How does a scale factor change area?

Area changes by the square of the scale factor. A scale factor of 2 makes the area 2 × 2 = 4 times as big.

What grade is this scale drawings worksheet for?

It is written for grade 7 and matches Common Core standard 7.G.A.1.

Can I get a different version of this scale drawings worksheet?

Yes. Use the free Mathify Kids test maker to make a new scale drawings worksheet with different numbers every time, with its own answer key.

Scale drawings worksheets

Map scales, lengths on a plan, scale factors, and the effect of a scale factor on area.

Children multiply to go from the drawing to real life and divide to go back.

Download the free scale drawings worksheet (PDF)

Scale drawings worksheet

PDF · US Letter · Grade 7 · 24 questions · answer key included

Download the PDF

What’s on the worksheet

24 questions on scale drawings, sized for US Letter paper
2 pages of questions plus an answer key on the last page
Written for grade 7, matching Common Core 7.G.A.1
Name and date lines at the top, and room to show the work

Sample questions from this worksheet

Scale 1 cm : 20 km. Two towns are 4.5 cm apart on the map. How far apart are they really?
Scale 1 inch : 2 feet. A wall is really 24 feet long. How long is it on the plan?
Scale 1 cm : 2 m. A room is 13 m long. How long is it on the plan?
A side 5 cm long is copied with a scale factor of 5. How long is the new side?
A 3 cm by 4 cm rectangle is enlarged by a scale factor of 2. What is the new area?
On a 1 : 50,000 map, how many km is 4 cm?

Quick reference: scale drawings

A scale links lengths on a drawing to real lengths. On a map with 1 cm : 20 km, every centimetre stands for 20 kilometres.

Drawing to real: multiply by the scale.
Real to drawing: divide by the scale.
Scale factor: multiply every length by it. Area changes by the scale factor squared.

Always change to the same units before using a scale. See the scale drawings lesson for pictures and a quiz.

Preview the worksheet and answer key

Make a new scale drawings worksheet

Need another page for extra practice, a retake or a second group in class? The free Mathify Kids test maker builds a fresh scale drawings worksheet with different numbers every time. Choose how many questions, print it with its own answer key, or let your child take it on screen and see the score straight away.

Make a new version

Scale drawings: a worked example (Scale 1 cm : 20 km. Two towns are 4.5 cm apart on the map.)

Each centimetre on the map stands for 20 km.
Multiply: 4.5 × 20 = 90.
The towns are 90 km apart.
Check: 4 cm would be 80 km, so 90 km makes sense.

How to use it at home and in class

At home

Draw a plan of your child’s bedroom with 1 cm for 50 cm. Measuring and scaling real furniture makes the idea stick. Ten problems a day works better than a whole sheet at once. Mark them together with the answer key, then ask your child to explain one they got wrong: finding the mistake themselves is where the learning happens.

In class

Use the first row as a warm-up, a full page for independent practice, or five questions as an exit ticket. For a retake or a second group, make a new version with the test maker so every child gets different numbers.

Mistakes to watch for

Dividing when you should multiply.
Mixing units, like metres with a scale in kilometres.
Thinking that doubling the sides doubles the area.

What to practice before and after scale drawings

Before: solving proportions. If this sheet is a struggle, go back a step.
After: ratio word problems, once this one is mostly right.
Learn it first: the scale drawings lesson.