Revised Division Policy

8/11/2019 Revised Division Policy

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PROGRESSION THROUGH CALCULATIONS FOR DIVISION

MENTAL CALCULATIONS

(Ongoing)

These are a selectionof mental calculation strategies:

Doubling and halvingKnowing that halving is dividing by 2

Deriving and recalling division facts

Tables should be taught everyday from Y2 onwards, either as part of the mental oral

starter or other times as appropriate within the day.

Year 2 2 times table

5 times table10 times table

Year 3 2 times table

3 times table

4 times table

5 times table

6 times table

10 times table

Year 4 Derive and recall division facts for all tables up to 10 x 10

Year 5 & 6 Derive and recall quickly division facts for all tables up to 10 x 10 and beyond

Using and applying division facts

Children should be able to utilise their tables knowledge to derive other facts.

e.g. If I know 3 x 7 = 21, what else do I know?

21 7 = 3, 21 3 = 7, 210 7 = 30, 2100 7 = 300 etc.

Dividing by 10 or 100

Knowing that the effect of dividing by 10 is a shift in the digits one place to the right.

Knowing that the effect of dividing by 100 is a shift in the digits two places to the right.

Use of factors

378 21 378 3 = 126 378 21 = 18

126 7 = 18


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Use related facts

Given that 1.4 x 1.1 = 1.54

What is 1.54 1.4, or 1.54 1.1?

MANY MENTAL CALCULATION STRATEGIES WILL CONTINUE TO BE USED. THEY

ARE NOT REPLACED BY WRITTEN METHODS.

THE FOLLOWING ARE STANDARDS THAT WE EXPECT THE MAJORITY OF

CHILDREN TO ACHIEVE.

Foundation

Children will understand equal groups and share items out in play and problem solving.

They will see division as repeated subtraction, using simple pictures to record their

calculations. The main focus is on sharing and halving.

Y1

Children will count in 2s and 10s and later in 5s and begin to use simple written annotations

to record, as well as using pictures.


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Y2

Children will develop their understanding of division and use jottings to support calculation

Sharing equally

6 sweets shared between 2 people, how many do they each get?

Grouping or repeated subtraction

There are 6 sweets, how many people can have 2 sweets each?

Repeated subtraction using a number line or bead bar

12 3 = 4

When dividing, make link to multiplying explicit. This can be done by always starting from

zero on the number line for any division calculation.

0 3 6 9 12

In this example, put 12 into groups of 3 or as the inverse, get 3 and keep getting it 4 times

0 1 2 3 4 5 6 7 8 9 10 11 12


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3 3 3 3

The bead bar will help children with interpreting division calculations how many 3s make

12?

Using symbols to stand for unknown numbers to complete equations using inverse

operations

2 = 4 20 = 4 = 4


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Y3

Children will continue to use:

Repeated subtraction using a number line

Children will use an empty number line to support their calculation.

24 4 = 6

0 4 8 12 16 20 24

Children should also move onto calculations involving remainders.

13 4 = 3 r 1

0 1 5 9 13

4 4 4

Again, counting on from zero makes the link to multiplication easier:

0 4 8 12 13

How many 4s are there in 13?

Using symbols to stand for unknown numbers to complete equations using inverse

operations

26 2 = 24 = 12 10 = 8


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Children will be explicitly shown that there are two types of division:

1 Sharing: for example, sharing 12 sweets between 3 people = 4 sweets each.

Children will become familiar with Shared equally between, rather than just saying,

shared. E.g. 12 sweets are shared equally between 3 people. How many sweets does

each person get?

2 Grouping: for example, how many groups of 3 sweets can I make from 12 sweets?

Grouping can be explicitly shown to be the inverse calculation of division as well as being

shown to be repeated subtraction.

When using written notation for division, children will be shown that this notation differs

from the other examples in that the divisor goes last the numbers are not written in the

order that they appear.

Example: 4 friends each have 3 apples. How many apples do I have = 4 x 3 = 12. The order

that the numbers appear does not matter, i.e. this calculation can also we written as

3x 4 = 12. (the rule of commutativity)

However, the rule of commutativity does not apply with division.

