Eastchurch Church of England Primary School

Mathematics Policy Reviewed: March 2017 Review date: March 2020

Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject. (National Curriculum 2014)

Introduction

The national curriculum for mathematics aims to ensure that all pupils:

become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.

reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language

can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

(National Curriculum July 2014)

At Eastchurch we aim to inspire all children to reach their full academic potential. In mathematics, this means ensuring a curriculum that is fully inclusive of all children which:

Develops children’s knowledge and understanding of Mathematical concepts whilst enabling them to practice and hone skills and methods;

Enables them to think critically and communicate their understanding;

Gives them opportunities to apply learnt mathematical skills in different contexts across the curriculum.

Provides opportunities to develop problem-solving skills useful for maths and across the curriculum.

Aims

The teaching of mathematics at Eastchurch School is geared towards enabling each pupil to develop their learning without labelling them by ability. We endeavour to not only develop the mathematics skills and understanding required for later life, but also an enthusiasm and fascination about maths itself.

We aim to increase pupil confidence in maths so they are able to express themselves and their ideas using the language of maths with assurance.

We recognise the importance of developing factual, procedural and conceptual knowledge.

We are continually aiming to raise the standards of achievement of everyone at Eastchurch School. This is being developed through our introduction of the mastery approach to teaching mathematics and incorporating a concrete, pictorial and abstract approach. We are also committed to developing the children’s conceptual and procedural understanding of the strategies being taught.

Our mastery approach aims to:

Deliver a gradual accumulative approach where core concepts are embedded before moving on.

Develop a ‘can do’ attitude where teachers believe that all children are capable of achieving in mathematics.

Enable children to show what they can do not what they cannot do.

Ensure each classroom encourages mathematical talk and the teacher encourages dialogue through effective questioning.

Ensure every classroom values the importance of active listening.

Promote problem solving and reasoning in every mathematics lesson.

Use a variety of concrete and pictorial representations to secure children's depth of conceptual understanding.

Encourage organised pre-teaching and reactive interventions.

Assessment

We aim to provide feedback to children through marking so that they have specific advice about improvements to their work. Children are given time to read and review their work following marking. Children are encouraged to reflectively review their work at the end of each lesson. They are also encouraged to respond to teachers’ comments; see separate Marking Policy for more information. Following the removal of levels, teachers have been developing the use of ‘low stakes’ assessment tools to assess learning. Such things as exit tickets, quizzes and ‘correct mistakes’ lessons have aided the formative assessment process.

Teachers also assess children against the Key Performance Indicators and Mastery Statements as identified through the Target Tracker Assessment Program.

Below Programme of study No understanding/knowledge Emerging At early stage of development (support needed) Expected Growing ability and independence (minimal prompting needed) Exceeding Exhibits skill independently

Mastery Exhibits skill spontaneously and with confidence in a range of concepts.

Resources

Resources for the delivery of the maths curriculum are stored both centrally and in classrooms. Everyday basic equipment is kept in classrooms and should be easily accessible in every maths lesson. Additional equipment and topic-specific items are stored in a central maths store.

Eastchurch Primary School uses a variety of published materials to facilitate the teaching of mathematics but recognises the need for the teaching of maths to be ‘scheme assisted not scheme driven’.

Materials are constantly updated, as new and relevant items become available. The maths subject leader orders new resources after consultation with the staff.

Equal Opportunities Pupils of all ethnic groups, both genders and all abilities have equal access to the Math’s curriculum. Positive images of such groups are promoted throughout the school, both in the use of subject specific language and in the provision of resources. Guidelines in the health and safety policy will apply with regard to use of ICT, all school based activities and out of school activities relating to mathematics.

Contribution in Mathematics to Teaching in Other Curriculum Areas

English Mathematics contributes significantly to the teaching of English in our school by actively promoting the skills of reading, writing, speaking and listening. ICT The effective use of ICT can enhance the teaching and learning of mathematics when used appropriately. When considering its use, we take into account the following points:

ICT should enhance good mathematics teaching. It should be used in lessons only if it supports good practice in teaching mathematics.

Any decision about using ICT in a particular lesson or sequence of lessons must be directly related to the teaching and learning objectives for those lessons.

ICT should be used if the teacher and/or the children can achieve something more effectively with it than without it.

Science Mathematical understanding will be developed in all areas of the science curriculum including; making careful and accurate measurements of both time, distance, capacity, mass and identifying differences within data from before and after investigations. The children will also be given the opportunity to develop their data handling skills as they present their findings in a variety ways.

