Scale Drawings and Maps (1 cm = 2 km)

R7Scale Drawings and Maps

Small drawing, real world — one scale connects them.

Scale drawings and maps shrink reality by a stated ratio: 1 cm = 2 km.

On a map, 1 cm stands for 2 km.

3.5 cm on the map → 3.5 × 2 = 7 km in real life

Map → real: multiply. Real → map: divide.

Learn the 3-Step Method

1Read the scale.

‘1 cm = 2 km’ — every map centimetre is 2 real kilometres.

1 cm = 2 km

2Map to real: multiply.

3.5 cm × 2 = 7 km.

× the scale

3Real to map: divide.

10 km ÷ 2 = 5 cm on the map.

÷ the scale

💡 Key IdeaSense-check the direction: real distances are BIG numbers, map distances small. 7 cm for 3.5 km of road? You divided the wrong way.

Worked Example

A model car is built at a scale of 1 : 20. The model is 15 cm long. How long is the real car?

Scale up

15 × 20 = 300

300 cm

→

Sensible units

300 ÷ 100 = 3

→

✓ Answer

3 m

a 3-metre car — sensible ✓

Watch Out! Common Mistakes

Multiplying when you should divide.

10 km on a 1cm=2km map → 20 cm ✕

Wrong way! Real → map divides: 10 ÷ 2 = 5 cm.

Ignoring the units in 1 : 20.

Same units! 1 : 20 means 1 cm to 20 cm (not 20 m). Convert to sensible units at the END.

Unsensible answers unchallenged.

real car = 3 cm ✕

Sense-check! Cars aren’t 3 cm long. If the size feels absurd, the scale went the wrong way.

⬇ Cheat Sheet

SCALE DRAWINGS AND MAPS

Read the scale: 1 cm = ? real units.
Map → real: multiply by the scale.
Real → map: divide by the scale.
Sense-check: real distances should be the big numbers.

Examples: 3.5 cm at 1cm=2km → 7 km · model 1:20, 15 cm → 3 m.

📖 Continue Your Journey

✓ R1 What Is Ratio?✓ R2 Simplifying Ratios ✓ R3 Sharing in a Ratio ✓ R4 Ratio and Fractions ✓ R5 Direct Proportion ✓ R6 Best Value R7 Scale Drawings and Maps R8 Recipes and Scaling R9 Ratio and Percentages R10 Ratio Problem Solving

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Next Lesson: R8 Recipes and ScalingCook for 6 from a recipe for 4.

📄 Free printable: Download the Scale Drawings and Maps cheat sheet (PDF) — keep it by your child's desk.

Quick summary

The scale links drawing to reality: 1 cm = 2 km.
Map to real: multiply (3.5 cm → 7 km). Real to map: divide (10 km → 5 cm).
Ratios like 1 : 20 use the same units both sides until the final convert.
Sense-check: the real-world number should be the big one.

Frequently asked questions

How do map scales work?

The scale says what one map unit represents: at 1 cm = 2 km, a 3.5 cm route is 7 km. Multiply map→real, divide real→map.

What does a 1 : 20 model scale mean?

Every 1 unit on the model is 20 of the same unit in reality — a 15 cm model car is 300 cm (3 m) long.

How can children catch scale mistakes?

Sense-check sizes: a 3 cm 'real car' or a 20 cm map for a 10 km walk means the scale was applied the wrong way round.

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