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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.

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”

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”

RUCSAC pack your bags, let’s hit the bar instead

Charlie Harber is the Deputy Lead Adviser for Primary Mathematics at Herts for Learning.  She has  researched the positive impact bar modelling has on pupils’ access to worded problems.

Recent analysis in many schools and discussion with subject leaders confirmed what many teachers have long suspected, that many children have the procedural skills but they  seemed to abandon all reasoning  when they need to apply them once they are embedded in a word/story problem. Many schools in the UK use RUCSAC to help the children, but have you considered why that doesn’t work? Is there a better way, one which just doesn’t prepare them to answer questions in tests, but also deepens operational understanding, exposes misunderstandings and develops reasoning – empowering the children to discuss the mathematics?

Simply put, yes I think there is a better way – bar modelling. Continue reading “RUCSAC pack your bags, let’s hit the bar instead”

Is mastery just a passing fad?

 

Nicola Randall, Mathematics Teaching and Learning Adviser at Herts for Learning

Before I even start to tackle this question, I think it is helpful to clarify what we mean by ‘fad’ and the best way I could think of doing this was to consider some examples.

  • Leg warmers worn anywhere other than inside a dance studio: fad
  • No make-up selfies: fad
  • Replacing actual laughing with the word “LOL”: fad
  • Dressing as clowns and scaring people: fad

Continue reading “Is mastery just a passing fad?”

KS2 SATs 2016 – Lessons Learned

Louise Racher is a Mathematics Adviser at HfL

“By three methods we may learn wisdom: First, by reflection, which is noblest; Second, by imitation, which is easiest; and third by experience, which is the bitterest.” Confucius.

As many practitioners ponder over the “new” KS2 tests, this article picks out some of our “noble” reflections on what would make a pupil confident to tackle the KS2 test without fear and trepidation. Pupils who met Age Related Expectations in 2016 (just over half of year 6 pupils nationally) demonstrated that they had a flexibility which allowed them to manipulate not only the calculations to find solutions with ease within the constraints of the time limit – but also had a good grasp of problem solving strategies. This enabled them to access some complex multi-step problems using higher order thinking skills and demonstrate that they were able to reason with confidence. Continue reading “KS2 SATs 2016 – Lessons Learned”

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