Equivalent Pairs

Why do this problem?

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

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 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. 

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.