Scale Factor and Maps
Ratio between drawing size and real size.
Key idea
Ratio between drawing size and real size.
In depth
A scale factor is the ratio of a drawing length to the real length. Multiply by it to scale up, divide to scale down. Lengths scale by k, areas by k², volumes by k³.
Worked example
On a 1:50,000 map, 3 cm represents 3 × 50,000 = 150,000 cm = 1.5 km.
Real-world uses
- Reading road maps and floor plans
- Scaling model cars or architectural drawings to real sizes
Common mistake
Scaling areas by k instead of k².
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Scale Factor and Maps?
Ratio between drawing size and real size. It is a topic at the intermediate level in Arithmetic & Number Sense.
Where is Scale Factor and Maps used in real life?
Real-world examples: Reading road maps and floor plans; Scaling model cars or architectural drawings to real sizes.
What should I learn before Scale Factor and Maps?
Make sure you are comfortable with Inverse Proportion, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Scale Factor and Maps?
Scaling areas by k instead of k².
How can I practise Scale Factor and Maps?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Scale Factor and Maps?
Move on to Unit Conversion next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.