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# Equivalent Pairs

## Equivalent Pairs

### Why do this problem?

### Possible approach

### Key questions

### Possible support

### Possible extension

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Age 5 to 7

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- Problem
- Student Solutions
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*Equivalent Pairs printable sheet*

The aim of this activity 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 show the same amount, they will stay face-up. If the two cards do not show the same amount, they will return to being face-down.

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

How do you know when a card matches another card?

Can you remember where particular cards are to help you match the pairs?

You might like to explore different ways of pairing the cards.

You may like to explore these alternative versions of the interactivity:

- 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.
- Play against the clock - can you beat your personal best?
- 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.

This problem is designed to deepen children's understanding of equivalence and offers an opportunity to practise number bonds.

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 number sentences/numbers on the cards:

- How might you group/sort 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?
- Share the cards out in a group of four. Take it in turns to read out 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.) If using the interactivity, it would also be useful to encourage them to record each pair of cards they match, for example on paper or a mini whiteboard. As they play, watch and listen, and make a note of anything you overhear that you'd like to refer to during a mini plenary or during the final plenary. It may be that you notice misconceptions or that there are particular methods you would like to share with the whole class.

In the final plenary, invite learners to explain *how* they knew that two particular cards are a match. Encourage other members of the class to comment on, or ask questions about, any reasoning that is verbalised. At this point, it will become apparent (if it has not already!) that there is more than one way to match pairs. You could use the interactivity with the cards face up to
explore this further and find, for example, all the cards which equal 10. (To see the cards face up from the start, click on the 'Settings' cog in the top-right corner and select 'Face up', then click on either of the two buttons at the bottom for the change to take effect.)

You may wish to take this opportunity to introduce or consolidate use of symbols to create a number sentences for two matching cards, for example, 9+1=10+0. This might reveal some further misconceptions, such as there can only be a single number after the equals sign and/or that an equals sign means 'the answer comes next'. Make time to talk about this with the whole group, encouraging learners to interpret the equals sign as 'the same number as' or 'the same amount as'.

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

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?

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.

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.

Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?