Key ideas
- Converting units: going to a smaller unit, multiply (you need more of them). Going to a bigger unit, divide.
- 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m.
- Scale factor: work from left to right, from shape A to shape B. Scale factor = new length ÷ original length, using a pair of corresponding sides (sides in the same position).
- A scale factor bigger than 1 is an enlargement. Smaller than 1 is a reduction.
- Check with another pair of corresponding sides: you should get the same scale factor.
- Using a scale like 1 cm : 5 m: put it in the top row of a table and multiply by your measurement.
- Measure lines in cm to 1 decimal place (each small mark is 1 mm = 0.1 cm). Start from the 0, not the end of the ruler.
Converting units
Change 2.45 m into millimetres.(2 marks)
Metres to centimetres.2.45 × 100 = 245 cm✓1
In plain EnglishCentimetres are smaller than metres, so multiply. There are 100 cm in a metre.
Centimetres to millimetres.245 × 10 = 2450 mm✓2
In plain EnglishMillimetres are smaller again, so multiply by 10. Going from m to mm is × 100 then × 10, which is × 1000 altogether.
Check it makes sense: a smaller unit means a bigger number. 2.45 m is a lot of millimetres.
Scale factor
Rectangle B is a scaled copy of rectangle A. Find the scale factor. Is B an enlargement or a reduction?(2 marks)
Find the scale factor.Scale factor = 12 ÷ 4Scale factor = 3✓1
In plain EnglishThe bottoms are corresponding sides. Work left to right, from A to B: new ÷ original = 12 ÷ 4.
Check, then decide.Check: 9 ÷ 3 = 3 ✓3 > 1, so B is an enlargement✓2
In plain EnglishThe heights give the same scale factor, so we can be sure. The scale factor is bigger than 1, so B is bigger than A.
Triangle B is a scaled copy of triangle A. Find the scale factor. Is B an enlargement or a reduction?(2 marks)
Find the scale factor.Scale factor = 6 ÷ 10Scale factor = 0.6✓1
In plain EnglishThe bases are corresponding sides. Left to right: B ÷ A = 6 ÷ 10.
Check, then decide.Check: 4.8 ÷ 8 = 0.6 ✓0.6 < 1, so B is a reduction✓2
In plain EnglishA scale factor smaller than 1 makes the shape smaller.
⚠ Left to right. 10 ÷ 6 would give the scale factor going backwards, from B to A.
Using a scale
A plan of a classroom uses the scale 1 cm : 2 m. The classroom is 4.5 cm long on the plan. How long is the real classroom?(2 marks)
Put the scale in a table.
2 × 4.5✓1= 9 m✓2
| Plan (cm) | Real (m) | |
|---|---|---|
| 1 | 2 | |
| 4.5 | 2 × 4.5 = 9 |
In plain EnglishThe scale goes in the top row: 1 cm on the plan is 2 m in real life. The plan length is 4.5 cm, so multiply both columns by 4.5.
Measuring with a ruler
The map shows a park. The scale is 1 cm : 50 m. Measure the straight line from the gate (A) to the café (B), then find the real distance.(3 marks)
Measure the line.AB = 6.2 cm✓1
In plain EnglishLine the 0 up with A. B is 6 whole centimetres and 2 small marks along: 6.2 cm.
Use the scale.
50 × 6.2✓2= 310 m✓3
| Map (cm) | Real (m) | |
|---|---|---|
| 1 | 50 | |
| 6.2 | 50 × 6.2 = 310 |
In plain EnglishScale in the top row, then multiply by the measurement.
Scale and changing units
On a map, the scale is 1 cm : 500 m. Two towns are 7.4 cm apart on the map. How far apart are they in real life, in kilometres?(3 marks)
Use the scale.
500 × 7.4✓1= 3700 m✓2
| Map (cm) | Real (m) | |
|---|---|---|
| 1 | 500 | |
| 7.4 | 500 × 7.4 = 3700 |
In plain EnglishMultiply the scale by the map distance. This gives the answer in metres.
Change to kilometres.3700 ÷ 1000 = 3.7 km✓3
In plain EnglishKilometres are bigger than metres, so divide by 1000.
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Your turn
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