# Matching Fractions, Decimals and Percentages

*To download a printable version of this game, use the links below. There are three sets - set A is the easiest and set C is the most difficult.If you print double sided, then the cards will have an NRICH logo on the back. Otherwise, you can just print the first page.Set A, Set B, Set C*

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

Click on a card in the interactivity below to turn it over. Then click on another one. If the two cards match, they will stay face-up. If the two cards do not match, they will return to being face-down.

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 Level 1 game:

- Play with face-up cards - the cards are all face-up at the start so you can focus on the maths rather than the memory aspect of the game. How quickly can you match them all?
- Play with a scoring system - you start with 100 points, lose 10 points whenever you turn over cards that don't match, and add 50 points whenever they do match.

Once you've mastered Level 1, there are four more levels to try, getting progressively more difficult:

- Level 2 Face-up Face-down
- Level 3 Face-up Face-down
- Level 4 Face-up Face-down
- Level 5 Face-up Face-down

What strategies did you use to work out that two cards matched?

Which pairs did you find easy to match?

Which pairs did you find more difficult to match?

**We would love to hear about the strategies you used as you played the game.**

One third can be represented in all the following different ways:

$$\frac{1}{3} \mbox{ or as an equivalent fraction e.g. } \frac{3}{9} \mbox{ or } \frac{5}{15}$$

A pupil from Gamlingay Village Primary sent in the following:

At first my card choices were random, but when I had remembered some cards I tried to match them and remember what was on each card. I also tried to convert the numbers on the cards into the same thing (e.g: decimals, fraction or percentage), which made it easier to tell if they matched one I had remembered.

Madeleine from the British School of Manila in the Philippines had a similar strategy:

My strategy was to look at random ones and guess at the beginning, then at the end I would remember where pairs were and do them quickly.

Callum from Wembrook Primary School wrote:

All you have to do is memorise the cards you have already flipped over and when you find one either in a decimal, a percentage or a fraction you have already found just match it to the equivalent card.

Erik from International School of the Hague (ISH) in the Netherlands wrote:

I did the matching fractions, decimals and percentages problem. The fastest way to get all the cards matched (if you are on cards up) is focusing on the easiest ones first. After you have matched all the easy ones, you have narrowed down the hard ones' possible answers. If you start on the harder ones, you will be looking through the flash cards to find an answer, and that will take you longer and you will get a higher time. Don't work hard, work smart.

Christopher from England wrote:

I recorded what each square was on a piece of paper as a fraction in its simplest form. Then, I matched them up, ticking them off as I went.

Mark from the International School of the Hague wrote:

First, I converted all the irregular values to decimals, to make them equal. For fractions, I converted the denominator to a hundred and then the numerator accordingly, so that the denominator was equal to hundred. The numerator was then the tenths and hundredths place of the decimal.

For the shapes, I counted how many there were in total and then how many were shaded to a fraction. The number of how many were shaded was the numerator and the total number was the denominator, I then did the same process as the fractions. And completed it.

Mahdi from Mahatma Ghani International School in India focused on finding the pairs as quickly as possible with the cards face-down, once you are already fluent with converting between the fractions, decimals and percentages. This is Mahdi's strategy:

For the face-down cards, I started to open the cards two at a time, labeled 1 and 2. If the two match, I open the 3rd and the 4th and continue. If 1 and 2 don't match (which is very likely), I proceed to open the 3rd one. I then recall whether the 3rd matches with any of the previous ones (1 and 2) in any simplified form. If not, I open the forth and continue. This was the general strategy I followed.

Also, I found out that [by] the 9th card I will definitely have a match. This is due to the pigeon-hole principle *(if the first 9 cards were all different to each other, then they would each still have a pair somewhere else - so there would be 9 partner cards - but there are only 16 cards altogether)*. So, in the worst-case scenario every card from 1 to 8
has a corresponding match from 9 to 16 in some order. Thus when I open the 9th card it will definitely have a match for one of the 1-8 cards. This makes the strategy easier because I only have to memorize cards till 8 if there is no match. Otherwise, the game will get a lot easier if I luckily get a match before that.

Why do this problem?

This game can be played to improve students' recognition of equivalent fractions, decimals and percentages.

### Possible approach

*There are three sets of printable cards, which you may find useful. Set A is the easiest, and set C is the hardest. Each half (top/bottom) is a stand alone set so you can combine these to form the size and difficulty that you would like.*

For example, you might want to combine the bottom half of set A with the top half of set B, or all of set B with the top half of set C.

If you print double sided, then the cards will have an NRICH logo on the back. Otherwise, you can just print the first page.

For example, you might want to combine the bottom half of set A with the top half of set B, or all of set B with the top half of set C.

If you print double sided, then the cards will have an NRICH logo on the back. Otherwise, you can just print the first page.

*Set A, Set B, Set C*

Demonstrate the game using the interactivity or the printed cards. Then invite students to play the game, moving on to the next level of difficulty when they are ready.

*Level 1 on the interactivity uses cards from Set A.Level 2 on the interactivity uses cards from Sets A & B.Level 3 on the interactivity uses cards from Set B.Level 4 on the interactivity uses cards from Sets B & C.Level 5 on the interactivity uses cards from Set C.*

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 different versions of the game.

Key questions

What could match with 0.3?

What could match with 25%?

What could match with $\frac35$?

Which cards did you find easier to match?

Which cards did you find more difficult to match?

### Possible support

Encourage students to play in face-up mode a few times before moving on to face-down mode.

Matching Fractions can be used to help children develop their understanding of fractions before moving on to this activity.

### Possible extension

Students can play the Fractions and Percentages Card Game where the card matching requires calculations.