Year 8 · Maths · Multiplicative change · Lesson 1

Direct proportion

Learn the unitary method for direct proportion: find the value of one, then multiply. Includes shopping, recipes, rates, best buys and checking whether two amounts are in proportion.

35-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

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What your child will learn

Understand what direct proportion means
Use a table to solve proportion problems
Use the unitary method: find the value of one first
Compare prices to find the best buy
Decide whether two amounts are in direct proportion

The method

Write what you know in a table.
Divide both sides to find the value of ONE.
Multiply both sides to find the amount you need.
Check: does the answer make sense?

Key words: direct proportion, unitary method, rate, best buy, value for money.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

5 pens cost £2. How much do 3 pens cost?

Step 1: Pens: 5, cost: £2
Step 2: Find one (÷ 5): 200p ÷ 5 = 40p
Step 3: Multiply (× 3): 40p × 3 = 120p = £1.20

Answer: £1.20

Question 2

4 apples cost £1.20. How much do 9 apples cost?

Step 1: Apples: 4, cost: £1.20
Step 2: Find one (÷ 4): 120p ÷ 4 = 30p
Step 3: Multiply (× 9): 30p × 9 = 270p = £2.70

Answer: £2.70

Question 3

8 stickers cost 96p. How much do 5 stickers cost?

Step 1: Stickers: 8, cost: 96p
Step 2: Find one (÷ 8): 96p ÷ 8 = 12p
Step 3: Multiply (× 5): 12p × 5 = 60p

Answer: 60p