Eightness of Eight
Problem
Watch the video above all the way through.
What do you see?
Play it again. You could pause it while you're watching, if you like. And you might like to watch it again more than once.
Describe what you notice.
Each time the counters are moved, what is the same? What is different?
Imagine you are making a similar video but with twelve counters.
What would it look like?
We would love to see your ideas - you could make a video, or you could take photos, or you could draw pictures, or...
You may be interested in the other problems in our Look More Closely Feature.
Getting Started
How will you know whether you have already made that arrangement before?
Student Solutions
Thank you to everybody who shared with us their ideas about ways to represent twelve. Dhruv from The Glasgow Academy in the UK used number bonds to twelve to make these representations:
The children at Priory Junior School in the UK sent in the ideas below. Some children made arrays to represent twelve, using multiplication facts to describe these, but some children found different ways of representing the number twelve:
Thank you all for sending in your ideas!
Teachers' Resources
Why do this problem?
This task offers the opportunity to explore several aspects of number and counting, such as subitising (recognising the number of items without counting), conservation (rearranging items does not affect the total number present) and composition of numbers (numbers being made up of other numbers). The aim of the video is to capture learners' curiosity so they want to explore other numbers in the same way and make new discoveries for themselves.Possible approach
Before playing the video, explain to the group that you would like them to watch it while trying not to say anything to anyone else. Tell them that you will play the clip all the way through without stopping and you would like them to think about what they see. Explain that you will then give them an opportunity to talk to a partner.As they discuss what they saw with someone else, move around the room and listen to their conversations. Write up snippets of what you hear on the board and draw learners' attention to this, merely explaining that this is what you have overheard. (You could read out what is written if children will struggle to read it independently.)
Play the clip again all the way through and ask the group to watch again. This time suggest they can talk while they watch if they wish. Give them chance to discuss further in their pairs and challenge them to describe what they notice. You could share some points and then play the video again, stopping and starting as necessary as you facilitiate the whole class discussion. Try to acknowledge all contributions, even if learners offer something that you had not thought of, or that seems irrelevant. For example, some may comment that the counters are different sizes. While this isn't a focus for the lesson, welcome the observation.
Through the discussion, draw out the key features of the video, such as
- the total number of counters (8) does not change even though they are moved into different arangements;
- 8 is made up of 7 and 1, or 6 and 2, or 3 and 3 and 2, and so on;
- it might not be necessary to count 8 each time as we might recognise some groups without counting.
Challenge children to create their own version of the video for the number 12. Provide them with counters and a way of recording their arrangements, for example large sheets of paper or cameras/tablets.
A plenary could focus on, for example, creating a whole class version of 12, which could be displayed on the classroom wall.
Key questions
What do you see?Describe what you notice.
How will you group the counters now?
Tell me about this arrangement of counters.