Art, Design and Technology Measurements are often needed in art, design and technology. Many patterns and constructions are based on spatial ideas and properties of shapes, including symmetry. Designs may need enlarging or reducing, introducing ideas of multiplication and ratio. When food is prepared a great deal of measurement occurs, including working out times and calculating cost.

History, Geography and Religious Education In history and geography children will collect data by counting and measuring and making use of measurements of many kinds. The study of maps includes the use of co-ordinates and ideas of angle, position, direction, scale and ratio. The pattern of the days of the week, the calendar and recurring annual festivals all have a mathematical basis. For older children historical ideas require understanding of the passage of time, which can be illustrated on a time line, similar to the number line that they already know.

Physical Education and Music

Athletic activities require measurement of height, distance and time, while ideas of counting, time, symmetry, movement, position and direction are used extensively in music, dance, gymnastics and ball games. Personal, Social and Health Education (PSHE) and Citizenship

Mathematics contributes to the teaching of personal, social and health education, and citizenship. The work that children do outside their normal lessons encourages independent study and helps them to become increasingly responsible for their own learning. The planned activities that children do within the classroom encourage them to work together and respect each other’s views.

WRITTEN and MANIPULATIVES POLICY

Progression in the four operations

Addition

Counting in ones

Starting from 0 and then from

any number

Counting out loud and practising 1:1 correspondence

(knowing that each object is a separate unit)

It is also important that each number represents a group

of objects (e.g. 3 = 3 teddies)

Practical Addition (first

‘count all’ and then ‘count

on’)

Count all – 2 + 3 is counted 1,

2 and then 3, 4, 5 (out loud)

Count on – 2 + 3 is counted 2

and then 3, 4, 5

Addition using

children's own jottings

Drawing a picture

There were 4 yellow

sharks and 1 blue. How

many sharks were there

altogether?

Dots or tally marks

3 children were on a bus

and then 4 more got on.

How many were on the

bus in total?

Part, Part whole model

Counting in ones along

a number line/track

5 children are at school.

4 children arrive late.

How many children are

at school now?

Children could use a pre-

drawn number line and

then begin to create their

own.

5 + 4 = 9

3 + 4 =7

Use Tens frames to

represent calculation

Bar Model start with

discrete model

7 + 5 = ?

+

This can lead in to addition bridging ten by knowing the composition of a

number:

Practical Addition

Use of Numicon

To help children to learn

number facts and

visualise quantities and

what digits represent.

To look for patterns and

relationships in number.

Use of Numicon number

line to add amounts.

Practical and informal

partitioning

Use of practical

apparatus such as

Numicon and Diennes to

partition and present

place value of digits.

Place value cards can be

used as an additional

support in the

understanding of place

value.

e.g. 47 + 1 2 = or 4 7 + 1 5 = 62

50 + 9 = 59

Using Addition facts to

10 to bridge the ten

during addition.

Numicon or Cuisinaire

are used to bridge the

ten. E.g. in 56 + 8 the 8

is split into two 4s in

order to form a number

bond of 6 + 4. This

enables the next multiple

of 10 (60) to be reached

before adding on the

remaining 4.

Bead lines can also be

used to show this

method.

24 + 10 = 24 + 6 + 4

The empty number line

The mental methods that

lead to column addition

generally involve

partitioning. Children

need to be able to

partition numbers in

ways other than into tens

and ones to help them

make multiples of ten by

adding in steps.

The empty number line

helps to record the steps

on the way to calculating

the total.

Steps in addition can be recorded on a number line. The steps

often bridge through a multiple of 10

One step in their

development when using

a number line is to first

be able to count on in

tens and of course ones.

Bar model used to

illustrate aggregation

and augmentation

Partitioning by

horizontal expansion

method

The next stage is to

record mental methods

using partitioning into tens

and ones separately. Add

the tens and then the

ones to form partial sums

and then add these partial

sums.

Partitioning both numbers

into tens and ones mirrors

the column method where

ones are placed under

ones and tens under tens.

This method builds on

mental methods as each

part is calculated mentally

and recorded. It also

makes the value of digits

clear to children.

Record steps in addition using partitioning:

47 + 76

47 + 70 = 117

117+ 6 = 123

or

47 + 76

40 + 70 = 110

7 + 6 = 13

110 + 13 = 123

AdditionAggregation – two quantities combined

I have 6 red pencils and 4 yellow pencils. How many pencils do I have?(I combine two quantities to form the whole)

6 4

?

