  # Scale Drawing

In this worksheet, students practise converting between real life and scale lengths Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Units and Measurement

Difficulty level:   #### Worksheet Overview

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

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