Matching Fractions

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

Begin by introducing the class to the printable cards before the interactivity. Give out sets of cards to each pair of learners and encourage them to lay them all out, face-up. You could offer any of the following prompts to encourage them to engage with the representations on the cards:

• How might you group/sort the cards?
• How might you order the cards?
• What is the same about the cards? What is different?
• Take three or four cards. Which one doesn't belong? Why? Can you choose a different card which doesn't belong? Why?
• Create another pair for the set. Can you create a pair which you think would be relatively easy to match? Can you create a pair which is harder to match? How did you decide which was easy and which was difficult.
• Rather than giving out all the cards, you could just give out half the set of cards so that each card does not have a pair. Invite learners to create a pair for each card they have been given.
• Share the cards out in a group of four. Take it in turns to describe what is on one of your cards without showing it to anyone else. Who has a card which shows an equivalent amount?

Once learners have explored the cards in some of these ways, show them the interactivity. You may like to begin to play the game on the interactive whiteboard with the whole group. You could choose a card and, before turning over a second card, invite learners to talk in pairs about what might match. As more cards are revealed, trying to remember which cards have already been seen and what they have on them becomes important too.

As soon as the class has a flavour of the game, suggest that they work in pairs at a computer, laptop or tablet. (They could use the printable cards if this is not feasible.) As they play in pairs, watch and listen, and make a note of anything you overhear that you'd like to refer to during a mini plenary. It may be that you notice a misconception more than once, or that you'd like to spend a few minutes inviting learners to explain how they knew that two particular cards are a match.

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. Perhaps the card that might be most challenging is the oblong with red shading. 

You could return to the interactivity in subsequent lessons, perhaps as a starter or during a plenary, where appropriate.

Key questions

What might the matching pair for that card have on it?
How do you know those two cards match?
Have we already seen a card that might be a match for that one?

Possible support

Playing the game with all the cards face-up is a great way to focus on the mathematics if the memory aspect proves tricky for some children. You can do this in this version of the interactivity.

Possible extension

Some pairs may enjoy challenging themselves to get as many points as possible using this version of the interactive game and/or trying to complete the game as quickly as possible (this version of the interactivity has a timer). Some of the suggestions in the opening paragraph of the 'Possible approach' above would make good extension tasks.