Search

Herts for Learning

Blogs for Learning

Category

Working Mathematically

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?”

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)”

Finding Maths in Storybooks – A Tale of Turning Training into Good Practice

In the Summer term 2016 Nicola Randall and Gillian Shearsby-Fox, Teaching and Learning Advisers for Mathematics at Herts for Learning, created and delivered a day of training on how to use books in maths. In this guest blog, Raj Khindey, an inspired maths subject Leader and Year 6 teacher at Chater Junior School,Watford; set about introducing the range of ideas she learned across her school.

In this blog she explains which ideas she trialled in her own class, as well as how she shared this good practise throughout KS2.

Following the training I was inspired to use a variety of fiction books that were recommended by Nicola and Gillian. I wanted to share this with the rest of the staff so the children as well as teachers could enjoy a different dimension to a traditional Maths lesson! So I held a staff meeting in Autumn Term and trialled some of the activities delivered in the course. Continue reading “Finding Maths in Storybooks – A Tale of Turning Training into Good Practice”

Do You Believe in Life After SATs?

Nicola Randall is a Primary Mathematics Adviser at Herts for Learning.  In this blog Nicola channels her inner Cher in order to provide Y6 teachers with some ideas for teaching mathematics in that difficult last half term. 

If you have ever taught in Year 6, you will be well aware of the mad rush of emotion and relief as the pupils complete their final SATs test in May. Glad that they got through it with minimal crying, relieved that they all followed your advice and double checked their answers (yeah, right!) and completely exhausted with the high expectations required to meet the expected standard.

The following week is a cross between the Walking Dead and Ferris Bueller’s Day Off, where the pupils either go completely bonkers or turn into exhausted little zombies, slurring their way through the poetry that you thought would be a good idea when you planned it before the SATs.

So after the dust has settled, what do you do in Year 6 for the remainder of the term? You know that you must continue topping up their subject knowledge and prepare them for life at secondary school but are also painfully aware that they have already metaphorically left the building.

My view is that the second half of the summer term is perfect for some outdoor learning and cross-curricular maths. It’s fun, motivating and keeps mathematical knowledge fresh.

Destination Estimation!

Many schools are lucky enough to live near a swimming pool, or even an outdoor lido, which provides an excellent treat for the weary Year 6’s. To make the most out of this, show the pupils the new Boots Advert, filmed at Letchworth Outdoor Pool in North Hertfordshire. Pause on the final frame, on the birds-eye view of the swimmers.

How many people do you estimate there are?

Gather pupil’s estimations on post-it notes and then ask them to discuss their strategies.

lifeaftersats2lifeaftersats3

 

Other images could then be explored for pupils to apply the different strategies and consider their effectiveness. Objects such as a pile of jelly beans, trees in a woodland or a flock of birds provide pupils the opportunity to hone their skills of estimation and rehearse place value of large numbers. You could even take the class outside and gather objects in the natural environment. How about estimating a pile of pebbles and then trying to organise them into arrays, or estimating how many leaves there are on a tree.

The book ‘Great Estimations’ by Bruce Goldstone is perfect for some inspiration and contains images that you could easily use with your class.

Using a photo as a stimulus can also be an opportunity to incorporate other areas of maths, such as money, measure and ratio.

For example, questions related to the swimming pool could be:

  • For a family of 3 adults and 2 children, what would the cheapest ticket cost be?
  • The pool works on a ratio of 75:2 for swimmers and lifeguard. How many lifeguards would be needed for 330 swimmers?
  • The greatest depth of the pool is 2.4m. Are there any animals that can stand upright and still be able to breathe?
  • There are 660,430 gallons of water in Letchworth Outdoor Pool. How many litres is this if there are 4.5L to the gallon?
  • What is the perimeter, area and volume of the pool? Compare this with measurements of other local swimming pools. What is the difference between them? Do any of them share the same area but have different perimeters?

References:

Goldstone, B ‘Great Estimations’ (2006)

Boots Summer 2017 advert [accessed on14.06.17] https://www.youtube.com/watch?v=kEzTnjKneU8


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.

Fifty Shades of Grey Addition

Charlie Harber is Deputy Lead Adviser for Primary Mathematics at Herts for Learning.  This blog aims to take the seemingly simple operation of addition and demonstrate how we can vary presentation in order that pupils see connections and do not fall into shallow procedural thinking. 

grey1

Would you agree that these are all shades of grey? (Who hasn’t spent time deliberating between shades on a paint chart?)  They are all different. So how can they be all grey?

We are generalising what is meant by GREY. Oxford online dictionary define grey as ‘Of a colour intermediate between black and white’ – so under this definition all these colours, despite being different, are grey because they share this similar property. For children to understand what grey is, what would you do? Would you just present them with a single shade? More likely, one activity you would do is present them with a range of objects in lots of different colours including shades of grey and ask them to sort the objects based on their colours. In mathematics we could refer to this as part of generalisation – the ability to see what is common amongst a range of different situations. Continue reading “Fifty Shades of Grey Addition”

Bar Modelling is a Leap of Faith

Charlie Harber is the Deputy Lead Adviser for Primary Mathematics at Herts for Learning.  A passionate advocate of bar modelling, her last blog on the subject RUCSAC pack your bags, dealt with a KS2 SATs question.  Here Charlie turns her attention to KS1 bar modelling.

In my last blog on bar modelling I used an example from the 2016 KS2 test. Subsequently, I had had a number of requests asking for a similarly worked example of a KS1 test question.

leap2 Continue reading “Bar Modelling is a Leap of Faith”

Blog at WordPress.com.

Up ↑