Numeracy Support: Written Calculations

• Written calculation methods are an important skill that children need to learn, and are practised frequently in school.

• However, there is also a great emphasis on developing the ability to calculate mentally and for children to choose a method which suits them.

• The important thing when supporting written calculations is that children understand what they are doing.

• Depends on the situation e.g. Are we solving word problems or doing a mental maths test? Would we need to be able to calculate mentally e.g. working out change when buying something in a shop?

• What do we notice about the numbers- are they close to one another? Are there any number bonds to help us?

• 13 + 17=• 25 x 12=• 356 - 148=• 245 x 16=• 189 – 99=

• In our school, we use a written method for multiplication which we call the ‘grid method’.

• Let’s try 56 x 7.

• 56 can be partitioned into 50 and 6.• 7 can’t be partitioned as it contains only units.

56 x 7=

x 50 6

7

56 x 7=

x 50 6

7 350 42

56 x 7=

• Next, we would add 350 and 42 to get the answer.

• This could be done mentally i.e. 350 + 40 + 2= 392• Or it could be added using a written method

i.e. 350 + 42

392

This method works with bigger numbers too...

• 146 x 28=

X 100 40 6

20 2000 800 120

8 800 320 48

Then add the numbers together to get your answer.

2000 + 800 + 120= 2920 800+ 320 + 48= + 1168

4088

So 146 x 28= 4088

With decimals..

• 34.6 x 6=

• 180 + 24 + 3.6= 207.6

x 30 4 0.6

6 180 24 3.6

With money...

• £6.65 x 7=

• £42 + £4.20 + 35p= £46.55

x £6 60p 5p

7 £42 £4.20 35p

Common Errors

• Incorrect partitioningE.g. 56 into 5 and 6 rather than 50 and 6.

• Errors in multiplicationE.g. times tables mistakes and ‘forgetting 0s’

Why do we use this method?

• Children understand the steps that they are taking to get to the answer.

• Drawing a grid means that children will not miss out a step as all the boxes have to be filled.

• Easier for adults to see where they have made errors.

• To divide by a single digit number, we use a traditional short division method.

72 ÷3=

Division by chunking

• Also known as repeated subtraction.

• We this method for larger numbers e.g. Dividing by a 2 digit number.

• Let’s look at a division problem...

384 / 24=

• 384 children in a school are put into groups of 24. How many groups would there be altogether?

• We work out how many groups of 24 there are in 384.

384÷24=How many 24s go into 384?

24 384 - 240 (10 x 24) 144 - 120 ( 5 x 24) 24

- 24 (1 x 24) 0

Finally, add up how many lots of 24 you have taken away ( 10 + 5 + 1 = 16) and

you have an answer. There would be 16 groups of children.

Lets try 317 ÷ 1212 317

-120 (10 x 12) 197-120 (10 x 12)

77 - 60 (5 x 12)

17- 12 ( 1 x 12) 5

Add the number of times you have taken away 12 ( 10 + 10 + 5 + 1= 26). 5 is the remainder so than answer to 317 ÷ 12= 26 r 5.

Why do we use this method?

• This method can take a while to get the hang of, but once children have grasped it they usually find it easy to use.

• They understand the steps that they are taking to reach an answer.

• Easier than long division and provides an alternative method.

• Adults can see what has caused the children to make errors.

Common Errors

• Subtraction errors• Forgetting or making mistakes when adding

the numbers in brackets.

• Younger children will begin addition by partitioning numbers and adding them

• e.g. 43 + 37= 40 + 30 is 70 3 + 7 is 10 70 + 10 is 80.

Addition

• Many children continue to use this method for certain calculations as the numbers do not require a written calculation .

• However, we do use written methods for addition in school.

Addition

134 + 291=

134 + 291

5 25

425

1

Subtraction

• We also use a traditional written subtraction method.

• However, children can choose their method depending on the numbers given.

• Would 2007- 1994 require a written method?• Most children would use a ‘ counting on’ method for

this subtraction.

Subtraction

• Let’s try 375- 169 as many children would choose a written method of subtraction for this question.

• The only real difference is that we try not to tell children to ‘borrow a 1’.

• If we borrow a 1- when is it paid back??• Instead we tell children to ‘take’ a 10 or 100.

Conclusion

• If you have any questions I will stay behind to answer them for you.

• Handouts can be kept to refer to if your child is having difficulty with calculations e.g. When doing their homework.

• If you would like further support feel free to ask!