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Proportional reasoning

Published: Feb 18, 2016 3 min read

michael anderson

Shoppers "fail to spot cheapest deals"

‘Best buy’ questions in mathematics are not new; they have been a staple of GCSE exams for years- so should we be surprised to hear the news that “shoppers fail to spot cheapest deals”?

Last week the Money Advice Service revealed that three quarters of customers are overspending at the supermarket thanks to the lure of special offers and deals. On average we spend an additional £11.74 every time we visit the supermarket - that’s £1,274 a year.

Only 2% of those who completed the Money Advice Service quiz managed to pick out the best value deal in all four cases - how do you think your students would perform? The questions, and link to the online quiz can be found below.

These findings support the need for the recent GCSE changes, in which ratio, proportion and rates of change now make up 20% of the subject content at Higher tier, and 25% at Foundation tier in GCSE examinations. Instead of explicitly covering proportion questions in a small number of unconnected situations, mathematics departments are now required to ensure key concepts of proportional reasoning are embedded within teaching in a variety of contexts. The resource collection ‘Proportion’ includes a number of ideas to get you started.

The quiz

1. Of the following options for milk, which represents the best deal?

a) Six pints of milk for £1.80

b) Four pints of milk for £1.40

c) Two six-pint cartons of milk on offer for £3.50

d) Two four-pint cartons of milk on offer for £2

2. Of the following options for buying 500g of lemons, which represents the best deal?

a) One 500g pack of lemons costing £1.20

b) 500g of loose lemons at £2.50 per kilo

c) Buy two get the third free deal on 200g packs of lemons costing 70p each

d) Buy one get one half-price deal on 250g packs of lemons costing 70p each

3. Of the following options for buying tomato ketchup, which represents the best deal?

a) One 460g bottle on offer at £1.50

b) One 910g bottle costing £2.49

c) Buy one get one half-price deal on 700g bottles costing £2.29 each

d) One 1.35kg bottle costing £3.50

4. Of the following options for buying eggs, which represents the best deal?

a) Six medium eggs for £1.10

b) Ten medium eggs on offer for £1.50

c) Fifteen medium eggs for £2.10

d) Two packs of six medium eggs on offer for £2

e) Buy one get one free offer on packs of 10 medium eggs priced at £2.20

 

Fill in the quiz online on the Money Advice Service's website.