Scale and Maps

Use scale factors to find real distances from maps and plans.

  • Define and explain Scale and Maps in your own words
  • Use key terms such as Scale factor accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

This lesson focuses on Scale and Maps: use scale factors to find real distances from maps and plans.

Definition: Scale and Maps

Use scale factors to find real distances from maps and plans.

Key ideas

Sharing in a ratio

Add the parts to find the total number of shares, then divide the amount by that total. For £30 in the ratio 2:3, there are 5 shares of £6.

Direct proportion

When one quantity doubles, the other doubles too — the ratio between them never changes. Recipes, currency and map scales all work this way.

Key term — Scale factor: The number you multiply by to enlarge or reduce a shape, recipe or map.

Worked example: Scale and Maps

A map scale is 1:50,000. A road measures 6 cm on the map. What is its real length in km?

3 km — 6 × 50,000 = 300,000 cm = 3 km.

Answer: 3 km — 6 × 50,000 = 300,000 cm = 3 km.

Common mistakes
  • Adding instead of multiplying when scaling Doubling a recipe means multiply by 2, not add 2 — scaling is always multiplication.
  • Simplifying only one part of a ratio Every part must be divided by the same number, or the comparison changes.

Practice

Simplify 12:18.
Divide by the highest common factor.

2:3 — both divide by 6.

Share £40 in the ratio 3:2.
How many shares in total?

£24 and £16 — 5 shares of £8 each.

5 notebooks cost £7.50. What do 8 cost?
Find the cost of one first.

£12 — one notebook costs £1.50, and 8 × £1.50 = £12.

Are the ratios 4:6 and 10:15 equivalent?
Simplify both ratios.

Yes — both simplify to 2:3.

Quick check

Scale and Maps — quick check

Which of these best defines "Scale factor"?

The number you multiply by to enlarge or reduce a shape, recipe or map.

A drink mixes juice and water in the ratio 1:4. How much juice is in 500 ml of drink?

100 ml — 500 ÷ 5 = 100.
Key takeaways
  • Scale and Maps: use scale factors to find real distances from maps and plans.
  • Sharing in a ratio: Add the parts to find the total number of shares, then divide the amount by that total.
  • Unitary method: Finding the value of one unit first, then scaling up to the amount you need.
  • Watch out for: adding instead of multiplying when scaling