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Maths - Percentages in the bag

Shopping brings some crucial calculations into the real world

Shopping brings some crucial calculations into the real world

Retailers rely on maths in many ways - from pricing and managing wages to the lure of "special offers". In textbook examples we have all seen the percentage-reduction questions that rely on subject X being in a sale. But there is a lot more you can do with percentages and shops - particularly when advertising often gets the maths so wrong.

An example of getting the pricing wrong in relation to the promised percentage reductions can be a good introduction. I use pictures of real examples, taken on my phone, to illustrate the points.

Example 1

On a shelf with a claimed reduction of at least 75 per cent, there was a stack of table cloths reduced to pound;1.99 from a starting price of pound;5.99 - probably an honest mistake, but I wonder how many people bought one without realising the error. I get students to calculate what the cost should have been if the maths had been correct, among other percentage calculations.

Example 2

This is more complex, but draws out a crucial point. Tesco had an online sale with 20 per cent off and claimed "That's VAT free". The VAT rate is 20 per cent at present, but the value of the offer depends on when that 20 per cent is taken off. I like to show this by letting students work through the possible combinations with something of high value, like a flat-screen TV. It's a great way to lead into questions like: "If the TV costs pound;800 once VAT has been added, what is the pre-VAT price?" I have found that students have been surprised that if the 20 per cent discount is applied after VAT is added they get a better deal than if VAT is not added at all.

Example 3

I dislike tags that promise "up to 30 per cent off", with the "up to" in small letters. I found an example where the price had been cut from pound;29.99 to pound;24.99, which is more like a 17 per cent discount. This may be technically "up to 30 per cent", but it's a long way from the saving you expected from a first casual glance.

All three examples make excellent starters or plenaries and can generate citizenship discussion. Aside from working out the figures, my students talk about whether the "percentage off" sign is important at all. Do we need it if we can see the "before" and "sale" prices. Surely people can work it out themselves?

I encourage students to look for these signs while they are out shopping. Some of them now stop me in the corridor with, "Sir, you won't believe what I saw in ."

Dave Gale is a mathematics advanced skills teacher in North Somerset. Find him on Twitter: @reflectivemaths.

What else?

Functional Maths - Everyday Maths from Axis Education is a popular resource for students to practise their skills in familiar situations

The My Money Citizenship Teacher Handbook from PFEG is designed for teaching pupils the importance of personal finance

Forum links Read advice from maths teachers on the easiest way to work out percentages, or see suggestions on how to do them without using a calculator

Wherever you see the number icon on these pages, visit to link to resources.

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