AdditionAugmentation- a quantity is increased

I have 6 red pencils and I buy 4 yellow pencils. How many pencils do I have now?(The bar I stated with increases in length)

The Bar is used to

illustrate the thinking that

underpins the problem

Part-whole model for addition and subtraction

The model represents a quantitative relationship among three variables: whole, part1 and part2. Given the values of any two variables, we can find the value of the third one by addition or subtraction.

Part 1 Part 2

Whole

with kind permission from Dr Kho Tek Hong

Vertical expansion

method

Vertical expansion using

Multibase and place

value counters.

Compact column

method

In this method, recording

is reduced further. Carry

digits are recorded below

the line, using the words

‘carry ten’ or ‘carry one

hundred’, not ‘carry one’.

Later, extend to adding

three two-digit numbers,

two three-digit numbers

and numbers with

different numbers of

digits.

2 5 8 3 6 6

8 7 4 5 8

3 4 5 8 2 4

1 1 1 1

Column addition remains

efficient when used with

larger whole numbers and

decimals. Once learned, the

method is quick and

reliable.

Subtraction

Mental Strategies required to subtract successfully

Count back in ones, and tens from any number

Recall all addition and subtraction facts to 10 and 20;

Subtract multiples of 10 (such as 160 – 70) using the related subtraction fact, 16 – 7, and their knowledge of place value;

Partition two-digit and three-digit numbers into multiples of one hundred, ten and one in different ways (e.g. partition 74 into 70 + 4 or 60 + 14).

It is important that children’s mental methods of calculation are practised and

secured alongside their learning and use of an efficient written method for

subtraction.

Counting backwards in ones

Starting from 10 and then from

any number

Counting out loud and singing number rhymes e.g. ‘Five

current buns’ or ‘ten green bottles’, using visual pictures

and puppets to show the process of getting less.

Practical subtraction (first

‘count all’ then ‘count on’)

Practical 1:1 correspondence

of finding the first number and

taking away the second to find

out what is left.

I found 3 pebbles on a beach

but I lost one! How many did I

have left?

Practical subtraction

Use of Numicon to subtract

using subatized pieces of

equipment.

Simple subtraction using

picture jottings, encourage

children to use their own

forms of recording

Drawing a picture

I had 5 apples but my teacher

ate 3 of them. How many did I

have left?

Dots or tally marks

There were 5 people on the

bus but 2 got off at the first

stop. How many people were

still on the bus?

5-2=3

Counting back in ones along

a number line/track

9 children are at school. 4

children go home because

they feel sick. How many

children are left in school?

Children could use a pre-

drawn number line and then

begin to create their own.

9 - 4 = 5

9 – 4 = 5

CHILDREN SHOULD USE COUNTING BACK BRIEFLY IN THEIR DEVELOPMENT

WHEN SUBTRACTING SMALL SINGLE DIGIT NUMBERS AND THEN MOVE TO USING

COUNTING ON IN TERMS OF FINDING THE DIFFERENCE PREDOMINANTLY.

5 - 2 = 3

Finding the difference

There are 10 children in our

class today and 7 of them are

having school dinner. How

many are having packed

lunch?

Children are taught to count

on from the smallest number

to find the difference. (This

can be done in their head or

on a number line)

The Bar also moves from

taking away to looking at

comparison

I had 10 pencils and I gave 6 away, how many do I have now? (This time we know the whole but only one of the parts, so the whole is partitioned and one of the parts removed to identify the missing part)

6 ?

10

Subtraction – Take Away

Subtraction - Comparison or Difference

Tom has 10 pencils and Sam has 6 pencils. How many more does Tom have?(The bar is particularly valuable for seeing the difference between the two quantities)

10

6 ?

Tom

Sam

Using Addition facts to 10 to

bridge the ten during

subtraction by counting up

to find the difference.

Here the use of a Numicon

can be used to help bridge the

ten when counting up to find

the difference.

E.g. in 64 – 56 =

4 is added to the 56 to reach

60 and then 4 again to reach

64. Thereby finding the

difference of 8 by counting up.

Bead lines can also be used to

show this method.

E.g. 34 – 24 = 6 + 4

Practical and informal

partitioning

Use of practical apparatus

such as Multibase and

Numicon.

Place value cards can be used

as an additional support in the

understanding of place value.

e.g. 47 - 1 2 = or 4 7 - 1 2 = 35

30 + 5 = 35

This works when the

units do not bridge

the ten.

