Many children really struggle with adding and subtracting mentally in their heads and often rely on using their fingers to count. I’ve seen this with children all the way up to Year 6. This really slows children down in arithmetic tests, mental maths tests and when using written column method to solve addition and subtraction. It can also be very frustrating for children and lower their confidence because they don’t feel they know any other way of mentally adding and subtracting.

The methods below are some of the foundations in helping your child build confidence and speed in their mental addition and subtraction skills.

__Number bonds__

**Number bonds to 10:**

Firstly, check that your child knows their numbers bonds to 10. These are the pairs of numbers which add together to make 10.

10 + 0 9 + 1 8 + 2 7 + 3 6 + 4 5 + 5 4 + 6 3 + 7 2 + 8 1 + 9 0 + 10

I often call these number buddies as certain numbers are best friends with another number. Once they know which numbers form bonds to 10, try some quick-fire shout outs of a number under 10 and ask your child to tell you the corresponding number bond to make 10. You can also do this with a 0 -10 dice, where your child rolls the dice and gives you the corresponding number bond to 10.

Then, move on to subtraction, asking your child to subtract a number bond from 10:

e.g. 10 – 6, 10 – 4, 10 – 7.

**Number bonds to 20:**

0 + 20 1 + 19 2 + 18 3 + 17 4 + 16 5 + 15 6 + 14 7 + 13 8 + 12 9 + 11 10 + 10

11 + 9 12 + 8 13 + 7 14 + 6 15 + 5 16 + 4 17 + 3 18 + 2 19 + 1 20 + 0

Once your child has mastered number bonds to 10, they can try number bonds to 20, using their knowledge of number bonds to 10.

Example 1: 17 + ____ = 20

Children know that 7 and 3 are a number bond to 10 so with the additional 10 that equals 20. Therefore, the answer is 3.

Example 2: 4 + ____ = 20

Children know that 4 and 6 are a number bond to 10 but they also have to add the additional 10 to make 20 so the answer is 16.

To practise these bonds, you can shout out a number under 20 and ask your child for the corresponding bond or use a 1 – 20 dice for your child to roll and give the number bond.

Then, move on to subtraction, asking your child to subtract a number bond from 20

e.g. 20 – 3, 20 – 6, 20 – 14.

**Number bonds to 100:**

Children can then move on to number bonds to 100.

Firstly, look at the easier number bonds to 100:

0 + 100 | 10 + 90 | 20 + 80 | 30 + 70 | 40 + 60 | 50 + 50 |

100 + 0 | 90 + 10 | 80 + 20 | 70 + 30 | 60 + 40 |

Show children the correlation between 2 + 8 = 10 and 20 + 80 = 100. If they know their number bonds to 10, they can use these to help with their number bonds to 100.

Once they are confident with these, move on to a random one or two-digit number below 100 and ask your child to work out the number bond to 100.

Example 1: 35 + ____ = 100

Encourage your child to count up to the next ten (+5), then, ask how many more tens to get up to 100 from 40 – think number bonds! (+60), then, add them together 5 + 60 = 65.

Example 2: 42 + ____ = 100

Encourage your child to count up to the next ten (+8), then, ask how many more tens to get up to 100 from 50 – think number bonds! (+50), then, add them together 8 + 50 = 58.

Once they are confident with addition, try subtracting the facts from 100

e.g. 100 – 30, 100 – 45, 100 – 62.

__Doubles, halving, near doubles and near halves__

Firstly, start with doubles by giving your child some numbers to double under 10 then increase with numbers up to 20 e.g. double 6 = 12.

Then, move on to giving your child some even numbers to halve – again start small and work up to two digit numbers e.g. half of 8 = 4.

Once they have cracked doubles and halving, then try near doubles and halves.

Near doubles example 1:

6 + 7 – this is very close to double 6 = 12 then add 1 = 13.

Near doubles example 2:

12 + 11 – this is very close to double 12 = 24 then subtract 1 = 23.

Now try: 4 + 5, 8 + 7, 12 + 13, 15 + 14

Near halves example 1:

30 – 14 – fourteen is half of 28 so add 2 = 16.

Near halves example 2:

27 – 13 – thirteen is half of 26 so add 1 = 14.

Now try: 43 – 20, 62 – 30, 31 – 15, 72 – 35

__Bridging through 10__

When a number bridges 10, e.g. 7 + 5 – encourage your child to work out how many more are needed to make the next 10 (3) then add on what is left (10 + 2 = 12).

Example 1: 8 + 6 – it is 2 more to make the next ten (which is 10), leaving 4 to add on so 10 + 4 = 14.

Example 2: 16 + 8 – it is 4 more to make the next ten (which is 20), leaving 4 to add on so 20 + 4 = 24.

Now try: 8 + 4, 9 + 5, 16 + 7, 27 + 5, 38 + 6.

__Quick fire addition and subtraction up to 20__

This is a case of practising adding and subtracting numbers under 20 in a quick-fire way to help your child with speed.

You can do this by shouting out different numbers under 20 to add or subtract or having two 0-20 dice and asking your child to throw them and then add or subtract the numbers. Hopefully, they will be able to use the methods we have already looked at – number bonds, doubles/halves, near doubles/near halves and bridging through 10 to help them answer some of the questions.

Try these with your child: 7 + 13, 7 + 8, 8 + 5, 6 + 4, 15 + 8, 4 + 5, 17 + 3, 6 + 6, 9 + 6,

10 – 3, 20 – 4, 12- 5, 20 – 7, 10 – 2, 10 – 4, 20- 18.

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