- 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.
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.
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.
- 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
2:3 — both divide by 6.
£24 and £16 — 5 shares of £8 each.
£12 — one notebook costs £1.50, and 8 × £1.50 = £12.
Yes — both simplify to 2:3.
Quick check
Which of these best defines "Scale factor"?
A drink mixes juice and water in the ratio 1:4. How much juice is in 500 ml of drink?
- 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