Maths Is Different – Thats Not How We Do It – Number Bonds

It is commonly said maths is different nowadays.  Up and down the country when parents try and help their children with maths homework often

  • either it is incomprehensible to the parent
  • or when they show their children something the children cry out

“That’s not how we do it”

Is it really true?  One thing I know for certain is that

Another thing I know is that in most things there are fashions and fads.  Different approaches to teaching the same material goes in and out of fashion.  New names are invented for the same ideas.

[update ]

See these posts for number bonds worksheets

Number bonds of 9 worksheets

Number bonds of 10 worksheets

Number bonds of 20 worksheets

All of the posts have a link to an Excel spreadsheet which will generate new number bonds questions each time it is recalculated.

[end update]

Number Bonds,  what are they. Well according to Wikipedia they are another name for “addition facts”.  More helpfully for any number, 5 say, the number bonds of 5 are just the pairs of numbers that add up to that 5.

numberBonds_5It’s a bit like saying if we’ve got 5 cans of beans and 2 carrier bags we can

  • Put them all the cans in  one bag and leave the other empty.
  • Put 4 cans in one bag and just 1 in the other bag, perhaps because we were worried the bag with 4 cans in would split.
  • Or put 2 cans in one bag and 3 in the other, if we were trying to share the cans as equally as possible between the two bags.

For 3 it is even simpler

numberBonds_3It is not absolutely necessary to learn number bonds. You can add using your fingers and toes, or step along a ruler.  But doing this takes longer than if you have learned some ‘number bonds’ or ‘addition facts’ so you can do the sum in your head.

If you think of starting to learn to drive a car, there seems to a mass of different things that have to be done all at the same time.  After a while you can do these tasks automatically which frees your mind to concentrate on what is happening on the road.

In a similar way learning some basic facts, such as number bonds, so they can be recalled automatically,  frees your children’s minds to think about more complicated problems.

Whether or not you call them number bonds, the number bonds for 3 and 5 will be learned as part of learning to count up to 10 and to add the numbers o to 9.

Number bonds of 9 are worth learning as it just so happens if you add the digits (the numbers in units and tens columns) for the numbers in the 9 times tables they add up to 9.  As you can see from the following table.

Actually it is not usual to list the number bonds both ways, so I’ll stop doing it!

Number bonds of 10 (without writing out reversed pairs) are well worth learning, especially the pairs of digits (1 through 9) that add up to 10 as these introduce the idea adding a pair of single digit numbers can sometimes result in a two digit number.

numberBonds_10Some pairs of digits will add up to more than 10, though usually the next number for which number bonds are learned is 20.


Comparing adding

3Add7and the corresponding teens


13Add7helps introduce the idea of adding in columns.

In all three cases adding 3 and 7 result in 0 (in the units column)

  • When adding two single digits,  a 1 is put to the left to of the 0 in the answer.
  • If one of the numbers has a digit in ‘the tens column’  that digit  is made one bigger.
  • Note we’re not coping with adding two 2 digit numbers yet.

So all in all a new name for an old idea, but something that is useful to do.

And, just like learning to ride a bike or drive a car, this is something you learn by doing.

As a parent you can help by asking your child questions which make them think about number bonds.  Or you can just get them to put cans of baked beans into 2 bags!

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