### Chocolate

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

### Doughnut

How can you cut a doughnut into 8 equal pieces with only three cuts of a knife?

### Rectangle Tangle

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

# Matching Fractions

## Matching Fractions

Click the cards to turn them over. Can you match them? What do you need to look for?

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Here is the set of cards

### Why do this problem?

Children sometimes think there is only one representation of fractions; usually pizzas or cake slices! This game is designed to help children see fractions in many different ways: by looking at a range of images of one fraction they can begin to develop a deeper understanding of what a fraction is.

### Possible approach

Children could play this in pairs at the computer, or you could use it as a whole class game using the IWB.

You could introduce the ideas by asking the group to tell you, or to draw, as many ways as they can of showing you a fraction, for example, a half or three quarters. Alternatively you could offer a couple of pictures and ask the children what fraction they represent, and how they know.

The different representations on the cards are not meant to be difficult to work out, but should give some opportunity for further discussion about why a particular image is a representation of a specific fraction. For this it can be useful to  have different mathematical equipment available, as well as paper and coloured pencils.

If you want to play the game using 'real' cards rather than virtual ones, here is the set of cards.

### Key questions

What fraction does this show?
And this one?
Is it the same? How?
Is it different? How?

### Possible extension

Learners could make their own sets of additional cards for the fractions used in the task or make additional sets of cards with different fractions. Here is a set of blank cards. The game could be changed to a 'Happy Families' type game where the children work with printed sets of cards or their own sets to make sets of four or more cards by exchanging cards with their neighbours. The task would then be to describe to their friend the card they are seeking. This would help them to develop descriptive language as well as their memory of who might hold the card.

### Possible support

An easier approach might be a sorting exercise in which children focused on sorting the printed cards into matching sets.