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Fair Exchange

Stage: 1 Challenge Level: Challenge Level:1

Fair Exchange


In your bank, you have three types of coins. The number of spots shows how much they are worth.

Coin with one spot. Coin with two spots. Coin with three spots.
1 2 5

Can you choose coins to exchange with the groups below to make the same total?

Full screen version

This text is usually replaced by the Flash movie.

Can you find another way to do each one?


Why do this problem?

This problem gives opportunities for children to practise numbers bonds in the context of a game. Children can try out different options to find sets with equal numbers of spots in them.
You could focus on encouraging learners to work systematically to find all possibilities.

Possible Approach

Introduce the activity to the class on an interactive whiteboard and ask them to choose a number to match from the three choices $5$, $8$ and $11$. The 'coins' in the game have the same number of spots as the number they represent which makes them easier for children to work with than either toy coins or real money. It would be possible to use real coins or toy money as an alternative.
Ask the children what each of the target numbers is in turn: $5$, $8$ and $11$. Then see if they can suggest different sets of coins that have the same value and try them out using the interactivity.
The children could then go on to creating their own equivalent sets of coins either using coins cut out from this Word document and pdf card showing coins worth $1$, $2$ and $5$.

Key questions

What is the total you've got to make?
How many more do you need?
Can you do it in a different way?
What is the largest coin you could use?
Could you make that amount with just twos?

Possible extension

Children can choose their own target numbers and see how many different equivalent sets they can make using coins worth $1$, $2$ and $5$. They coulc use real coins instead of the printed version and even move on to higher deniminations such as $10$p or $20$p.
Learners could try Weighted Numbers which uses more numbers.

Possible support

Plenty of practice with exchanging small collections of coins may be needed by some children. Understanding that $5$ penny pieces are worth the same as one $5$p piece is tricky and may take time to establish with young children.