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Adding single digit numbers: an under-practised skill!

I’m sure there are many out there that may disagree but my personal feeling is that there is one particular area of maths that is massively under-practised, yet it is so important in so many other areas of maths that it can cause real difficulties for those who don’t master it before moving on.

What skill am I talking about?  Adding single digit numbers.

Of course many children can count on using their fingers or a number line but does this then serve them well enough when they come to crossing tens barriers when adding 2 digit numbers, or multiplying using repeated addition, or converting mixed numbers to improper fractions or….. I could go on but I won’t!

The strange thing is that this vital skill is under-practised both in school and at home.  In a typical year 1 classroom, the teacher will spend a few lessons exploring how numbers can be made by combining different pairs of smaller numbers, e.g.

7   =   5+2   or   6+1   or   4+3

The children will produce wonderful part-whole diagrams, bar models and many other representations using practical equipment….and then they move on.  That’s it.  They’ve covered it.  They’ve shown understanding.  So they move on.  This is not necessarily the fault of the teacher but down to a crammed curriculum which includes so much content that there is pressure to keep moving forward rather than consolidating.

The thing is, they may well have shown understanding at the point of learning, but what about 1 week later?  What about 3 months later?  Are they using this knowledge of splitting numbers in their calculations or are they reverting to simply counting up and down with the help of their fingers (I’m not completely against using fingers to help by the way).

I am still lucky enough to work with many children every week, often individually or in small groups and it seems that children fit into one of two categories:  those who have an excellent grasp of numbers up to ten and can split them into two parts to make calculations easier; and those who simply rely on counting on.  Let me illustrate this with an example:

Question: 8+7

Child A: Starts at 8 and counts forwards seven, putting a finger up each time until they have seven fingers up, ending at 15.

Child B: Knows that if they add 2 to the 8 it will make 10 so they split the seven into a 5 and a 2 and know that it will give 15.

Although they both get to the correct answer, child B has a much better understanding of numbers and will eventually be able to apply this in other contexts.  Child A also has the potential for errors by including the number 8 in their counting and ending up at 14 instead.  They won’t notice this error as they have put up seven fingers so why should it be wrong?

Trying to explain to Child A in the above example what they could have done using words alone will only lead to a confused face – I know as I’ve tried!  What they need is to see visually what happens using concrete resources such as counters and tens frames like this:

Question: 8 + 7 = 15

Once they understand the concept, this is where the hard work comes in – practice!  The only way that children will begin to do this naturally without much thought is if they practise, practise and then practise some more.  This can be done using hands-on physical resources or there are many free online tools that will do the same job, for example this great Tens Frame tool from ICTgames:

www.ictgames.com/mobilePage/tenFrame/index.html

Once children become fluent at this process with practical equipment, they can go on to trying it with visual clues only.  Our Number Stacks digit cards are perfect for this as there is a visual representation of each digit on the card so it is easy to see how they need to split the smaller number to make the calculation easier:

These cards come in our Resource Kits or can be downloaded for free as part of our DIY Resource Kit: https://www.numberstacks.co.uk/diy-resource-kit/

The final step is to apply the concept without any practical or visual clues.  There are many games ideas available on our website for Number Stacks members (www.numberstacks.co.uk/games) that can help make practising the above skills more fun, including: Roll-A-Robot, Total Wipeout, Tug-Of-War and Four-In-A-Row Addition.

If we can build children’s understanding and confidence in manipulating single digit numbers, I’m sure that it will have a massive impact on their ability to grasp future calculation methods and mathematical concepts much more easily, so let’s all make a promise to give this area of early maths the time and practice it deserves!

 

Thanks for reading.

James

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The Summer Slump

I always remember the first day back at school in September as a child. Trying to pick up a pencil and write a sentence - it was as if I’d never ever done it before! The muscles in my hand that used to finely (okay not that fine as handwriting never was my strong point!) control the pencil had been reduced to ruins after 6 weeks of inactivity. Don’t get me wrong, the holidays were actually very active, but mainly in the form of playing football and cricket with my younger brother in the garden or at the beach.

