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A Lesson in KS1 Greater Depth – Simple Complexity

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.

KS1GD - 5

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.

  • the 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.

gdks1-4.jpg

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.


References

https://cdn.oxfordowl.co.uk/2015/07/22/13/54/09/24/Year1_TeachingforMastery.pdf


Herts for Learning is a not for profit organisation that provides a wide range of training and CPD courses, events and conferences  to support teachers and school staff in their professional development and also offers an extensive range of resources to support their offering through the HfL e-Shop.  Please visit the website for more information.

Differentiation – How different does it have to look?

Nicola Adams is an adviser for Primary Mathematics at Herts for Learning.  In this, her first blog, she considers how differentiation or meeting the needs of all learners in the classroom is crucial but not always evident to those observing a lesson. She builds on Rachel Rayner’s blog FOMA – Fear of Maths Accountability to demonstrate how three boxes for differentiation is missing the point, and that observers must engage with the teacher before making judgements.

Picture this. Somebody is coming in to observe your maths lesson and what they see is all of the children doing the same thing. They all have access to the same manipulatives; they can all see the same working wall; they are sat in mixed-ability partners, they are playing a mathematical game… and there is conversation happening. The horror! Are they going to say that you are not challenging your more able? Are they going to ask why your lower ability children are not being supported by an adult? Are they going to say that your more able children simply don’t need the same manipulatives as the others? Just where is the differentiation? Continue reading “Differentiation – How different does it have to look?”

Help Parents’ Needed! Parental Engagement Has Big Benefits.

Kate Kellner-Dilks is a teaching and learning adviser for primary mathematics at Herts for Learning.  Kate has been successfully working with schools to increase the engagement of parents in supporting their children with mathematics.  Here she shares this advice. 

From conversations I have with primary school teachers and leaders, they often want to engage parents in the mathematics they are teaching. They have a feeling it will help the children, but are not sure the best way to go about it.

Research tells us that children are more successful at school, if their parents support their learning; ‘Family engagement in school has a bigger influence on a pupil’s achievement than socio-economic background, parents’ education level, family structure and ethnicity…’ (www.engagingwithfamilies.co.uk, 2017) Continue reading “Help Parents’ Needed! Parental Engagement Has Big Benefits.”

Ever thought about what comes before counting? Pre-number learning in the Early Years.

Deborah Mulroney is a Teaching and Learning Adviser for Primary Mathematics at Herts for Learning.  She has been working alongside Early Years Advisers on the Early Years Fluency Project in several Hertfordshire schools.  In this blog she explains the practices and impact of the project – be prepared to grin. 

You know you’ve heard it when the proud parent turns up for his first day and boasts that Charlie knows all his numbers up to 50 and why not be proud? Of course we know that Charlie hasn’t got a clue what one more than 3 is, but hey it’s an amazing feat of memorisation. Continue reading “Ever thought about what comes before counting? Pre-number learning in the Early Years.”

An Inspector Calls – Advice for Leaders of Mathematics

Nicola Randall is a Primary Maths Adviser at Herts for Learning.  Here she sets out her advice for core subject leaders in surviving Ofsted inspections. 

All subject leaders know the anxiety caused by waiting for that call, looking for the tell-tale signs: the headteacher’s door closed with a ‘Do Not Disturb’ sign on, the mysterious and impromptu staff meeting to be held after school and the rushing around of office staff trying to get paperwork out to parents. I haven’t met anyone who enjoys an inspection, but in my experience, subject leaders tend to fall into 2 camps: those who feel the fear and those who say ‘bring it on!’ Continue reading “An Inspector Calls – Advice for Leaders of Mathematics”

The ‘Goldilocks Principle’ and Curriculum Design

Rachel Rayner is a Primary Mathematics Adviser at Herts for Learning.  The team are currently engaged in designing a mathematics curriculum for schools and teachers.  In this blog she considers how curriculum design impacts on learners.  This will be the first of a series of blogs on progression and design.

As a maths team we are currently writing every sequence of learning from Year 1 week 1 Autumn term to Year 6 final week Summer term. More on that later.  But I don’t mind telling you that it’s raised quite a few questions on the team about what a great curriculum for maths should look like.  Curriculum ‘14 for mathematics raised age-old debates – acceleration versus breadth and depth, knowledge versus engagement – let the twitter set debate. Furthermore, the new curriculum is being regularly referred to as a ‘mastery curriculum,’ heralding a bewildering array of products stamped with the ‘mastery’ brand all claiming to revolutionise your curriculum and behave rather like you might imagine a magic wand to work. And yet, and yet…still we battle to build a secure curriculum framework and schools are desperately seeking something (even after they have discovered concrete-pictorial-abstract).  One in which, age-related expectations become the norm for all pupils irrespective of their prior attainment – though we know there are a few children for whom added provision is ever needed irrespective of the curriculum. On top of that OfSTED are looking at how curriculum design supports learning for all pupils even beyond the mathematics lessons.  So where do we even begin? In this the first of a series of blogs I want to set out the current landscape as I see it (and sorry but no, I don’t possess even a modicum of fairy dust or a magic wand) before focusing in further in future blogs.  Continue reading “The ‘Goldilocks Principle’ and Curriculum Design”

KS2 SATs 2017 – Lessons Learned (The Sequel)

Louise Racher is a Mathematics Teaching and Learning Adviser at HfL, in this she gives her own interpretation of what priorities teachers might have had leading up to KS2 SATs, and what the priorities might be for next year following the second year of “New Curriculum” SATs.

Year 6 teachers had their game face on for the second year of the newly revised end of KS2 SATs.  Greater awareness of how the papers would be presented meant it was a slightly fairer fight and lessons learned from the previous year were taken on board and assimilated back into classrooms across the land.  Continue reading “KS2 SATs 2017 – Lessons Learned (The Sequel)”

Rebalancing sums – and the ripple effect

In the tried and tested articles, advisers will share some of their interesting tried and tested approaches to teaching mathematics.   In this sequence, the Rachel Rayner focuses on developing the skill of rebalancing as a mental strategy.

Rachel Rayner is a Primary Mathematics Adviser for Herts for Learning

Have you ever noticed how introducing a new drop in the mathematics ocean causes pupils to think differently about already learned concepts?  What follows is a sequence of learning, much loved by me, as it has caused all kinds of new links with number to be made for pupils as well as deeper understanding of core concepts such as conservation and sum from Year 2 to Year 6.  It also challenges pupils preference for working left to right in their calculations (I certainly found that my children’s favourite option) but instead attend to the numbers involved, allowing a far better informed decision about the strategy selected.   The strategy also focuses on the nearness of landmark numbers and the skill of rounding.  This supports estimation and a sense of what is reasonable for further development of number sense. Continue reading “Rebalancing sums – and the ripple effect”

Year 5: Making the Last Term Count

Calling all Year 5 teachers! Louise Racher sets out what your pupils need to secure this term in readiness for their final year at primary.  

Yes, the summer term is fast approaching. Year 5 are pulling up their socks, straightening their ties and getting ready to oust the current Year 6 pupils from their top spot.  Year 6, this final year of primary school, or the end of Key Stage for those in middle schools.  Along with Year 6 comes the end of Key Stage assessments which the school will be accountable for, whether they are good, bad or ugly.  Continue reading “Year 5: Making the Last Term Count”

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