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Scale factors and maps
Scale drawings, enlargements and map scales.
A toy car looks just like a real car, only smaller. A map shows a whole island on one page. A photo can be made bigger without looking squashed. All of these use a scale. In this lesson you will learn how to:
- spot an enlargement, and find its scale factor
- find a missing length on an enlargement
- read a scale drawing and work out real sizes
- use a map scale and a scale bar to find real distances, even round bends
- work backwards from a real distance to the map
1. Enlargements and scale factors
Example: enlarging a robot by scale factor 2
The robot is 2 squares wide and 3 squares tall. With scale factor 2, the width becomes 2 × 2 = 4 and the height becomes 3 × 2 = 6. Every length is twice as long, so it is still the same robot. The last robot only had its width doubled, so it looks squashed.
Robot resizer
- Drag the red handle on the corner to make the picture bigger or smaller. You can also tap the handle and use the arrow keys.
- Make it the size you are asked for, then press Check. Does it still look right, or is it squashed?
Enlargement builder
- Copy the small shape onto the big grid, made bigger by the scale factor. The red dot is your first corner. Tap the dot where each next corner goes. The lit-up side on the small shape is the one to copy.
- Two shapes with no slips moves you up a level. Level 1 has rectangles, level 2 has shapes with more corners, and level 3 has sloping sides.
2. Finding a missing length
Example: the big rectangle is an enlargement of the small one
- Match the sides:the 4 cm side goes with the 12 cm side
- Find the scale factor:12 ÷ 4 = 3
- Multiply the other side:3 cm × 3 = 9 cm
Shape twins
- The big shape is an enlargement of the small one. Find the scale factor, then the missing side.
- Two with no slips moves you up a level. Level 1 finds the scale factor, level 2 a side on the big shape, level 3 a side on the small shape, and level 4 turns the big shape round, so you must tap the matching side first.
3. Scale drawings
Example: a plan of the school playground
Put the 0 of the ruler at one end of the pitch. On the plan the pitch is 6 cm long. Each centimetre stands for 2 m, so the real pitch is 6 × 2 = 12 m long.
Going backwards
The real shed is 4 m long. How long is it on the plan? Each 2 m is 1 cm, so divide: 4 ÷ 2 = 2 cm.
A scale written as a ratio
A model car is made to a scale of 1 : 20. That means the real car is 20 times as long as the model, in the same units. The model is 18 cm long, so the real car is 18 × 20 = 360 cm long.
Measure the playground
- Drag the ruler onto the plan to measure. Press “Turn the ruler” to measure up and down. Then work out the real size.
- Two with no slips moves you up a level. Levels 1 and 2 use whole centimetres, level 3 has half centimetres, and level 4 asks you to draw something new on the plan.
4. Map scales
Example: how far is it from the Village to the Windmill along the trail?
- Measure each piece:3 cm and 5 cm
- Add them:3 + 5 = 8 cm on the map
- Use the scale (1 cm stands for 2 km):8 × 2 = 16 km
A scale bar
Some maps show the scale as a scale bar instead of words. Each block of this bar is 1 cm long and the numbers go up in 2s, so 1 cm stands for 2 km.
Explorer’s trail
- Drag the explorer along the trail (or tap the explorer and use the arrow keys). The counter shows how far you have walked on the map, and in real life.
- In Challenges the real distance is hidden: you work it out. Two with no slips moves you up a level. Level 1 uses 1 cm for 2 or 3 km, level 2 bigger scales, level 3 a scale bar, level 4 metres and half centimetres, and level 5 gives you the real distance to walk.
5. From real life to the map
Example: the pirate’s clue
From Skull Rock, walk 6 km east, then 4 km north. Dig there!
The scale is 1 cm stands for 2 km. East: 6 ÷ 2 = 3 cm. North: 4 ÷ 2 = 2 cm. So go 3 squares east and 2 squares north, and dig.
Treasure hunt
- Read the clue, change each real distance into centimetres on the map, then tap the grid point where you would dig.
- Two finds with no slips moves you up a level. Level 1 has one direction, level 2 has two, and level 3 uses a scale bar and metres.
6. Practice: pick your level
Start with Foundation if you are in Year 4 or just starting. Move up when you are getting most of them right.
The mistakes that cost marks
- Adding instead of multiplying. A 4 cm side becomes 12 cm, so the 3 cm side becomes 3 + 8 = 11 cm. 4 to 12 is × 3, so the 3 cm side becomes 3 × 3 = 9 cm.
- Stretching one way only. Doubling the width of a shape but not its height. in an enlargement every length is multiplied by the scale factor.
- Matching the wrong sides. Dividing the long side of the big shape by the short side of the small one. short side with short side, long side with long side.
- Multiplying when you should divide. Turning 6 km into 12 cm on a map where 1 cm stands for 2 km. real life to the map is divide: 6 ÷ 2 = 3 cm.
- Measuring straight across a bending route. measure every straight piece and add them before you use the scale.
- Reading the ruler or the scale bar from 1. both start at 0. Find what one centimetre, or one block, stands for.
- Leaving off the unit. Writing “12” when the answer is 12 m. say which unit: cm on the drawing, m or km in real life.
Quick checklist
Tick each one when you can do it without help.
All ticked. Brilliant work! You have finished Lesson 4.3.
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