I imagine I was not alone and from my years of teaching primary aged children, I KNOW that the same is true in thousands of households across the country every summer. This phenomenon has been named the Summer Slide or (as I prefer) the Summer Slump.

Now if six weeks of inactivity can have that effect on a child’s hand muscles, think what it will have on the brain! Already in the month or so since SATS, I have noticed the year 6 pupils I work with outside of school lose quite a few of the skills they had become ‘expert’ at only a short time ago. Add the summer break onto this and teachers far and wide will despairingly cry in September, ‘How on earth was this child assessed as Expected / Greater Depth?!’

So what can be done to help avoid this Slump?

Firstly, I want to stress that summer holidays should be just that - a holiday! It is important to get some quality family time, enjoy the weather if it is nice, and give children experiences that they won’t get at school. However, if we can throw in a bit of reading, some short, fun maths activities and even a bit of writing (to keep those hand muscles alive) then it’ll make a massive difference come September.

I believe the key here is doing things in short bursts. Avoid workbooks and worksheets and make activities practical. For younger children, add a notebook and pens into their games to encourage writing: menus, packing lists for holidays, recording scores of garden sports matches, anything you can think of! Take part in the Summer Reading Challenge at your local library but don’t rush it - spread it out over the whole six weeks and give your children ownership of choosing their own books to read.

For maths, you could go over some of the skills they learnt last year and then use these in some number games and challenges. Our Number Stacks videos and games are ideal for short bursts of learning and, because they are all practical, children don’t see it as ‘work’. If you haven’t already, check out what’s on our website: www.numberstacks.co.uk

Six weeks will fly by so don’t put it off - make a promise to yourself to squeeze some short learning activities in amongst all the fun. Your child (and their new teacher!) will certainly be thankful when that first day back at school comes along and they can pick up where they left off!

Thanks for reading 🙂

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What is subitising and why is it important?

When you are playing a game with a dice and you roll a six, do you count the dots before realising it’s a six?  I’m sure the answer is a resounding NO because you have grown up using a dice and so you can instantly recognise the numbers from the arrangement of the dots.

The ability to recognise numbers of things without counting them is called subitising and it develops from a very early age.  Young children have powerful visual memories and some find it easier to remember images than words. Subitising can help children to build visual images for numbers, which in turn helps them to learn number facts.

Why is it important?

Subitising is an essential skill when it comes to adding and subtracting larger groups of numbers.  Recognising a larger group by combining smaller groups numbers (known as conceptual subitising) helps children to manipulate numbers to make calculations easier.

For example, when calculating 8+5, it is easier if you know that 5 can be broken into a 2 and a 3 so that you can add the 2 first to make 10, and then the 3 to make 13.

What can I do to help?

Exposing children to visual representations of numbers from an early age will help to develop their ability to subitise.  Simply learning how to count on a number line is not enough as children need to use practical equipment to ‘build’ and then draw these numbers to understand their value.  Playing board games with a dice is a great start and one that is all too often forgotten in today’s technology-dependent world.  Having a set of digit cards from 1 to 10 and getting children to build these numbers using counters, toys, sweets, coins or anything you can find will all help them to develop a better understanding of the value of numbers.

Number Stacks is a great tool for developing subitising. Visual representations of single digit numbers is one of the very first skills covered in our Number Stack video tutorials.

NPV1: Read & Write numbers to 10

To practise conceptual subitising, encourage children to look for smaller groups of objects within a larger group and see if they can put these together.  To help with this, I have created a simple card game with different representations of numbers up to 10.  Initially, children may have to count the number of red ‘ones’ on each card but with repeated practice, they should begin to instantly recognise the larger of the two groups on the card and count on the extra, before eventually recognising the two groups and adding them with no counting.

When I have played this game with children, we work through the cards, timing how long it takes to correctly identify the number shown on every card in the set.  Children are very keen to beat their time and eventually become very fast!

Download our Subitising Card Game Here

You can download the whole set of cards using the link above.  I have laminated my set (what teacher doesn’t love a laminator!) but you can just as easily print them on paper and stick them on card to make them last.

Feel free to share your best times with us on Twitter or Facebook (@NumberStacks).

