# My best lesson - Hit the January sales to explore percentages

9th January 2015 at 00:00

Percentages: a straightforward topic to teach? Maybe, but a wide variety of prior learning is guaranteed among your students, and you will need a task that can be extended to keep the whole class engaged. The following activity does just that.

You go to buy a coat in town. The one you want is on offer in four shops. In each case, it was originally on sale for pound;120. The shops are now offering four different sale deals:

• Shop 1: 40 per cent off, then pound;10 off
• Shop 2: pound;40 off, then 10 per cent off
• Shop 3: 10 per cent off, then pound;40 off
• Shop 4: pound;10 off, then 40 per cent off
• Which is the best offer? It's a motivating challenge for students.

The order of generosity for the shops in the problem is 1, 4, 3, 2. But a possible surprise follows: this order changes if the original price of the coat changes.

Suppose the initial price is pound;80; which is the best deal now? We find that the order of generosity for the shops is now 3, 2, 1, 4.

Some questions present themselves. Will shop 3 always be better than shop 2? Will shop 1 always be better than shop 4? Can a pair of shops ever be equal to each other? What if the percentage discount is equal to the pound discount? What if the cost of the coat is pound;100?

You can take the exercise into even more advanced territory by downloading the spreadsheet tool (follow the link in the red panel below). Students can change the initial cost of the coat, or the pound and percentage reductions, to calculate the final price for a number of scenarios. So pupils can see, for example, whether a pound;120 coat is cheaper when 20 per cent is taken off the price followed by a further pound;20, or when pound;20 is taken off followed by a further 20 per cent reduction.

The options are extensive, and students can set questions for each other based on their discoveries. That's enough to keep everyone busy!

Jonny Griffiths teaches at a sixth-form college in Norfolk

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