Fractions · Ages 11–12

Map and model scales worksheet

Part of: Ratio and rate

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Fractions · Ages 11–12

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.The map's scale is 1 cm to 8 km. Read the ruler: how far apart are ⭐ and 🌳 really, in km?
Answer:
2.A map's scale is 1 cm to 4 km. Two places 44 km apart are how many centimetres apart on the map?
Answer:
3.A map's scale is 1 cm to 3 km. Two places 36 km apart are how many centimetres apart on the map?
Answer:
4.1 m = 100 cm. A model bus is made to a scale of 1 : 25, and the model is 44 cm long. How long is the real bus, in metres?
Answer:
5.1 m = 100 cm. A map's scale is 1 : 1000. How many metres does 9 cm on the map stand for?
Answer:
6.1 m = 100 cm. A map's scale is 1 : 20000. How many metres does 6 cm on the map stand for?
Answer:
7.1 m = 100 cm. A model bus is made to a scale of 1 : 20, and the model is 60 cm long. How long is the real bus, in metres?
Answer:
8.1 m = 100 cm. A model bus is made to a scale of 1 : 25, and the model is 36 cm long. How long is the real bus, in metres?
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9.1 km = 1000 m and 1 m = 100 cm. On a map, 3 cm stands for 3 km. The map's scale is 1 :
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10.1 km = 1000 m and 1 m = 100 cm. On a map, 6 cm stands for 1.5 km. The map's scale is 1 :
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13.1 km = 1000 m and 1 m = 100 cm. A hiking map has a scale of 1 : 25000. A trail is 6 cm long on the map. How long is the trail really, in km?
Working:
Answer:
14.1 m = 100 cm. A model Star Ferry is made to a scale of 1 : 50, and the model is 66 cm long. How long is the real ferry, in metres?
Working:
Answer:
15.Ka-yan draws a plan of the bedroom with 1 cm standing for 0.5 m. The bedroom is 6 m long. How many centimetres long should it be on the plan?
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Answer:
16.1 km = 1000 m and 1 m = 100 cm. A map's scale is 1 : 50000, and two villages are 12 cm apart on it. Ming walks at 3 km/h. How many hours does it take to walk from one village to the other?
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Answer:
17.1 km = 1000 m and 1 m = 100 cm. A hiking map has a scale of 1 : 50000. A trail is 4 cm long on the map. How long is the trail really, in km?
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Answer:
18.1 km = 1000 m and 1 m = 100 cm. A map's scale is 1 : 50000, and two villages are 12 cm apart on it. Ka-lok walks at 3 km/h. How many hours does it take to walk from one village to the other?
Working:
Answer:

Show the answers and working

Map and model scales worksheet: Answers and working

1. 64 km
Read off the ruler how many centimetres apart ⭐ and 🌳 are on the map. Each cm stands for 8 km.
They are 8 cm apart on the map, each cm 8 km: 8 × 8 = 64.
2. 11 cm
Real to map: divide. How many lots of 4 km are there in 44 km?
Real to map, divide: 44 ÷ 4 = 11.
3. 12 cm
Real to map: divide. How many lots of 3 km are there in 36 km?
Real to map, divide: 36 ÷ 3 = 12.
4. 11 m
1 cm of the model stands for 25 cm. Find the real bus in centimetres, then change to metres.
44 × 25 = 1100 cm, which is 11 m.
5. 90 m
1 : 1000 means 1 cm on the map stands for 1000 cm. Find what 9 cm stands for in cm, then change to metres.
9 × 1000 = 9000 cm; 100 cm = 1 m, so 9000 ÷ 100 = 90 m.
6. 1200 m
1 : 20000 means 1 cm on the map stands for 20000 cm. Find what 6 cm stands for in cm, then change to metres.
6 × 20000 = 120000 cm; 100 cm = 1 m, so 120000 ÷ 100 = 1200 m.
7. 12 m
1 cm of the model stands for 20 cm. Find the real bus in centimetres, then change to metres.
60 × 20 = 1200 cm, which is 12 m.
8. 9 m
1 cm of the model stands for 25 cm. Find the real bus in centimetres, then change to metres.
36 × 25 = 900 cm, which is 9 m.
9. 100000
Change 3 km into centimetres first, then see what 1 cm on the map stands for.
3 km = 3 × 100000 cm; 3 cm stands for that, so 1 cm stands for 100000 cm.
10. 25000
Change 1.5 km into centimetres first, then see what 1 cm on the map stands for.
1.5 km = 1.5 × 100000 cm; 6 cm stands for that, so 1 cm stands for 25000 cm.

11. A. 1 cm on the map stands for 100 m
Both terms of 1 : 10000 are in the same unit: 1 cm stands for 10000 cm. Then change that to metres.
1 cm stands for 10000 cm, and 10000 ÷ 100 = 100: 100 m.
12. A. 1 cm on the map stands for 20 m
Both terms of 1 : 2000 are in the same unit: 1 cm stands for 2000 cm. Then change that to metres.
1 cm stands for 2000 cm, and 2000 ÷ 100 = 20: 20 m.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 1.5 km
1 cm on the map stands for 25000 cm. Find what 6 cm stands for in cm, then change to km.
6 × 25000 cm; 1 km = 100000 cm, so it is 1.5 km.
14. 33 m
1 cm of the model stands for 50 cm. Find the real ferry in centimetres, then change to metres.
66 × 50 cm, then ÷ 100 for metres: 33 m.
15. 12 cm
Real to plan: divide. How many lots of 0.5 m are there in 6 m?
Real to plan, divide: 6 ÷ 0.5 = 12.
16. 2 hours
First find the real distance, 12 × 50000 cm, and change it to km.
Then time = distance ÷ speed.
The real distance is 12 × 50000 cm = 6 km; 6 ÷ 3 = 2.
17. 2 km
1 cm on the map stands for 50000 cm. Find what 4 cm stands for in cm, then change to km.
4 × 50000 cm; 1 km = 100000 cm, so it is 2 km.
18. 2 hours
First find the real distance, 12 × 50000 cm, and change it to km.
Then time = distance ÷ speed.
The real distance is 12 × 50000 cm = 6 km; 6 ÷ 3 = 2.

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