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Empowering Parents To Support Their Children

I read an article last week which stated that a recent @YouGov study found 52% of parents don’t feel confident in their times tables.  Now obviously I take these surveys with a pinch of salt but it did make me think about the confidence of parents when it comes to supporting their children.

Throughout my years as a class teacher, I heard many parents say it was the maths homework that they struggled to help their children with, particularly when I taught in upper Key Stage 2.  They were quite happy to hear their child read, or practise phonics and spellings with them, but they seemed to just leave maths to the school.

Unfortunately, with ever-decreasing budgets, it is becoming more important for parents to help support their children as schools just can’t afford the teaching assistants who would have been on hand to address gaps in understanding as they start to appear.  Of course, teachers do an amazing job in juggling the mixed abilities of up to 30 (and sometimes more) children in a class, but the fact is that the maths curriculum is now so vast that there comes a point where they have to move on in order to cover everything expected.

With many parents keen to support at home, it can take a huge amount of time for a teacher to tailor home-learning activities to each child’s needs and then explain these activities to each parent.  Even then, a set of written instructions can often be misinterpreted which in turn leads to more confusion for the child.  Also, parents are unlikely to have the practical resources that schools have available and so this ends up with them jumping straight to an abstract explanation (skipping the concrete or pictorial representations) which again leaves the child no better off in terms of understanding than they were before.

Number Stacks was created to help empower parents to support their children by taking the job of explaining mathematical concepts away from them.  All Key skills are explained in simple video tutorials which are designed to be watched by parents and children together.  Activities are clearly demonstrated and the parent simply becomes a facilitator, helping their child imitate what they have just seen.  What’s more, every activity in the videos uses the practical equipment included in the Number Stacks resource kit, meaning the children don’t miss the vital step of building and manipulating numbers physically so that they gain a better understanding of what’s actually happening to the numbers within a calculation.

Teachers can feel confident that children are being supported correctly without having to spend time creating and writing activities; parents can feel confident in helping their child whilst also learning the Key elements of the primary maths curriculum themselves at the same time; and most importantly, children get personalised attention to help them fill gaps in understanding that, if left untouched, will continue to hold them back in future year groups.

Everyone’s a winner!

Whether you’re a parent who wants to use Number Stacks at home with your child, or a school who wants to use it as an intervention in school or promote it for parents to use at home, visit our website or email us for more information: support@numberstacks.co.uk

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Number Stacks or Numicon?

With Numicon being such an established, concrete maths resource that many people have been using for a long time, I have been asked whether switching to Number Stacks would be confusing for a child. The simple answer is that you don’t need to switch - they can be used alongside each other to help develop a child’s number sense.

I have been a fan of Numicon ever since I was introduced to it many years ago and quickly invested in sets to be used across my previous school. The ability for children to associate numbers with physical tiles (I never did find out the correct name for the pieces if there even is one!) was brilliant in helping them link numerical digits and names to the quantities they represent. Once a child is familiar with the shapes, they no longer need to count each number which is brilliant when it comes to calculation.

It is not surprising therefore that in the early Number Stacks videos, without thinking I used the Numicon shapes when arranging the counters within tens frames. It has been pointed out to me that I have used them ‘upside-down’ as I fill the tens frames vertically from top down rather than bottom up. The reason I do this is that if a child wants to use a pictorial method (let’s say for adding two 2-digit numbers) they can draw the counters or circles from the top down on the page which means they don’t have to make a pre-judgement on how much space to leave in order to fit the number in if they drew from the bottom up!

Parents of children who have been using Numicon have shared with me how this has really helped their child in recognising numbers quickly without the need to count the counters. If a child hasn’t used Numicon, they will still build recognition of the number arrangements in Number Stacks but it may just take them a bit longer.

So Numicon is brilliant at helping children develop early number sense but where Number Stacks takes over is with visually representing larger numbers and also with calculation.

