# Fractions and Percentages Card Game

* Fractions and Percentages Card Game printable cardsIf you print double-sided, the cards will each have an NRICH logo on the back. If you would prefer them to be blank on the back, just print the first page.*

The aim of this game is to match pairs of cards.

Click on a card in the interactivity below to select it. Then click on another one. If the two cards match, they will change colour. If the two cards do not match, select another pair.

The game ends when all the cards have been matched in pairs.

Click on the links below if you would like to try some alternative versions of the game

We would love to hear about the strategies you used to work out which pairs matched.

A useful strategy for working out percentages of quantities is to work out 10% first, and then use fractions or multiples of that amount.

Chris described a method for finding the percentages as amounts of money:

To find out a percentage out of a number you can divide the number by $100$ or $10.$ [Say] you divide the percentage by $10.$ After that you find out what the number divided by $10$ and the percentage by $10$ and you times it.

Eg. $40\%$ of $ £11.20,$ $11.20\div10 = 1.12.$

You divide $40$ by $10$ which equals $4.$

$1.12x4= £4.48.$ Therefore $40\%$ of $ £11.20$ equals $ £4.48$

Mark from International School of the Hague described a method for the fractions:

First I figured out what the fractioned numbers were by converting them to decimals. I did this by converting the denominators to a hundred. Then I [multiplied] the decimals by the currency that was on the same card and then I had different currencies that were equal to each other. I selected these and finished.

Sienna from Greenacre Public School in Australia described a way to speed up the matching:

However, there is a way to make to make this process faster. For example, $25\%$ of $4,$ you could assume that it would be less than a half of it. This would make the other options much more limited.

Erik from International School of the Hague described another way to speed up the matching:

The easiest way of doing this exercise is doing the easiest ones first. Also, you really need to know your fractions of a number, and percentages of a number really well for this exercise. If you do the easiest ones first, you have less space so you can find the answers to the harder ones easier, and if you leave the hardest flashcard to the last, you will automatically know the answer.

### Why do this problem?

This game offers students an opportunity to practice calculating fractions and percentages of amounts.

### Possible approach

For some students it may be appropriate to have access to calculators or pencil and paper, or you could challenge students to work out the calculations in their heads.

Bring the class together and ask for any tips or strategies that help with the game.

You could invite students to create their own sets of cards that they can share and use to play their own versions of the game.

### Key questions

Which fractions and percentages are easy to work out?

Which are more difficult?

If you know 10% of a quantity, how could you work out 30%? 5%? 15%?

### Possible support

Students could work on Matching Fractions, Decimals and Percentages first.

### Possible extension

Fair Shares is a challenging investigation involving fractions of amounts.