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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.”

FOMA – Fear of Maths Accountability

Rachel Rayner is a Primary Mathematics Adviser at Herts for Learning.  Reflecting on her travels around schools, Rachel shares her observations about what can cause teachers to focus on aspects of planning that hinder teachers’ delivery of lessons. 

At the beginning of every year I work with new schools and teachers who are new to my existing schools.  In my last blog Teachers Reclaim Your Inner Artisan, I talked about how schools are changing their view of planning, how they are being unshackled from the ‘accepted planning routes’.  But I have also spent time with teachers over the last few weeks who are or feel they are, and that is an important distinction here, tied to a certain proforma, a definitive process for planning.   Continue reading “FOMA – Fear of Maths Accountability”

Cashing in on the Latest Craze – Lego Cards

Louise Racher is a Primary Maths Adviser for Herts for Learning.  In this blog she harks back to the crazes that have blighted or enlivened the teachers’ year and how we can exploit the latest one for mathematical ends in KS1 this summer.  

As another academic year comes to a close it is time to reflect on all the crazes which have dominated children’s (and parents’) lives.  The dab (may it rest in peace), bottle flipping, fidget spinners and last but not least Lego Cards!

Not all these crazes might have touched your lives, but as a teacher, it is hard to remain aloof when a certain craze occupies pupils conversations in and out of class.  Teachers are creative and flexible, along with a craze comes an opportunity to be seized.  Before you know it you’re measuring the length of time a fidget spinner can spin unaided, comparing that to other varieties, conjecturing about whether the weight affects the length of spinning time.  Word problems will no longer feature sweets, it is the number of dabs, the price of a fidget spinner and the mean average of time a bottle can be successfully flipped which are included in order that they have a bespoke context relevant to the pupils. Continue reading “Cashing in on the Latest Craze – Lego Cards”

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.

So you have textbooks…so what?

Siobhan King is a Mathematics Adviser at Herts for Learning

I have been thinking about maths text books: what they add to lessons and how they can be used effectively.  I am a firm believer in not reinventing the wheel and know that teacher time is finite and exceptionally valuable.   Furthermore, I agree with Tim Oates’ assertion that “high quality textbooks support both teachers and pupils – they free teachers up to concentrate on refining pedagogy and developing engaging, effective learning.”  (Oates, 2014, p4) Continue reading “So you have textbooks…so what?”

Supporting Children with Dyslexia in Mathematics

Gill Shearsby-Fox is a Primary Mathematics Adviser for Herts for Learning.

Many people think that Dyslexia purely impacts upon children’s learning of reading and spelling and therefore does not have a huge influence on their mathematics. A difficulty in reading does of course lead to children finding most of the curriculum difficult because it is an essential skill and is needed to access learning and succeed. However, having dyslexia does impact on children’s learning of mathematics in more ways than having difficulties reading the questions. Continue reading “Supporting Children with Dyslexia in Mathematics”

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