Once you get beyond 2-digit numbers, Numicon becomes more difficult to represent as there is no hundred tile without bundling tens together, whereas Number Stacks has counters for hundreds and thousands. Once children have learnt the principle of exchanging 10 ones for a tens counter, or ‘swapping’ as I refer to it in the videos, they can apply the same rules to hundreds and thousands with ease.  They can also stack the counters under place-value header cards to neatly represent numbers meaning the working area isn’t littered with different tiles.

For calculation, my biggest issue with Numicon is that you can’t break down the tiles; you have to swap them for two others which is an extra step that some children find tricky. I’ll try and explain this with an example:

When adding 8 and 5, you eventually want the child to split the 5 into a 2 (to make the 8 up to 10) and a 3. With Numicon, they would have to swap the 5 tile for two others to accomplish this but with Number Stacks, they can simply break up the stack of 5. This also has the advantage of allowing the child to experiment with how they need to partition the 5 as they could try moving one counter across first before then realising they need to move a second before they have made ten.

Number Stacks is also very good for representing subtraction as you can simply build a number using the counters and then remove the amount you need to subtract, exchanging or ‘swapping’ where required. E.g. for 53 - 17, you would build 53 and then swap one of the tens counters for ten ones counters so that you could then remove 7 ones and 1 ten to get your answer. This is all demonstrated step by step in the video tutorials and builds up gradually through the Key Skills.

So going back to the question at the start of this Blog, the answer is simply both! Numicon and Number Stacks can both be used side by side to develop early Number Sense in children with skills transferable between the two resources. However, if you are yet to start on your number sense journey, we believe that Number Stacks is more adaptable as you move through the Key Skills and therefore would be the best option if you had to choose one over the other.

You can visit our website at www.numberstacks.co.uk  to explore the Number Stacks Resource Kit and to view sample video tutorials or follow us on Twitter or Facebook @NumberStacks to see some of the learning journeys that our users are sharing with us.

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And Number Stacks Was Born!

I’ve been thinking about starting a Blog for a while now but decided that it was time to stop thinking and start typing!

After 16 years in Primary education, I decided last year that it was time to take a break and try something new.  I had gone straight from university into a PGSE course and then into my first teaching job in a junior school in Colchester, Essex.  After five happy years, during which I somehow found myself as a leading ICT teacher delivering staff-training around the county, I took a new job as deputy head at Dedham C of E Primary School.  We worked hard to achieve an Outstanding Ofsted grading in 2012 and when the Headteacher retired in 2016, I became the new Head.

Now many people would think that this was the perfect thing to happen – to step up into Headship in a school where I was known and respected and had worked closely with the previous Head to shape the curriculum, assessment system and other policies exactly how I wanted them to be.  The thing was, I always had a nagging doubt that I would miss being in the classroom and it turned out to be true.  Despite my best intentions to keep my teaching skills sharp, the inevitable Headteacher ‘To Do’ list just seemed to grow and grow.  Safeguarding, performance management, pupil progress meetings, monitoring and assessment, behaviour management, health and safety, meetings with parents and governors reports (to name but a few) seemed to suck up all of my time.  Perhaps I should have delegated more but I was conscious of the increasing demands on my staff and the drive to reduce (not increase) workload.

The whole reason why I chose to become a teacher in the first place was to teach children!  To be creative and to try and explain things to children in ways that they would understand, engage with and remember!  After my first year of Headship, I decided that it just wasn’t right for me and so I gave the Governors another year’s notice so they could find the right person for the job and set about planning my next career move.

Thinking about what I liked most about my class teacher roles, I decided that there were two aspects I really enjoyed:

  1. Working with the children.

When you strip back teaching to its basics (and remove all of the ‘extras’ that are now put upon us by the delightful people at the DfE and, dare I say it, Ofsted) it is about getting children to learn new things.  That amazing moment when things click into place and a child suddenly realises they understand something, never fails to brighten even the hardest of days.  Also, the in-depth conversations you have with children about their own lives and the relationships you build with them throughout their time at school is something I wanted to somehow keep.

