Simple addition

Home educators and other parents sometimes wonder how to teach their young children the basics of arithmetic. The page number bonds: introducing addition tells you how to introduce the concepts of adding and subtracting numbers up to ten, with links to some online games to play.

Before you embark on any formal or structured teaching of addition, please read that page and ensure that your child is familiar with the basic concept of how numbers fit together in patterns. This makes all arithmetic much easier than it was thirty or forty years ago, when teachers expected children to understand symbols without any overview of what they meant.

Familiarity with number bonds

So let’s assume that your child is confident about the numbers that add up to ten (eg 9+1, 8+2 etc). He doesn’t have to be able to do this in his head, necessarily – it’s fine to use fingers, or Cuisinaire rods, or lego pieces. Some children think in concrete ways, and there’s really no reason why they shouldn’t have something they can see to aid their memories or understanding. With home education, you can take mathematical understanding at your child’s pace, after all.

But eventually he will probably want either to add some numbers for which he hasn’t learned the number bonds. If he knows that 3+6 = 9, what can he do with 300+600? Or 33+66? Some children seem naturally to ‘get’ this kind of leap into higher numbers. To others, even the thought of three hundred apples is overwhelming, and they have no idea how to handle larger numbers

Importance of place value

If this is the case, you may want to read the page on place values. Understanding the significance of the number of digits and what zero means is vital before children can add numbers beyond those they can easily visualise. This, too, may take some time. If your child isn’t yet ready to understand place value, then he isn’t ready for more than the most basic arithmetic. He may have an instant understanding of the concept, or it may take weeks, even months. Again, it doesn’t matter how long it takes; children learn at different rates.

So, if your child has a good understanding of place value, then he will know that 300 is simply three lots of a hundred, and that 600 is six lots of a hundred. He knows that three apples and six apples give nine apples, so it may be immediately clear that three hundred apples and six hundred apples give nine hundred apples. But don’t worry if it isn’t. Just play a few ‘guessing games’ with him over a week or two – asking him, for instance, what two thousand pears and four thousand pears make, or three million bananas and five million bananas … the point is to help him see that large numbers are just big groups of smaller numbers.

Two digit addition

Eventually your child should become comfortable with adding large numbers of that form. Then – if he’s still interested – you can start to show him how to add more complicated numbers.

First of all, show him how to write them in columns, one below the other, and tell him the ‘plus’ or ‘addition’ symbol, +, and the underline convention to show that the answer will be underneath:

33
+66

Remind him that 33 means three lots of ten, and three lots of one, while 66 means six lots of ten and six lots of one. So to add them, you can first add the lots of one – which we call ‘units’ – to give nine lots of one. And then add the lots of ten, giving nine lots of ten. So the answer is:

33
+66
99

If your child has no difficulty with that, try writing out the sum of 333 + 666; you’ll probably find that he immediately sees that the answer is 999. If not, don’t worry – it will come sooner or later. Try other simple sums, ensuring that you don’t make any of the digits add up to more than ten at this stage. For instance, you could ask your child to add 11+35, or 123 + 456, or many others.

Don’t make this a drill, whatever you do; don’t write down twenty sums for him to work out (unless he requests that!) Just play around with one or two at a time – maybe using fridge magnets, or writing them in the sand at the beach, or drawing on a foggy window, or using different coloured pens to represent the different digits. Be creative – the aim is for your child both to understand basic arithmetic, and also to enjoy doing so, so that he wants to learn more.

Addition with carrying

Sooner or later, your child will want to add numbers where the digits add to more than ten. For example, 55 + 76. Write this out in columns, as above, and ask about the units. What is five plus six? Your child may know the answer is eleven, or can work it out by counting on fingers or blocks. He may want to write 11 under the units part of the sum; if so, ask him what 11 means in terms of tens and ones. He should know that it’s one lot of ten, and one unit. If not, back-track a bit and think some more about place value.

If he understands that 11 is the representation of 10+1, it may be obvious to him that the 1 should be written in the units column of the answer, and that an extra ten needs to be added to the tens column. Traditionally we call this ‘carrying’ – the ten is ‘carried over’ to the tens column. We usually write this as a little subscript 1 under the tens column, so the partially done sum would look like this:

55
+76
. 1
1

The next thing to do is to add the tens column. 50 + 70 (five tens and seven tens) is 120, and the extra ten from the units column makes it 130, or thirteen lots of ten. If your child has grasped the concept fully, he will realise that this is one lot of a hundred and three lots of ten, meaning that the three goes beneath the tens column, and the single hundred can be written as another subscript. Then, since there are no hundreds in the original sum, the answer will be 131.

Addition with bigger numbers

Once your child is familiar with this kind of concept, you can play around with more sums of this sort, including larger and larger numbers if your child is fascinated – as so many are – with thousands and millions. Just follow the same principles, adding one column at a time and remembering what each digit refers to – and you shouldn’t go wrong.

You can also try adding up three numbers, or four – the principles are exactly the same, although you may need to be more careful to keep track of where you are. If you have numbers that add up to more than twenty in a column, then you use a subscript of 2 to carry them over to the next column to the left. You can always keep a calculator handy to check your answers if you’re not entirely confident in addition – and show your child how to use it to play with numbers. Calculators are a way of life these days, and there’s no reason why difficult addition should ever be done on paper. Understanding the concepts is far more important than being able to work out complicated sums without a calculator.

Examples to try: 22 + 88; 234 + 432; 456 + 567; 22 + 33 + 44; 10000 + 234 + 7000

Other basic maths for young children:

Maths for toddlers
Beginning multiplication
Fractions for four-year-olds
Simple subtraction