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Help at home · Maths

How to explain proportion and scaling to your child

Scale amounts up or down: a recipe for 4 people made for 6, or 'If 3 pens cost £1.20, how much do 7 cost?'

The note

How schools teach it now

Children use the 'unitary method' (find the cost of one first, then multiply) or a ratio table, scaling both columns by the same number. Double number lines are also common.

5-minute kitchen-table activity

Pick a recipe for 4 people and rewrite it together for 6. 'If 200 g of flour serves 4, how much for 6?' (Find it for 2 people: 100 g. Six people is three lots: 300 g.)

Worked example

3 pens cost £1.20. How much do 7 pens cost?

  1. Find the cost of one pen: £1.20 ÷ 3 = 40p.
  2. Seven pens: 7 × 40p = 280p.

Answer: £2.80

Common mistakes to watch for

  • Adding instead of multiplying when scaling up.
  • Mixing up pence and pounds in the answer.
  • Scaling only some of the ingredients in a recipe.

Encouragement

Try saying
“What would just one cost?”
Rather than
“Think harder, it's simple.”

Practise proportion and scaling with marked questions

Academy11+ marks every answer, shows how your child is doing in each topic and puts the right home-help note next to the ones they find hard.