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Convert Scale Diagrams to Real Measurements

In this worksheet, students will apply scale factors to find the real life values of specific scaled elements or calculate the scale which has been used to create a scale diagram or model.

'Convert Scale Diagrams to Real Measurements' 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, and a toy car doesn't really want to be the same size as a normal car, does it? 

 

When we have an issue like this in maths, we use a scale diagram or a scale model.

 

 

What Is a Scale Diagram / Model?

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, but every element must be reduced by exactly the same factor. 

 

 

How Are Scales Written?

Scales are written as ratios, such as 1: 100 or 1:50,000.

 

 

What Does a Scale Mean? 

Scales are read from left to right.

For example, the scale 1:100 would mean that every 1 unit of length on the scale is the same as 100 units in real life.

So an element that was 2 cm long on a scale diagram, would be 200 cm long in real life.

 

 

 

Let's look at this concept in action with some examples now. 

 

 

e.g. A model car is 1.5 cm tall. If the scale used to create it is 1:100, how tall would the car be in real life?

 

All we need to do here is multiply by the scale factor:

1.5 × 100 = 150 cm

 

So the car would be 150 cm or 1.5 m tall in real life. 

 

 

 

e.g. A model is made of a 2 m tall man. If the model is 4 cm tall, what scale has been used?

 

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

There are 100 cm in 1 m, so 2 m = 200 cm.

 

Now, we need to write these numbers as a ratio (remember that the model comes first):

4:200

 

Our final step is to simplify this ratio:

4:200 ÷ 4

1:50

 

 

 

In this activity, we will apply scale factors to find the real life scale values of specific scaled elements or calculate the scale which has been used to create a scale diagram or model. 

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