Example: How many groups of 3 sweets can I make from 12 sweets needs to be written as

12 3 = 4, not as 3 12

Children will be introduced to the language of division at this stage, namely:

a)

The quotient the answer to a division calculation

b) The dividend the number that is to be grouped or shared

c)

The divisor the number that is divided into the dividend.


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Y4

Children will develop their use of repeated subtraction to be able to subtract multiples of

the divisor. Initially, these should be multiples of 10s, 5s, 2s and 1s numbers with which

the children are more familiar.

72 5

0 2 7 12 17 22 27 32 37 42 47 52 57 62 67 72

-2 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5

Moving onto:

-50

_______________________________________________________

0 2 7 12 17 22 72

As in year 3, the links to multiplication can be shown by starting (counting on) from

zero and can be effectively modelled simultaneously with the method of repeated

subtraction.

Then onto the vertical method:

TU U (Chunking method)

72 3

3 ) 72

- 30 10 groups

42

- 30 10 groups

12

- 6 2 groups

6

- 6 2 groups

0

r2-5 -5 -5 -5

101 1 1 1


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Answer: 24

The term groupsneeds to be use when recording in year 4. When children are

secure with their understanding this term can be removed, as in the year 5 example

below.

Leading to subtraction of other multiples:

96 6

1 6

6 ) 96

- 60 10 groups

36

- 36 6 groups

0

Answer: 16

Any remainders should be shown as integers, i.e. 14 remainder 2 or 14 r 2.

Children need to be able to decide what to do after division and round up or down

accordingly. They should make sensible decisions about rounding up or down after division.

For example 62 8 is 7 remainder 6, but whether the answer should be rounded up to 8 orrounded down to 7 depends on the context.

e.g. I have 62p. Sweets are 8p each. How many can I buy?

Answer: 7 (the remaining 6p is not enough to buy another sweet)

Apples are packed into boxes of 8. There are 62 apples. How many boxes are needed?

Answer: 8 (the remaining 6 apples still need to be placed into a box)


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Y5

Children will continue to use written methods to solve short division TU U.

Children can start to subtract larger multiples of the divisor, e.g. 30x

HTU U (chunking method):

196 6

32 r 4

6 ) 196

- 180 30x

16

- 12 2x4

Answer : 32 remainder 4 or 32 r 4

Any remainders should be shown as integers, i.e. 14 remainder 2 or 14 r 2.

Children need to be able to decide what to do after division and round up or down

accordingly. They should make sensible decisions about rounding up or down after division.

For example 240 52 is 4 remainder 32, but whether the answer should be rounded up to5 or rounded down to 4 depends on the context.

Children will continue to use written methods to solve short division TU U and HTU U.

Long division HTU TU (chunking method)

972 36

27

36 ) 972

- 360 10x

612

- 360 10 x

252

- 180 5x

72

- 72 2 x

0

Answer : 27


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Short division:

Short division should be shown as an efficient method when the divisor is a single digit

number. This method is particularly important when compared to the chunking method as

it will give a decimal answer, rather than an answer with a remainder.

Any remainders should be shown as decimals, i.e. if the children were dividing 32 by 10,

the answer should be shown as 3.2.

Example 1: 1 83 524

Progressing to:

Example 2:

87 6 11.1258 89102040

As with multiplication, children should estimate their answers prior to solving the

calculation. They can use their times table knowledge to assist them, e.g. 11 x 8 = 88, so

the estimate is 11

+ - + - + - + - + - + - +

Y6

Children in year 6 will be shown how to use long division so that a decimal answer can be

achieved, rather than keeping an answer with a remainder.

Children will be shown the links between long and short division but with an emphasis that

long division is better suited to be used when the divisor is a two digit number orgreater.


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Children will be able to see how the chunking method of division was a link to be able to use

long division methods and is a combination between chunking and short division methods.

Example 1:

324 16

Using Long division -

20.25

16 324.0032

04032

80

Using short division -

20.2516 324.4080

By the end of year 6, children will have a range of calculation methods, mental and

written. Selection will depend upon the numbers involved.

Children should not go onto the next stage if:

1) They are not ready.

2) They are not confident.

Children should be encouraged to approximate their answers before calculating.

Children should be encouraged to check their answers after calculation using an

appropriate strategy.Children should be encouraged to consider if a mental calculation would be appropriate

before using written methods.

Documents

Revised Division Policy