Scale Drawing

Syllabus tag: Kenya CBC | Grade 8 Mathematics | Strand 4.0 Geometry | Sub-Strand 4.3 Scale Drawing (14 lessons)

Lesson objectives

By the end of this sub-strand, you should be able to:

• Convert actual length to scale length, and scale length to actual length
• Interpret and write linear scales in statement form and ratio form
• Convert linear scales between statement form and ratio form
• Make scale drawings in real-life situations

Scale Drawing

A classroom will not fit on a page. A scale drawing shrinks it by a fixed amount so the shape stays exactly right.

a) What a scale means

A scale tells you how many units on the ground one unit on the drawing stands for.

Take a scale of 1 : 200. One centimetre on the drawing stands for 200 cm on the ground.

The ratio has no units, because both sides are measured in the same unit. That is what lets the same scale work for centimetres, metres or kilometres.

b) Statement form and ratio form

Statement form is written in words: 1 cm represents 50 m.

Ratio form is written as numbers: 1 : 5 000.

To convert a statement to a ratio, put both sides into the same unit. So 1 cm to 50 m becomes 1 cm to 5 000 cm. The ratio is 1 : 5 000.

To convert a ratio to a statement, choose a convenient unit for the larger number. 1 : 100 000 means 1 cm to 100 000 cm, which is 1 cm to 1 km.

c) Actual length to scale length

Divide by the scale number, after putting both into the same unit.

Convert first, then divide. Dividing 6 by 200 gives 0.03, which is wrong. The 6 was in metres and the 200 in centimetres.

d) Scale length to actual length

Multiply by the scale number, then convert to a sensible unit.

The two directions are opposites. Going onto the drawing divides. Coming off it multiplies. If a real wall comes out at 3 cm, you divided when you should have multiplied.

e) Choosing a scale

The scale must make the drawing fit the paper, and leave it big enough to read.

Work out the longest measurement, then try a scale. If a 20 m room at 1 : 100 gives 20 cm, that fits an exercise book. At 1 : 50 it gives 40 cm, which does not.

Choose round numbers. Scales like 1 : 50, 1 : 100 and 1 : 500 are easy to work with. A scale of 1 : 137 is not.

f) Making a scale drawing

Write the scale on the drawing. Without it the drawing cannot be interpreted.

Convert every measurement before you start drawing, and list them.

Use a sharp pencil, a ruler and a set square. Small drawing errors become large real ones after multiplying by the scale.

Check one measurement backwards at the end. Measure it on your drawing and multiply by the scale. You should get the figure you started with.

g) Where this is used

An architect draws a house plan. A surveyor maps a plot. A tailor scales a pattern. Every map you have used is a scale drawing.

Words to know

• Scale -- the fixed relationship between a length on a drawing and the actual length it represents.
• Statement form (scale) -- a scale written in words, such as "1 cm represents 5 km."
• Ratio form (scale) -- a scale written as a ratio between two lengths in the same unit, such as 1:500,000.

:::checkpoint Check yourself

1. Write the scale "1 cm represents 20 m" in ratio form.
2. On a 1 : 500 drawing, a path measures 6 cm. How long is it really?
3. A field is 80 m long. How long is it on a 1 : 2 000 drawing?
4. Why must both sides be in the same unit before writing a ratio? :::

Bridge to practice

Try the exercises below -- on converting between actual and scale length, and between statement and ratio form.