Is there really three ways to add numbers? OK, OK! There’s way more than three ways! So what do we mean? Well, initially when children start to add things together they “count all” which basically means exactly how it sounds, you count everything you have in front of you. In England, we normally start off with two strategies for addition. These are

1. Count all – Counting everything in a systematic way so not to count anything twice
2. Count on – generally starting with the largest number and “adding on” the remainder

These two strategies are taught from reception onwards where a heavy emphasis is placed on counting on rather than counting all as this is the more efficient method. Many children still struggle with counting on as they have yet to form a clear understanding of number and are not sure why counting on works. Thankfully there are various strategies we use to make sense of it all for children aged 4-6 years old. One strategy is to start to understand counting on from an early age. How could we do this?

To begin with, let’s think about the superheroes above. How many superheroes can we see? Ohh 5, excellent – How did you know that was 5 without counting them all? Ohh every time the first row is full, we know it’s a 5! Excellent subitising everyone! Now I want you to look at another set of heroes, and try to work out how many superheroes we have, are you ready….?

What’s happened here? Ohh, you can see an extra hero? So how many are there now? What can we do to work this out? Can you talk to your partner and tell them what you did to work out how many there are altogether? Ohh some of us have counted each of the superhero’s – 1, 2, 3, 4, 5 and 6 but some of us did something different. Can you explain what you did? You saw that there was a 5? How did you know that? Ohh because you remembered that every time the row is complete, we have 5, well done! So what did you do after that? After 5 is 6, so you saw 5 and then counted one more, perfect, well done!

The above method briefly outlines a possible teacher-class interaction using ten-frames as a cue to add on. The teacher may not mention, the fact that they have used a strategy called adding on because that would formalise the lesson, but what would happen is the pupils would go through different questions which allow them to use what they know and ‘add on’ the rest. This approach is using both Zoltan Dienes’ theory,  where he informs us to use informal approaches to understanding concepts first before moving onto formalise learning and also Jerome Bruner’s Concrete Pictorial and Abstract (CPA) approach which is a very important aspect of learning for all children.

Making Ten – A third strategy for addition

Addition using ten-frames doesn’t stop there, however. As our specialism is in Singapore Maths, we would like to introduce a third way to add called ‘Make 10’. This method may not be taught in Reception but you will see this in the Singapore Maths (UK Curriculum) books from Year 1 onwards. It is exactly how it sounds, you encourage children to make 10. In essence, it is something we do often in mental maths but we find it more difficult to teach this method and so the CPA approach really does help to demonstrate this important strategy. Take for example 9+6….

This looks interesting! We have 9 superheroes in one of our ten-frames and 6 in another. Can you see that we are just one away from a ten in the first ten-frame? And we have one sticking out in the second ten-frame?

Ahh, we can move that 1 from 6 and give it to the ten-frame with 9, but what would that mean to the numbers? What would happen? Ok, so when you take 1 from 6, does that mean we still have 6? That’s right, we now have one less, which is? 5, well done. And we gave that 1 to 9, look at your ten-frame, when we give 1 to the 9 what does that make? So we have 10 and 5? So what do we get when we add 6 to 9?

To summarise the strategy, pupils are encouraged to make 10 using their number bond knowledge. They do this by splitting the smaller number so that you can make 10 with a part of the smaller number and then add the remaining part. In the above example, 6 became 5 and 1 and the 1 was used to make 10. This is a very effective approach and can be used further down the line when looking at addition with two digits. For example 19+16=20+15; using just abstract approaches is definitely not as effective as if you used a ten-frame for this example. Have a go and let us know what you think.

Strategies for addition using ten-frames is easier to understand than just using abstract tools to show something which can be fairly complicated for children. Understanding the strategy goes a long way especially if you are thinking of mastery. Memorising strategies will only work for a select few groups in a class and the others will fall behind and rely on inefficient strategies such as count all. This is why using a hands-on approach and tools, such as ten-frames, to demonstrate and illustrate ideas can be so much more effective.