Wallands Community Primary School

Mathematical MethodsMathematical MethodsInformation for parents

Key Stage 2Key Stage 2

Mathematical Methods

• Addition• Subtraction• Multiplication• Division

This booklet is designed to give you information about the main methods for calculating in mathematics that your children are

learning in school. The children start by learning mental methods and informal jottings and progress to formal written calculations.

AdditionAddition

++Key Words

add, addition, plus, total, sum of, more, increase,

altogether

Mentally children should add using a count on method.

They may imagine an empty number line in their heads, e.g.

count on…

85 + 47 =

85+40 +7

125 132

Or they may partition into tens and units adding each separately, e.g.

85 + 47 = 132

80 + 40 = 120

5 + 7 = 12

120 + 12 = 132

For trickier additions they are more likely to use a column method as shown below:

8 5+ 4 71 3 2 1

To help with addition, practise quick recall of number bonds to 10 and adding through multiples of 10, e.g. 18 + 7, 43 + 9 etc

SubtractioSubtractionn

--Key Wordstake away, subtraction, subtract, minus, decrease, difference, less than, leave, left over

Here is the answer, 3+30+5 = 38Remember you can re-order the numbers in an addition. Put the biggest number first so 30+5+3 = 38

For subtraction we use an empty number line method as this encourages the children to understand what is happening in the calculation.

count on…

85 - 47 =

47

+3 +550 85

When we count on, we are actually finding the difference.• Place the lowest number on the left of the number line.• How much do you need to count on to get to the larger number?

38-7 -40

45 85

Some children prefer to count back.• Place the highest number on the right of the number line.• Count back splitting the number into tens and units.

…count back

Here is the answer

80

+30

Or, you could do it like this…

Most children find it easier to count on.

For trickier subtraction the children will learn a column method. First they will learn an expanded method where the numbers are split into hundreds, tens and units.

By teaching the children this expanded method, they are able to

understand decomposition of numbers (borrowing) when it comes

to more complex subtractions.

56 – 32 =

T U TU

50 + 6 56

- 30 + 2 - 32

20 + 4 24

Decomposition:

754 = 700 + 50 + 4

- 286 200 + 80 + 6

-------- ------------------

700 + 40 + 14 - 200 + 80 + 6 600 + 140 + 14 - 200 + 80 + 6 ---------------------- 400 + 60 + 8 = 468

Start with the units.

4 – 6 can’t be done!

So 700 + 50 + 4 becomes

700 + 40 + 14

Now the units column can be subtracted, work it out and move on to the tens and the hundreds etc.

The final stage in subtraction is to use a more compact and efficient method like this:

6 14

7 514 - 2 8 6

4 6 8

Don’t forget to line up the hundreds, ten and units carefully!

When children are confident with this type of subtraction, they will work with bigger numbers and decimals in exactly the same way.

MultiplicationMultiplication

xxKey Word

multiplication, multiply by, times, product, multiple, lots of, groups of, product, array

When multiplying quick recall of tables is the most important thing. So knowing multiplication

and division facts up to 10x10 is vital.

Grid method multiplication involves partitioning each number into tens and units before multiplying and then adding back together.

X12 x 4 =

410 2

10x4= 40

2x4= 8 40 + 8 = 48

When using repeated addition a number line or informal jottings can be used, e.g.

…or children may count up in multiples, e.g. 3 x 5

“3… 6… 9… 12… 15!”

…or children may draw an array, e.g. 4 x 2

By setting the final adding part out vertically as in this example, children are able to see how this links to short multiplication.

X68 x 7 =

7

60

8

60x7=420

7x8=56

4 2 0+ 5 64 7 6

X40

50 2

40x50=2000

40x2=80

2 0 0 0+ 4 5 0 8 0 1 82 5 4 8 1

52 x 49 =

9 50x9=450

9x2=18

Short multiplication is taught in Year 6.It is a quick method which is particularly useful when multiplying using decimals.

7. 9 2x 6

4 7. 5 25 1

1 2 5 8x 3

3 7 7 41 2

Estimate your answer first:7.92 x 6 = 7.92 is between 7 and 8, but closer to 8.7 X 6 = 428 x 6 = 48

So the answer must be between42 and 48 but closer to 48.

It is very important for children to estimate their answers before starting a calculation!

÷DivisionDivision

Key Wordsdivide, division, divided by, divided into, share, group, split into equal groups, count in multiples, repeated subtraction remainder, factor, quotient, divisible by, inverse

When using repeated subtraction children use informal jottings to group, e.g. How many 3’s in 15?

…or children may count on in multiples like this:

When dividing it is vital that children know their division facts, e.g. 15 ÷ 3 = 5

Children are encouraged to ask a division as…… How many 3’s are there in 15?

…or children may share out into groups like this:

Children learn about division through practical activity. They need lots of practice sharing out to

make groups and counting in multiples.

Chunking Chunking (division as the inverse of (division as the inverse of multiplication)multiplication)

After lots of practical work and using known division After lots of practical work and using known division facts children will move onto the first written facts children will move onto the first written method of division – chunking. This method makes method of division – chunking. This method makes use of their multiplication facts, which they should use of their multiplication facts, which they should feel fairly secure in by the time they attempt feel fairly secure in by the time they attempt chunking (usually around Year 4). Chunking helps chunking (usually around Year 4). Chunking helps them to see how division is the inverse of them to see how division is the inverse of multiplication. multiplication. 91 ÷ 7 =

The inverse of this is 7 x ? = 91

Work out how many 7s are in 91

Use multiplication facts that you feel confident with and build up towards your target number. Your target number is 91. This is the number you want to reach by counting up in 7s as you want to find out how many 7s are in 91, which is the same This is the as 91 ÷ 7. It will take too long to count number you up 7,14,21 etc so take a short cut by multiply by using your multiplication facts.

7 x ? = 917 x 10 = 70 This is close to 91, but not close enough.

7 x 3 = 21 Can you fit anymore 7s into 91?

Add this column to get your answer. This is how many times you multiplied 7 to get 91, which is the same as saying 91 ÷ 7. 7 x 13 = 91So, 91 ÷ 7 = 13

9 67 ) How many 7’s are there in 9? How many 7’s are there in 26?

1 3 r 52

Bus stop methodBus stop method

Chunking is a great method to help Chunking is a great method to help children really understand what is children really understand what is happening in division. The bus stop happening in division. The bus stop method is a more efficient method once method is a more efficient method once the understanding is there. We always the understanding is there. We always teach chunking first. teach chunking first.

4 ) 78How many 4s in 8? 2

2 1 r 3

How many 4s in 7?

1 and 3 left over.