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Methods to divide whole numbers. Understanding division as grouping and division with remainders. Chunking method of division.

1.
Coffee and

DIVISION ÷

Workshop 4

DIVISION ÷

Workshop 4

2.
Aims of session

To help you:

Develop your knowledge of the methods children

are taught and use in school for division

Understand the progression in methods used as

children move up through the school

Support your child’s learning at home

To help you:

Develop your knowledge of the methods children

are taught and use in school for division

Understand the progression in methods used as

children move up through the school

Support your child’s learning at home

3.
Now onto division

Of all of the four operations, children find

division the trickiest to master.

They need to have a secure knowledge of lots of other

mathematical concepts.

-Times tables

-Division facts

Of all of the four operations, children find

division the trickiest to master.

They need to have a secure knowledge of lots of other

mathematical concepts.

-Times tables

-Division facts

4.
Vocabulary of division

5.
Tricky Vocabulary

12 ÷ 3 = 4

The ‘dividend’ is the number being

divided into (12). The ‘divisor’ is the

number it’s being divided by (3).

The ‘quotient’ is the answer (4).

12 ÷ 3 = 4

The ‘dividend’ is the number being

divided into (12). The ‘divisor’ is the

number it’s being divided by (3).

The ‘quotient’ is the answer (4).

6.
Mental Strategies for Division

To divide successfully, children need to be

able to:

understand the relationship between multiplication

and division

understand and use multiplication and division as

inverse operations.

recall multiplication and division facts to 10 × 10 and

recognise multiples of one-digit numbers

know how to multiply single digits by multiples of 10 or

know how to find a remainder working mentally - for

example, find the remainder when 48 is divided by 5;

To divide successfully, children need to be

able to:

understand the relationship between multiplication

and division

understand and use multiplication and division as

inverse operations.

recall multiplication and division facts to 10 × 10 and

recognise multiples of one-digit numbers

know how to multiply single digits by multiples of 10 or

know how to find a remainder working mentally - for

example, find the remainder when 48 is divided by 5;

7.
Written methods for Division

To carry out written methods of division

successfully, children also need to be

able to:

understand division as repeated subtraction;

estimate how many times one number divides

into another - for example, how many 6s there

are in 47, or how many 23s there are in 92;

multiply a two-digit number by a single-digit

number mentally;

subtract numbers using the column method.

To carry out written methods of division

successfully, children also need to be

able to:

understand division as repeated subtraction;

estimate how many times one number divides

into another - for example, how many 6s there

are in 47, or how many 23s there are in 92;

multiply a two-digit number by a single-digit

number mentally;

subtract numbers using the column method.

8.
Foundation Stage

Practical activities involving grouping and

sharing

How should we plant the daffodil bulbs in these 3

pots?

Can we share these cakes out fairly? How shall we

do it?

I am going to divide this apple in half – how many

pieces do I have?

Lets sort these toys into 2s – how many groups

have we made?

Practical activities involving grouping and

sharing

How should we plant the daffodil bulbs in these 3

pots?

Can we share these cakes out fairly? How shall we

do it?

I am going to divide this apple in half – how many

pieces do I have?

Lets sort these toys into 2s – how many groups

have we made?

9.
Written methods for Division

Initially division is introduced as ‘sharing’ using

real objects or pictures.

Share 10 apples equally between 2 children

which eventually becomes 10 ÷ 2 = 5

Initially division is introduced as ‘sharing’ using

real objects or pictures.

Share 10 apples equally between 2 children

which eventually becomes 10 ÷ 2 = 5

10.
10 ÷ 2 = 5

11.
Key Stage 1

Continue to practically group and

share

Record work using pictures and

number lines

Learn alongside multiplication

4x2=8

8÷4=2

Continue to practically group and

share

Record work using pictures and

number lines

Learn alongside multiplication

4x2=8

8÷4=2

12.
Children are taught to understand division as

sharing and grouping

There are 6 colouring

6 colouring pencils are pencils.

shared between 2 How many children can

children. have two each?

How many pencils do

they get each?

Sharing between 2

Grouping in twos

sharing and grouping

There are 6 colouring

6 colouring pencils are pencils.

shared between 2 How many children can

children. have two each?

