Maths Library

Proportion and Unit Rates: Year 9 maths

This topic covers direct proportion, unit rates, and best-buy comparisons. Students practise using unitary methods to scale quantities up and down in practical scenarios.

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What this covers

Proportion and Unit Rates is taught in Year 9 (age 13 to 14, KS3) as a main teaching focus. It sits in the Ratio strand.

Worked example

If 5 pens cost £3.50, find the cost of 8 pens.

  1. Find the cost of 1 pen: 3.505 = £0.70
  2. Multiply by required quantity: 0.70 x 8 = £5.60
  3. State final value

Answer: £5.60

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Unitary scaling using whole integer multipliers (e.g. 1 to 4 items)
  2. Finding 1 unit first to calculate multiple units with integer answers
  3. Unit rates involving decimals and money (e.g. cost per item or per 100g)
  4. Best-buy comparisons between two different packet sizes
  5. Recipe adaptations and inverse proportion problem scenarios

Common mistakes

  • Adding the difference instead of multiplying by the scale factor
  • Inverting the rate division (e.g. doing grams divided by pence instead of cost per gram)

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Solve direct and inverse proportion problems using unit rates and fractional comparisons.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Proportion and Unit Rates

Year 9 maths

Qs
6
Marks
12
NameDateScore / 12
1.
3 packets cost £12. How much do 6 packets cost at the same rate?
[2]
2.
6 packets cost £24. How much do 12 packets cost at the same rate?
[2]
3.
8 packets cost £64. How much do 12 packets cost at the same rate?
[2]
4.
6 packets cost £18. How much do 12 packets cost at the same rate?
[2]
5.
8 packets cost £40. How much do 11 packets cost at the same rate?
[2]
6.
2 packets cost £10. How much do 6 packets cost at the same rate?
[2]

Answer key

  1. £24One packet costs 12 ÷ 3 = 4; 6 × 4 = 24
  2. £48One packet costs 24 ÷ 6 = 4; 12 × 4 = 48
  3. £96One packet costs 64 ÷ 8 = 8; 12 × 8 = 96
  4. £36One packet costs 18 ÷ 6 = 3; 12 × 3 = 36
  5. £55One packet costs 40 ÷ 8 = 5; 11 × 5 = 55
  6. £30One packet costs 10 ÷ 2 = 5; 6 × 5 = 30