Rachel Rayner is a Teaching and Learning Adviser for Primary Mathematics at Herts for Learning. She has previously blogged about greater depth at KS1 here, and after pictures of a session she ran at one of the schools she supports became very popular on Twitter, we thought it might be useful to share her approaches. The lesson was taught to a mixed group of Year 1 and 2 pupils at Huntingdon Primary School, Cambridgeshire.
I’m going to come completely clean here, it wasn’t my idea this problem. I found this from the NCETM Teaching for Mastery – Questions, tasks and activities to support assessment document for Year 1. Like any good magpie not all my ideas are completely original – I’m always looking for simple little items that glitter.
But with meeting the needs of all learners in mind – I began by thinking about access.
What would allow pupils to explore this deeply more quickly, to get to the heart of the problem without distraction?
Firstly I felt that the ‘squiggles’ were too abstract alone and thought that Numicon (or unicorn as some of the Year 1s called it on the day) would be useful for a number of reasons.
- he shapes can be moved, allowing for adjustment without the commitment of putting pencil to paper
- the holes in the shapes can be used for estimation – Do you think there are more holes in this line or this line?
- the holes are countable and can be subitised – when young pupils get tired they can revert to counting but the holes might help them stay calculating for longer by subitising
- they can be easily arranged to test equality
- pupils at the school I knew were familiar with the resource
I also began with a pre-teach – I simply drew 5 boxes in a line horizontally on a whiteboard and arranged Numicon 1-5 shapes in them. Then drew another 5 boxes underneath and arranged the Numicon shapes in a different order. I wanted to check that pupils understood that the sum would remain constant whichever order we placed the shapes in. Pupils seemed convinced and so I modelled the problem – incorrectly of course at first as we don’t want to give the crown jewels away completely. And off they went, often in mixed age pairs which we (the teachers and I) all found fascinating to observe the dynamics of.
And off they went – some of the pairs literally did not raise their heads for another 40 minutes, so fascinated were they with trying to find magic numbers! They estimated, calculated (and then counted to check as they started to tire). We asked the pupils to record, which they all did beautifully, very differently in each pair and sometimes with the lovely idiosyncrasy of children – joyous (one pair decided the lines of the cross were sleaping lines and standing lines in their written recording). Some pupils began to notice the balancing arms of the problem – a feature I wasn’t sure they would. As they noticed this they began to work differently, purposefully considering the shape in the middle and how they would balance the remaining four shapes equally.
In the pictures you can see pupils solving the problem finding magic ten, nine and eight.
At this point I felt I could take the learning two different ways. Either draw their attention to the fact that the shape in the middle was always odd and direct them to find out if they could make the problem work if an even number was in the middle – then consider why, or we could apply what they were thinking about in terms of balancing the arms with this simple case to a slightly larger case.
I decided on application as I felt this was a stronger focus for the pupils in this lesson. Simply we used a new larger cross and Numicon shapes 1-9.
Within ten minutes one pair had produced this example with the Y2 child in the pair explaining to me that they had made all of the arms equal nine – and he also knew the magic number was 27. Other pairs were working in the same way and soon after another reached the same conclusion.
Sadly the hour ended too soon – that lovely simple complex activity that pushed beyond just adding single digit numbers.