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🧩 7th grade math · Patterns & Algebra

Scale drawings

A scale says what 1 unit on the drawing stands for. 1 cm = 25 km means each 1 cm is 25 km in real life. Drawing to real life: multiply. Real life to drawing: divide. A 4 cm length on that map is 4 × 25 = 100 km.

Worked example

A model ship is built to this scale: 1 inch stands for 2 feet. The model is 2 inches long. How long is the real ship?
Answer: 4 feet
The scale says 1 inch stands for 2 feet. The drawing length is 2 inches, so 2 × 2 = 4 feet.

For grown-ups: Scale drawings. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS 7.G.A.1
What this practises, for teachers

Practices scale drawings (7.G.A.1). A printable sheet with its answer key, worked answers on the page, no accounts.

▶ Practise it

For your class

🖨️ Printable sheet and key

Try three

  1. A map uses this scale: 1 inch represents 20 miles. Two towns are really 120 miles apart. How far apart are they on the map?
    Show the answer and how
    Answer: 6 inches
    The scale says 1 inch stands for 20 miles. The real length is 120 miles, so 120 ÷ 20 = 6 inches.
  2. A floor plan uses this scale: 1 inch represents 3 feet. A room is really 27 feet long. How long is it on the plan?
    Show the answer and how
    Answer: 9 inches
    The scale says 1 inch stands for 3 feet. The real length is 27 feet, so 27 ÷ 3 = 9 inches.
  3. A model ship is built to this scale: 1 inch represents 16 feet. The real ship is 176 feet long. How long is the model?
    Show the answer and how
    Answer: 11 inches
    The scale says 1 inch stands for 16 feet. The real length is 176 feet, so 176 ÷ 16 = 11 inches.

Before and after

Learn first: Proportional or not? (7th)

Comes next: Slope and proportions (8th)

Name: ____________________Date: ____________Score: ____ / 12

Scale drawings (7th grade)

  1. A map uses this scale: 1 cm = 10 km. Two towns are really 40 km apart. How far apart are they on the map?
  2. A map uses this scale: 1 cm stands for 5 km. Two towns are really 35 km apart. How far apart are they on the map?
  3. A map uses this scale: 1 inch stands for 20 miles. Two towns are really 100 miles apart. How far apart are they on the map?
  4. A model ship is built to this scale: 1 inch stands for 4 feet. The model is 2 inches long. How long is the real ship?
  5. A model ship is built to this scale: 1 cm represents 5 m. The model is 5 cm long. How long is the real ship?
  6. A model ship is built to this scale: 1 inch stands for 4 feet. The model is 12 inches long. How long is the real ship?
  7. A model ship is built to this scale: 1 inch represents 6 feet. The real ship is 42 feet long. How long is the model?
  8. A model ship is built to this scale: 1 cm = 4 m. The model is 7 cm long. How long is the real ship?
  9. A scaled copy of a photo is made with scale factor 2. A side of the copy is 24 cm long. How long is the matching side of the original?
  10. A rectangle has a side 4.5 cm long. A scaled copy is made with scale factor 3. How long is the matching side of the copy?
  11. A model ship is built to this scale: 1 cm stands for 24 m. The model is 11.5 cm long. How long is the real ship?
  12. A model ship is built to this scale: 2 cm = 24 m. The real ship is 138 m long. How long is the model?

Answer key

  1. 4 cm
  2. 7 cm
  3. 5 inches
  4. 8 feet
  5. 25 m
  6. 48 feet
  7. 7 inches
  8. 28 m
  9. 12 cm
  10. 13.5 cm
  11. 276 m
  12. 11.5 cm

More 7th grade skills: all 7th grade math skills, or every grade at math skills.