewest.
4. 2 colours
Start colouring from the first house, switching colour each time. Can you keep taking turns with just two?
In a row, two colours taking turns are enough: red, blue, red, blue… for all 9.
5. 2 colours
Start from the left, switching colour each time. Can you keep taking turns with just two?
In a row, two colours taking turns are enough: red, blue, red, blue… for all 11, so 2 is the fewest.
6. 2 colours
Start colouring from the first house, switching colour each time. Can you keep taking turns with just two?
In a row, two colours taking turns are enough: red, blue, red, blue… for all 4.
7. 2 colours
Start from the left, switching colour each time. Can you keep taking turns with just two?
In a row, two colours taking turns are enough: red, blue, red, blue… for all 9, so 2 is the fewest.
8. 2 colours
Start colouring from the first house, switching colour each time. Can you keep taking turns with just two?
In a row, two colours taking turns are enough: red, blue, red, blue… for all 12.
9. 2 colours
Start from the left, switching colour each time. Can you keep taking turns with just two?
In a row, two colours taking turns are enough: red, blue, red, blue… for all 3, so 2 is the fewest.
10. 2 colours
Start colouring from the first house, switching colour each time. Can you keep taking turns with just two?
In a row, two colours taking turns are enough: red, blue, red, blue… for all 5.
11. 4 colours
First work out the colours for the ring alone. The middle touches every ring region: can it share any of their colours?
The ring of 9 needs 4 − 1 colours, and the middle touches them all, so 1 more: 4.
12. 3 colours
Count the regions in the ring, then take turns with two colours all the way round. Is there a clash back at the start?
The ring has 9 regions: an even number takes turns with 2; an odd number clashes on the way round and needs 3.
Part B: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 2 colours
Think of a chessboard: how are the colours of squares that share an edge arranged?
Two colours taking turns like a chessboard work for all 3 × 2 squares: 2.
14. 3 colours
First work out the colours for the ring of 12 alone, then see whether the middle bed can use any of them.
The ring needs 3 − 1 colours and the middle bed touches them all, so 1 more: 3.
15. 3 colours
The beds make a ring. Is 11 odd or even? Try taking turns with two colours all the way round.
A ring of 11: an even number manages with 2 taking turns; an odd number needs 3.
16. 2 colours
Think of a chessboard: how are the colours of squares that share an edge arranged?
Two colours taking turns like a chessboard work for all 8 × 8 squares: 2.
17. 4 colours
First work out the colours for the ring of 3 alone, then see whether the middle bed can use any of them.
The ring needs 4 − 1 colours and the middle bed touches them all, so 1 more: 4.
18. 2 colours
The beds make a ring. Is 10 odd or even? Try taking turns with two colours all the way round.
A ring of 10: an even number manages with 2 taking turns; an odd number needs 3.
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