Why do this problem?
This number activity
can be stated very simply but has huge potential. It simulates pupils' curiosity, engaging them in thoughtful work and motivating them to challenge and deepen their own understanding of number.
You could build further on children's natural curiosity by encouraging them to ask "I wonder what would happen when...?". If you are interested in pursuing curiosity in particular, then please see the 'Further note' at the bottom of this page.
You could begin by introducing the task and giving time for children to record one way of making 8 on a mini whiteboard, on their own. Then invite them to record another way. Then another way. Continue this so that they have at least five examples. Then ask them to turn to a partner and share ideas.
Bring everyone together and ask how they felt being asked for another example, then another, then another... This way of working often encourages learners to challenge themselves in a way that asking for a particular number of examples all at once doesn't do. This raises children's awareness of the range of examples open to them rather than immediately opting for the first one that sprang
to mind. (See John Mason's Open University course booklet Working On Your Own Mathematics
, 2017, for more information about this approach.)
Invite pairs to share their ideas and record them on the board for all to see. You may find it helpful to try to group their suggestions into the four rules of number: addition, subtraction, multiplication and division, if applicable. The prompts you use will depend on the sorts of statements offered by the children, and how varied they are. If, for example, most statments use exactly two
numbers, point this out and ask children to try to use three or four numbers to get 8. If they have used addition only, suggest that they could start with a biggish number and then take some away and then have to take some more away in order to end up with only 8. They may be motivated to create examples that they think no-one else will have thought of.
Allow plenty of time for pairs or individuals to work further on the task. A mini plenary might draw attention to those contributions that follow a particular pattern e.g. 1 + 7, 2 + 6 ... , encouraging children to write 'etc' to indicate that there were some more if they thought so. This activity could be left 'simmering' so that you come back to it later in the week and leave a space on
your working wall for contributions in the meantime.
Tell me what you are doing here.
How have you got these?
Could you find any more like that?
You might find that, for example, a pupil continues with lots and lots of subtractions, raising the starting number by just one each time. It is useful to allow that to happen for a while as there are some fruitful conversations to be had about the patterns and how long they will continue. However, after a suitable period, encourage them to venture further. You might deliberately drop
in a prompt about a certain area of mathematics (e.g. halves), even if the class has not formally been taught that topic. You may be surprised!
If a pupil has eight objects then they can make a start on this activity by putting the eight into a number of groups and say "this, plus this, plus this, makes 8".
You may be interested in the following talks given by Professor Susan Engels, which focus on encouraging curiosity and are available on YouTube:
The Rise and Fall of Curiosity
- the extract from 23.50 to 37.15 on adult encouragement and teacher behaviour is particularly worth viewing;
The Hungry Mind: The Origins of Curiosity
- the extract from 8.22 to 12.29 on children asking questions is especially useful.