Why do this problem?
is an interesting context in which to practise addition and subtraction, and it extends children's thinking to look at all possibilities. It requires a systematic approach and recording is key. It is also easy to extend for high-attaining pupils.
A simple but effective way to introduce this problem would be to suggest to the class that you have five coins in your pocket and you'd like them to find out how much money you might have. Give them a few minutes to talk to a partner and then ask some children to share their thoughts. Start to write up their suggestions on the board, for example by listing the five coins and the total. Ask
them what the largest and smallest amounts would be (for example £10 and 5p when working in Sterling). At some point during this initial discussion, you may wish to list all the different coins for reference.
At this point, it would be good to focus the problem and one way of doing this would be to restrict the coins to just the two lowest value coins (for example 1ps and 2ps when working in Sterling). Alternatively, you could suggest that the five coins must all be different from each other. Whatever you decide, emphasise that you are keen for the class to find ALL the different ways and that is
what you will be looking for - good ways of making sure that every possibility is found.
Give them some time to begin work on this - they will find it useful to have mini-whiteboads or large sheets of paper for recording. At a suitable opportunity, have a mini-plenary to share some strategies. Some children might be listing coins at random, while others will have developed a system, for example, by starting with the smallest amount and gradually working upwards. Highlight the
benefits of a system of some kind so that you are sure none of the combinations is missed out.
Then leave learners more time to continue working. In the plenary, you could share your own way of working systematically and see whether your solution is the same as the children's.
How are you making sure you will find all the different combinations?
Challenge children to find all the totals between, for example, 5p and £1 (when working in Sterling) that can be made with five coins.
Having coins at the ready will be helpful for many pupils. Some may prefer to starting with just three coins and also just certain types of coins.