How many pencils do

they get each?

Sharing between 2

Grouping in twos

13.
Understanding division as grouping

It is this aspect that links division facts to corresponding

multiplication facts. Children need a solid understanding of

multiplication as making ‘groups of’ or ‘lots of’ (repeated

addition) in order to then carry out the inverse process of

making groups or lots from a given total (repeated subtraction).

Children should be encouraged to visually see the link between

the two operations. Lots of practical work using objects to

create these groups will help the initial understanding of this

aspect of division.

2+2+2 From 6 – 2 – 2 – 2

3 groups of 2 = 2 x 3 = 6

6÷2=3

It is this aspect that links division facts to corresponding

multiplication facts. Children need a solid understanding of

multiplication as making ‘groups of’ or ‘lots of’ (repeated

addition) in order to then carry out the inverse process of

making groups or lots from a given total (repeated subtraction).

Children should be encouraged to visually see the link between

the two operations. Lots of practical work using objects to

create these groups will help the initial understanding of this

aspect of division.

2+2+2 From 6 – 2 – 2 – 2

3 groups of 2 = 2 x 3 = 6

6÷2=3

14.
12 ÷ 4 =

4 apples are packed in a basket.

How many baskets can you fill

with 12 apples?

Grouping in fours

Here 12 dots can be split up into groups of 4

Division shown

as repeated

Start with 12 apples/dots and takeaway a group of 4, then another

subtraction group and then another. 12 – 4 – 4 – 4 = 3 groups

4 apples are packed in a basket.

How many baskets can you fill

with 12 apples?

Grouping in fours

Here 12 dots can be split up into groups of 4

Division shown

as repeated

Start with 12 apples/dots and takeaway a group of 4, then another

subtraction group and then another. 12 – 4 – 4 – 4 = 3 groups

15.
Grouping can be shown easily on a number line

This means how

many groups of

4 in 12

12 ÷ 4 =

+4 +4 +4

0 4 8 12

The hops or jumps along the number line show

how many groups of 4 there are in 12. Start from

zero and count in multiples of 4 up to 12.

12 ÷ 4 = 3

This means how

many groups of

4 in 12

12 ÷ 4 =

+4 +4 +4

0 4 8 12

The hops or jumps along the number line show

how many groups of 4 there are in 12. Start from

zero and count in multiples of 4 up to 12.

12 ÷ 4 = 3

16.
28 ÷ 7 =

A comic costs 7p.

How many can I buy with 28p?

0 7 14 21 28

To work out how many 7’s there are in 28, draw jumps of 7

along a number line. This shows you need 4 jumps of 7 to

reach 28. So, I can buy 4 comics.

A comic costs 7p.

How many can I buy with 28p?

0 7 14 21 28

To work out how many 7’s there are in 28, draw jumps of 7

along a number line. This shows you need 4 jumps of 7 to

reach 28. So, I can buy 4 comics.

17.
With larger numbers, I can count in 6’s up to

84÷6= 84 but it would take a long time – it’s not

efficient!

Instead, I jump in several groups of 6 at a time

I need 6 drawing pins to put up a picture.

How many pictures can I put up with 84

pins?

6x10 ( 10 groups of 6) 6x4 (4 groups of 6)

0 60 84

To be more efficient, jump on in bigger ‘chunks’. A jump of 10

groups of 6 takes you to 60. Then you need another 4 groups of 6

to reach 84. Altogether, that is 14 groups of 6.

S0, I can put up 14 pictures with my drawing pins.

84÷6= 84 but it would take a long time – it’s not

efficient!

Instead, I jump in several groups of 6 at a time

I need 6 drawing pins to put up a picture.

How many pictures can I put up with 84

pins?

6x10 ( 10 groups of 6) 6x4 (4 groups of 6)

0 60 84

To be more efficient, jump on in bigger ‘chunks’. A jump of 10

groups of 6 takes you to 60. Then you need another 4 groups of 6

to reach 84. Altogether, that is 14 groups of 6.

S0, I can put up 14 pictures with my drawing pins.

18.
192÷8= How many groups of 8 can

we make from 192?

8 pencils fit into one packet. If you have 192

pencils, how many packets can be filled?

