The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Converting Real Measurements to Scale Diagrams

In this worksheet, students practise converting between real life and scale lengths.

'Converting Real Measurements to Scale Diagrams' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change, Mensuration

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Units and Measurement

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

A lot of the time, it's not really the best idea to have things full size. A map would be useless if it was full size, a toy car dowsn't really want to be the same size as a normal car.

When we have this issue, we use a scale diagram or a scale model.

 

What is a scale diagram.

A scale diagram is just a diagram where everything has been reduced by the same factor, it could be half the size, a tenth of the size or anything else.

 

How are scales written?

Scales are written as a ratio such as 1: 100 or 1:50 000

 

What does this mean:?

Scales are read left to right. The scale 1:100 for example, would mean that every 1 unit of length on the scale is the same as 100 units in real life.

So something that was 2 cm long in real life would be 200cm long in real life.

 

Example 1: A model car is 3m tall. If the scale is 1:100, how tall would the model car be?

We know that there is a factor of 100 and that the model is smaller

All we need to do here is change the units into cm and divide by the scale factor.

300 ÷ 100 = 3 cm

 

Example 2: A model is made of a 2 m tall man. If the model is 4 cm tall, what is the scale?

The first thing we should notice here is that the units are different, so we need to make them the same.

2m = 200 cm

Step 2 is to write these numbers as a ratio (remember the model comes first))

4:200

Out third and final step is to simplify this ratio.

1:50

A scale of 1:100 means that 2 m on a model is 2 cm in real life

Always

Sometimes

Never

A car is 1.8 m wide. If it is made into a 1:48 scale model, how wide is the model in cm?

A model railway is built at a scale of 1:500.

If the real track is 2.8 km long, how many metres will the model track be?

 

A model is made of a garden at a scale of 1:1000

 

How tall in cm would the model tree be if the real one were 1.2 m tall

1200

0.12

Match the scale with the measurements.

Column A

Column B

5cm real , 1cm model
1:5
14cm real, 1.4cm model
1:10
15m real, 7.5 m model
1:12
4.8 cm real, 0.4cm model
1:2

A lorry is 7m long. If I make a model that is 3.5 cm long, what is the scale?

Column A

Column B

5cm real , 1cm model
1:5
14cm real, 1.4cm model
1:10
15m real, 7.5 m model
1:12
4.8 cm real, 0.4cm model
1:2

The Burj Khalifa in Dubai is 828 metres tall. If I made a 1: 50 scale model, how tall would it be?

Which of these measurements are correct for the scale 1:150

A woman is 1.32m tall. If I made a 2cm tall model, what would the scale be?

 building has a surface area of 1600m2.

Would a scale model (1:1000) have a surface area of 1.6m2?

Yes

No

  • Question 1

A scale of 1:100 means that 2 m on a model is 2 cm in real life

CORRECT ANSWER
Sometimes
EDDIE SAYS
This is true, but not always. What it means is that the real-life model is 100 times bigger.
  • Question 2

A car is 1.8 m wide. If it is made into a 1:48 scale model, how wide is the model in cm?

CORRECT ANSWER
375
3.75 cm
3.75cm
EDDIE SAYS
We know that 1:48 means the real-life car is 48 times bigger than the model car. If we divide by 48, we get...
  • Question 3

A model railway is built at a scale of 1:500.

If the real track is 2.8 km long, how many metres will the model track be?

 

CORRECT ANSWER
5.6m
5.6 m
5.6
EDDIE SAYS
Again, we know that the track is 500 times longer in real life so we simply divide by 500.
  • Question 4

A model is made of a garden at a scale of 1:1000

 

How tall in cm would the model tree be if the real one were 1.2 m tall

CORRECT ANSWER
0.12
EDDIE SAYS
We are making a smaller model here, so we need to divide by 1000
  • Question 5

Match the scale with the measurements.

CORRECT ANSWER

Column A

Column B

5cm real , 1cm model
1:5
14cm real, 1.4cm model
1:10
15m real, 7.5 m model
1:2
4.8 cm real, 0.4cm model
1:12
EDDIE SAYS
Did you remember the rule? - Make the units the same - Write it as a ratio (with the scale size first) - Cancel the ratio
  • Question 6

A lorry is 7m long. If I make a model that is 3.5 cm long, what is the scale?

CORRECT ANSWER
EDDIE SAYS
With these, start by making them the same units and writing them as a ratio. 3.5: 700 Then just cancel it down.
  • Question 7

The Burj Khalifa in Dubai is 828 metres tall. If I made a 1: 50 scale model, how tall would it be?

CORRECT ANSWER
16.56
16.56m
16.56 m
EDDIE SAYS
A scale of 1:50 means the scale model building is 828 ÷ 50
  • Question 8

Which of these measurements are correct for the scale 1:150

CORRECT ANSWER
EDDIE SAYS
We can quickly tell if it fits the scale by dividing one of the numbers by the other when they have the same units. 15 ÷ 1 does not give 150
  • Question 9

A woman is 1.32m tall. If I made a 2cm tall model, what would the scale be?

CORRECT ANSWER
EDDIE SAYS
A nice and easy one, the 1.32m is 132 cm. Writing these two numbers (with the model one first) and cancelling down would give...
  • Question 10

 building has a surface area of 1600m2.

Would a scale model (1:1000) have a surface area of 1.6m2?

CORRECT ANSWER
No
EDDIE SAYS
This one is testing how closely you read the intro. Scale factors like this are only given for lengths, not areas.
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Start your £1 trial today.
Subscribe from £10/month.