Category: Blog

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

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: [email protected]

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.