  1. Being creative!

I loved trying to think of new ways to help children understand.  Using practical equipment or ICT to bring learning to life.  Using drama and role play to allow children to be a part of things rather than just reading or watching.  Setting games and challenges for homework rather than just endless sheets of questions that we had already done in class.  In my early teaching years I sometimes spent hours planning lessons that would only last half that time but it all seemed worth it.  As you move into management, you have to strike a balance between your teaching and your management responsibilities and then as a Head, those opportunities for creativity can all but disappear.

 

So, I knew what I liked about the job and didn’t want to waste all my knowledge and experience that I had built up over my years of teaching.  I decided that it was time to be brave.  I didn’t like the idea of stepping back into the classroom – not yet anyway – so for the fist time since leaving university, I left a job without another one waiting for me.  I set up my own tuition business and was fortunate to have many parents from my old school approach me to work with their children.  I was also very lucky that my In-laws had a large office space going free that they allowed me to set up as a mini-classroom to run tuition groups in the afternoons and evenings.  This was my ideal job!  I got to spend my time doing the two parts of the job I loved without any of the bad parts!  Okay, it was a bit of a hefty pay-cut but it was completely worth it!  I got to fall in love with teaching all over again.

The best part of my new tuition business was that I had my daytime hours free and this was when I would put part 2 of my plan into action.  As a maths subject leader for most of my time in teaching, I had always wanted to create my own primary intervention:

  • Something that was hands-on and used practical resources to help children understand what numbers looked like and what was happening to them rather than just learning an abstract method.
  • Something that didn’t require sending teachers and teaching assistants on time-consuming, expensive training before they could start implementing it.
  • Something that didn’t take longer for the supporting adult to read and understand the instructions for an activity than it did to actually run each session with a child.
  • Something that didn’t require mountains of printing or running around looking for different pieces of equipment for every session.
  • Something that could easily show progress for children that perhaps didn’t quite fit the mould of many of the new assessment systems that were commonly being used (not ours – we created our own so that it reflected the progress made by ALL of our pupils!).
  • And finally, something that could be used by parents at home. We were lucky enough to have lots of engaged parents who would ask what they could do to support their children at home.  In a time when budgets were shrinking too, I also wanted to create something that meant if a school had to reduce TA numbers, children could still be supported by any willing adult (parents, relatives, volunteers) regardless of experience so that they didn’t fall behind.

I had been a massive fan of place-value counters ever since I first used them at a maths subject-leader update but always thought they would be better if they were thicker and easier to handle and could be stacked to ‘build’ numbers rather than being spread messily around a table.

And so Number Stacks was born!

I wanted to make everything as simple as possible to follow so I broke Key Maths Skills into strands and sorted them by year group:  Number & Place Value, Addition & Subtraction; Multiplication & Division; Fractions; Decimals & Percentages.  This ended up giving a total of 69 Key skills, progressing in each strand from EYFS to Yr6.

I put together a kit of equipment that would be needed to explain these Key Skills in a way that children would understand.  I then created videos for each Skill that were designed for an adult and child to watch together.  This meant no instructions for the adult to read so all the time could be spent working with the child.  Finally, fluency activities to allow children to put in to practice what they had learnt, initial assessments to allow adults to work out each child’s starting point, and games (from the many I have created over the years) to consolidate existing skills were added to complete the resource.

6 months later I had many hours of edited video, along with hundreds of fluency activities, assessments and games that I needed a home for.  My website building skills were limited to updating the old school website from time to time and I didn’t have the financial resources to pay anybody else to do it so I went back to school.  Well, Google School!  Weekends and evenings were spent learning the ins and outs of WordPress to build a membership site.  It’s not perfect, and I’m sure others could do a better job, but I’m happy with what I created.  It allows people to see what the product is all about, order Number Stacks resource kits and buy memberships to access the videos and other resources.

You can see the fruits of my labour at www.numberstacks.co.uk

We are still only half way through our first year and have been absolutely blown away by the feedback we have received from our early adopters, particularly those educating their children at home.  It gives me confidence that Number Stacks will help so many children who just need an extra boost with their learning in maths and who knows, it may allow me to continue doing the things I love whilst still making a difference.

If you’ve read this far, thanks for sticking with me.  I hope to be a bit more maths-focused in my future posts but just wanted to share my story!

Until the next time….

James