8x20 8x4

0 160 192

Using chunking on the number line

To be efficient you can jump in several groups of 8 i.e. Chunks/multiples

of 8. The first jump is 20 groups of 8 which lands you on 160 and then

you can choose another multiple of 8 to get to 192. In this case using

times tables you can jump 4 groups of 8 which is a chunk of 32 to reach

we make from 192?

8 pencils fit into one packet. If you have 192

pencils, how many packets can be filled?

8x20 8x4

0 160 192

Using chunking on the number line

To be efficient you can jump in several groups of 8 i.e. Chunks/multiples

of 8. The first jump is 20 groups of 8 which lands you on 160 and then

you can choose another multiple of 8 to get to 192. In this case using

times tables you can jump 4 groups of 8 which is a chunk of 32 to reach

19.
Division with remainders

How many groups of 7

121 ÷ 7 can we make from 121?

7x10 7x5 7x2 +2

10 groups of 7 5 groups of 7

2 groups of 7

0 70 105 119 121

121 ÷ 7 = 17 r 2

How many groups of 7

121 ÷ 7 can we make from 121?

7x10 7x5 7x2 +2

10 groups of 7 5 groups of 7

2 groups of 7

0 70 105 119 121

121 ÷ 7 = 17 r 2

20.
Moving towards more formal methods

184÷7=

I need 184 chairs for a concert. I arrange them in rows of 7.

How many rows do I need?

184

- 1 4 0 20 groups (7 x 20)

44

- 4 2 6 groups (7 x 6)

2

= 26 r2

I would need 27 rows.

i.e. 26 complete rows and one more to accommodate the extra 2 chairs to make

sure I have enough for the concert

This method is known as chunking

In this example, you are taking away chunks of 7. First subtract 140 (20

groups of 7) and you are left with 44. Then subtract 42

(6 groups of 7), to leave 2.

Altogether, that is 26 groups of 7 with a remainder of 2.

184÷7=

I need 184 chairs for a concert. I arrange them in rows of 7.

How many rows do I need?

184

- 1 4 0 20 groups (7 x 20)

44

- 4 2 6 groups (7 x 6)

2

= 26 r2

I would need 27 rows.

i.e. 26 complete rows and one more to accommodate the extra 2 chairs to make

sure I have enough for the concert

This method is known as chunking

In this example, you are taking away chunks of 7. First subtract 140 (20

groups of 7) and you are left with 44. Then subtract 42

(6 groups of 7), to leave 2.

Altogether, that is 26 groups of 7 with a remainder of 2.

21.
Formal Written Methods

Short Division

2 64 r 2

7 18 4

3. 4

Short division can also

be used for decimals

4 13.6

1

Short Division

2 64 r 2

7 18 4

3. 4

Short division can also

be used for decimals

4 13.6

1

22.
Long Division for HTU ÷ TU

The next step is to tackle HTU ÷ TU, which for most children will be in

Year 6. Long division using chunking involves children subtracting

multiples of the divisor (24) from the dividend (560). Children need to

be confident in multiplying to keep this method efficient and reasonably

compact. It is focused on repeated subtraction but is more difficult to

use with decimals as the focus is on the whole of the starting number.

2 3 r8

24 x 20 8

24 560

24 x 3

Short division can be used for

the same calculation and many

children prefer it.

The next step is to tackle HTU ÷ TU, which for most children will be in

Year 6. Long division using chunking involves children subtracting

multiples of the divisor (24) from the dividend (560). Children need to

be confident in multiplying to keep this method efficient and reasonably

compact. It is focused on repeated subtraction but is more difficult to

use with decimals as the focus is on the whole of the starting number.

2 3 r8

24 x 20 8

24 560

24 x 3

Short division can be used for

the same calculation and many

children prefer it.

23.
Division: Learning to show the remainder

23÷ 5

23 ÷ 5 = 4 r 3 As a remainder

3

23 ÷ 5 = 4 5

As a fraction

23 ÷ 5 = 4.60 As a decimal

fraction

23÷ 5

23 ÷ 5 = 4 r 3 As a remainder

3

23 ÷ 5 = 4 5

As a fraction

23 ÷ 5 = 4.60 As a decimal

fraction

24.

25.
Any