Scale drawings - KS3 Maths - BBC Bitesize (2024)

• Scale drawings represent real objects with accurate lengths reduced or enlarged by a given .

• are commonly seen as smaller representations of large objects including buildings, gardens and vehicles. Scale drawings may also be a larger representation of small objects such as parts for a watch or a medical instrument.

• Scales are expressed in form comparing a length on a diagram to the corresponding real length. In a scale drawing, all dimensions have been reduced by the same proportion and measurements are most often in centimetres and millimetres. For example, 1 cm on a scale drawing representing 1 metre in real life is a scale of 1 : 100

• When writing and using scales, understanding conversion between units, simplifying ratios and solving ratio and proportion problems can help.

Many scales are written as :

• 1 : n informs the user that one unit on the scale drawing represents a certain number (n) units in real life. For example, a scale of 1 : 500 means that 1 cm on the scale drawing represents 500 cm in real life.

• n : 1 informs the user that a certain number (n) of units on the scale drawing represents one unit in real life. For example, a scale of 200 : 1 means that 200 mm on the scale drawing represents 1 mm in real life.

To write a scale as a ratio:

1. Write the length on the scale drawing first, then the corresponding length on the real object.

2. Convert the lengths to be in the same, smaller units.

3. Write the ratio without the units.

4. If one or both values are decimals, multiply both values by a power of ten to ensure they are both values.

5. Simplify the ratio by dividing both values by their .

To find the lengths on a scale diagram that is smaller than the real object:

1. Write the scale as a unitary ratio in the form 1 : n.

2. Convert each real length to centimetres.

3. Divide each real length by the scale (n).

To find the lengths on a scale diagram that is larger than the real object:

1. Write the scale as a unitary ratio in the form n : 1

2. Multiply each real length by the scale (n).

3. Convert each real length to centimetres, if appropriate.

To find the actual lengths from a scale diagram, where the object is larger:

1. Write the scale as a unitary ratio in the form 1 : n.

2. Multiply each scaled length by the scale (n).

3. Convert the units, if appropriate.

To find the actual lengths from a scale diagram, where the object is smaller:

1. Write the scale as a unitary ratio in the form n : 1

2. Divide each scaled length by the scale (n).

3. Convert the units, if appropriate.

Scale drawings are used by designers to plan and adjust details before actual production so that all problems can be addressed.

CAD (computer- aided design) relies heavily on scaling software, interpreted by automotive, structural and civil engineers. A scale drawing of a car has the same shape as the real car that it represents but a different size.

People searching for a house to buy can access floorplans of properties and see a scale drawing that enables them to get a feel for the layout of the house. They may plan what furniture to buy that will fit in each room.