Number bonds

For many parents who have bad memories of maths in school, it might sound like a daunting task to teach children to add. Yet simple addition is something we do in daily life without even thinking about it. We’re having two guests to lunch, and there are four in our family, so how many places do we need to set at the table? I had four books out of the library, my son had three, and my daughter had five – how many library books do we need to find?You might ‘know’ the answers to these questions instantly, you might need to write down a ‘sum’ of numbers on paper, you might reach for a calculator, you might use your fingers. There is no ‘right’ or ‘wrong’ method of adding, or doing any other kind of arithmetic, so long as it works.

Simple ‘adding’ language

As a parent, you probably used simple ‘adding’ language with your child from an early age. ‘How many feet do you have? One, two! How many shoes are you wearing? One! We need to find one more shoe, ah here it is, now we have two!’ Yes, it sounds stilted when typed out, but education starts at birth, whether or not you plan to educate your child at home when they reach compulsory education age.

As your child grows up he or she will be aware, as general knowledge, that one item and another similar one make two of that item. Or that two lots of one item make two items. The so-called ‘addition fact’ 1+1=2 is exactly the same thing is the so-called ‘multiplication fact’ 2×1=2. Multiplication is a shorthand for repeated addition, and for that matter subtraction is addition in reverse. So if your child learns to add, the other arithmetic skills are likely to follow naturally.

Number bonds

Because of the importance of understanding simple addition, modern educationalists talk about ‘number bonds‘ as pairs which make up each number. The number bonds for seven, for instance, are 3+4, 2+5, 1+6 and 0+7. To have a quick grasp of addition and subtraction, it’s vital to know number bonds for each number up to ten.

Adding games

When your child can count to ten accurately, perhaps using his fingers and thumbs, he’s ready to understand what simple addition means – although of course you don’t need to use the word ‘addition’. You can play games, perhaps holding up six fingers and asking how many are hiding. Or showing a few fingers from one of your hands, and asking him to show a few from his hand, and then asking how many fingers are showing altogether.

Some children will rapidly remember answers, others will count every time. It doesn’t matter – what they’re learning, however slowly, is that numbers are constant. If you show three fingers and your child shows four, there are seven altogether. If he shows three and you show four, there are still seven. If you have three cakes and four cakes, there are seven cakes. This is the algebraic principle 3y + 4y = 7y which needs to be understood before we write it as the arithemtical shorthand 3+4=7.

So long as your child has played around with this kind of ‘real’ sum, and is fully comfortable with the principles, he will have no trouble with algebraic concepts such as a+b = b+a. Difficulties with this kind of statement only arise when the child has never really grasped what the ‘arithmetic facts’ actually mean, and how they work in real life.

Turning number bonds around

When your child is familiar with working out simple addition, turn the question around: ‘What plus six makes ten?’ Or, if you prefer it in words, ‘If we have ten people for lunch, and we’ve only got six clean plates, how many more do we need to wash?’ Numbers refer to items in the real world, and many children are much more comfortable thinking about arithmetic in terms of concrete objects than as symbolic abstractions.

Once your child is aware of the different ways a number can be made up, he already has a firm grasp of addition. You may want to move on, using two pairs of hands (or hands and toes, or 20 pieces of lego, or anything else lying around) to think about number bonds of numbers between 11 and 12. There are more of these, and they’re not so easy to spot.

Number patterns

However some children will realise that some of the patterns are similar: for instance, 17 has several number bonds, but some of them (10+7, 11+6, 12+5, 13+4, 14+3, 15+2, 16+1, 17+0) look very similar to the number bonds for 7, with the extra ‘1’ at the beginning. If your child sees this, he may be good at spotting patterns – an important part of mathematical ability – and may be ready for explanations about the decimal system of counting. Moreover, he will realise that the only ‘new’ number bond of 17 is 9+8 (or 8+9, which a pattern-spotting child will see as identical anyway).

Using number bonds, it’s easy to see that there is far less to learn than simply presenting children with ‘facts’ about individual pairs of numbers and their totals. 5+2 has the same result as 6+1. Put together lego bricks of these sizes, and your child may see this instantly. He may also spot that 6+2 is the same as 7+1, and realise that similar patterns work for all numbers. In other words, he’s grasped the algebraic principle that y+2 = (y+1) + 1. Very important, should he ever go on to study some field requiring formal algebra.

If your child likes playing computer games, he might like to spend time at this number bond machine site.

You’ll probably have realised that the idea of number bonds teaches a child not just addition but simple subtraction, without any extra work. Once he knows the number bonds of ten, he can take anything away from ten and know the answer instantly.

If your child is confident with number bonds and wants to understand more advanced adding, you might like to read the pages about place value, and basic addition.

Other basic maths for young children:

Maths for toddlers
Beginning multiplication
Introducing fractions
Prime numbers and factors