Percentages game: discounts, VAT and shop deals
A maths game for using percentages where they are really used: in a shop. A product tag appears showing the journey of its price (the price, the percentage and the final price), and one of the three is unknown. You work out how much you pay with a discount, how much you save, what percentage the reduction is, how much it costs with or without VAT, what the price was before the sale, or which shop is cheaper with deals like 3 for 2 or the second one half price. When you answer, the «?» fills in and the full working appears. The wrong options are not random: they are the typical percentage mistakes.
Mathematics · Primary, Secondary
Almost every percentage mistake comes from adding or subtracting the percentage as if it were euros. The game explains each answer with the multiplier: 25% off is × 0.75 and VAT is × 1.21. That single idea handles discounts, increases, the old price and chained changes.
Going up 20% and down 20% does not leave the price unchanged; 20% off plus an extra 10% is not 30%; taking 21% off a price with VAT does not give the price without it. Those wrong answers are among the options, and falling for one once (and seeing why) is the best vaccine.
Comparing 3 for 2 with 30% off, or knowing whether a sale is as good as it looks, is something people do every day. The products and prices are realistic, from a €12 T-shirt to a €900 laptop, and the numbers come out exact to the cent.
"A pair of trainers costs €50. In January the price goes up 20% and in the sales it comes down 20%. What does it cost now? Almost everyone says €50, and that option is there. The working is 50 × 1.2 = €60 and then 60 × 0.8 = €48: the 20% reduction is worked out on €60, which is more than €50, so more is taken off than was added."
Prefer to learn without screens? Try this analogue version:
Cut out five products with their price and discount from leaflets or a shop’s website.
For each one, work out the final price with the multiplier and check it matches the advertised one.
Find a 3-for-2 or “second one half price” deal and work out what percentage discount it is equivalent to.
Decide which is really the best deal of all and explain why.
If you like Sale!, these activities work similar skills:
Multiple choice on percentages, the rule of three, direct and inverse proportion and scales, with an explanation for each answer.
Type in your own exercise (a discount, an increase, what % it is) and it solves it showing every step.
With a real supermarket receipt, find which products were discounted, then work out the total saved and what percentage of the receipt it is.
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