Five More Coins
This problem follows on from Five Coins so we would recommend looking at that one first.
Ben has five coins in his pocket.
How much money might he have? If possible, talk to someone else about your ideas.
Can you name an amount of money that Ben's five coins couldn't add up to? Why couldn't he have that amount of money?
Dayna is trying to guess how much money Ben has. She knows that altogether he has less than £1.
Dayna starts writing down all the amounts of money less than £1 that Ben's five coins could add up to.
Could Ben have any amount of money between 5p and £1 in his pocket, or do you think there are some amounts that would be impossible for him to have?
Have a go at writing out Dayna's list of numbers, showing how Ben could make each total with five coins. If there are any numbers missing from the list, can you explain why these amounts are impossible for Ben to have?
Why do this problem?
This activity is an interesting context in which to practise addition and subtraction, and it helps learners to become more familiar with coin denominations. It requires a systematic approach and recording is key.
This task follows on from Five Coins, and so it would be worth having a go at that problem before tackling this one.
Introduce the first part of the problem, with Ben having five coins in his pocket. Give them a few minutes to talk to a partner about how much money Ben might have, 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. (You may wish to list all the different coins for reference.)
Challenge learners to suggest an amount of money that they think would be impossible to make from five coins, and importantly, why that total is impossible. For example, some pairs might offer a total that is less than 5p, or more than £10; some might suggest an amount which includes a fraction of a penny, such as 20.5p. (You may wish to explain that there used to be a halfpenny coin, but it
was removed from circulation at the end of 1984.)
Lead into the main part of the task by introducing the character Dayna. What is the class's 'gut' feeling - will all the totals from 5p to £1 be possible, do they think? Give everyone time to begin work on this challenge. At a suitable opportunity, have a mini-plenary to share some approaches. Some children might be working up from 5p, to 6p, to 7p... i.e. starting with the
smallest amount and gradually working upwards. Highlight the benefits of a system of some kind in this context - learners might get a feel for the idea that replacing a 1p with a 2p will always increase the total by 1p, for example.
Leave learners more time to continue working. You could invite pairs to contribute to a list of totals, and the five coins that make each total, on the board or on a wall display. If you dedicate part of your wall space, you could leave the challenge 'simmering' for a few days and encourage children to contribute combinations and totals as they find them.
In a final plenary, focus on the totals that have not been made. Are they impossible, or is it just that we haven't found a way of making them with five coins yet?
How are you going about this challenge?
If you can't find a way of making a particular total, are you certain you have tried all possibilities? Or is this total impossible? How do you know?
Five Coins is a good problem to try before this one. Having coins at the ready will be helpful for many pupils.
Encouarge learners to tweak the task themselves by asking "I wonder what will happen if we...?"