Proportional reasoning – Calculating voucher discounts KS3 lesson

What's included?

PDF lesson plan and resources

Key Stage

KS3

Age

Years 7-9

Subjects

In this proportional reasoning lesson, students consider pairs of alternative discount vouchers in a restaurant and reason about which one will save them more money.

This involves comparing percentage reductions when the total bill is of different sizes, and the answer depends on how much money is being spent.

There are opportunities to consolidate understanding of percentages and graphical representations of relationships to make sense of a real-life problem.

Why teach this?

This proportional reasoning lesson helps students to make reasoned choices about which option will save them more money.

Key curriculum links

Extend understanding of the number system; make connections between number relationships, and their algebraic and graphical representations
Begin to model situations mathematically and express the results using a range of formal mathematical representations
Interpret fractions and percentages as operators

Starter activity

Suppose you go to eat in a restaurant. You have two discount vouchers, but you can only use one of them. Which one will save you more money? Why?

Voucher 1: £6 off your entire bill
Voucher 2: 30% off your entire bill

Students will realise that as the bill increases the ‘30% off’ will increase as well, and eventually overtake the fixed ‘£6 off’.

So, the thing to work out is where this critical point is: 30% of what amount = £6? This amount is £20. So, if your entire bill is less than £20, use voucher 1, and, if your entire bill is more than £20, use voucher 2. (And if your bill is exactly £20 then it doesn’t matter which voucher you use!)

Colin Foster is a Reader in Mathematics Education at the Mathematics Education Centre at Loughborough University. He has written many books and articles for mathematics teachers. Follow him on X at @colinfoster77. Browse more KS3 maths games and lesson ideas.