Practical partitioning where

the units bridge the

ten/hundreds

As there are only 2 units

children should be taught to

exchange 1 ten for ten units.

This now means that there are

12 units and 2 tens (still 42).

Children are then able to

subtract 6 units and 1 ten, as

in the previous example.

4 2 - 1 6 = 2 6

Using an empty number

line to find the difference

Finding an answer by

calculating up

The steps can also be

recorded by counting up from

the smaller to the larger

number to find the difference,

for example by counting up

from 27 to 74 in steps totalling

47 (shopkeepers’ method).

With practise, children will

need to record less

information and decide

whether to count back or

forward. It is useful to ask

children whether counting up

or back is the more efficient for

calculations such as 57 – 12,

86 – 77 or 43 – 28.

74 – 27 =

or:

The method can successfully

be used with decimal

numbers.

This method can be a useful

alternative for children whose

progress is slow, whose

mental and written calculation

skills are weak and whose

attainment is below their

current programme of study.

22.4 – 17.8 = or:

4 + 0.6 = 4.6

4.4 + 0.2 = 4.6

Partitioning

Subtraction can be recorded

using partitioning to write

equivalent calculations that

can be carried out mentally.

For74 – 27 this involves

partitioning the 27 into 20 and

7, and then subtracting from

74 the 20 and the 7 in turn.

This use of partitioning is a

useful step towards the

most commonly used

column method,

decomposition

Subtraction can be recorded using partitioning:

74 – 27

74 – 20 = 54

54 – 7 = 47

Expanded layout, leading

to column method

(Decomposition)

Partitioning the numbers into

tens and ones and writing one

under the other mirrors the

column method, where ones

are placed under ones and

tens under tens.

This does not link directly to

mental methods of counting

back or up but parallels the

partitioning method for

addition. It also relies on

secure mental skills.

The expanded method leads

children to the more

compact method so that

they understand its

structure and efficiency. The

amount of time that should

be spent teaching and

practising the expanded

method will depend on how

secure the children are in

their recall of number facts

and with partitioning.

Example: 563 - 241, no adjustment or decomposition

needed

Expanded method

500 60 3

− 200 40 1

300 20 2

Start by subtracting the ones, then the tens, then the

hundreds. Refer to subtracting the tens, for example, by

saying ‘sixty take away forty’, not ‘six take away four’.

Example: 72 - 47, adjustment from the tens to the units so that units can be taken away

using Multibase and place value

Example: 563 - 317, adjustment from the tens to the units so that units can be taken

away

50 13

500 + 60 + 3

- 200 + 40 + 6

300 + 10 + 7 = 317

Begin by reading aloud the number from which we are subtracting: ‘five hundred and sixty-

three’. Then discuss the hundreds, tens and ones components of the number, how there is

a ‘snag’ with the ones and the need to exchange a ten. To release ones 60 + 3 can be

partitioned into 50 + 13. The subtraction of the tens becomes 13 minus 6,

This method can be quite labour intensive which is why manipulative strategies are

preferable to demonstrate this process which can then lead straight to the method.

Compact Method

5 1

5 6 3

2 4 6

3 1 7

Ensure that children can explain the compact method, referring to the real value of the

digits. They need to understand that they are repartitioning the 60 + 3 as 50 + 13.

Example: 563 - 271, Compact Method

4 1

5 6 3

2 7 1

2 9 2

Begin by reading aloud the number from which we are subtracting: ‘five hundred and

sixty-three’. Then discuss the hundreds, tens and ones components of the number, and

how 500 + 60 can be partitioned into 400 + 160. The subtraction of the tens becomes ‘160

minus 70’, an application of subtraction of multiples of ten. Ensure that children are

confident to explain how the numbers are repartitioned and why.

The Bar is used at all levels to illustrate the thinking behind problem

solving

Multiplication

It is important that children’s mental methods of calculation are practised and

secured alongside their learning and use of an efficient written method for

multiplication.

Developing the mental image of multiplication

Develop the mental image of multiplication

Putting objects into equal

groups

Putting objects into equal

groups and then checking

there are for example, 2 in

each group. Begin counting in

equal steps by counting the

number in 2 groups and then 3

and then 4 etc…

2 4 6 8

Counting in equal steps,

starting with 2s, 10s and 5s,

then progressing to 3s, 4s

and then 6s, 7s, 8s and 9s

Using practical apparatus such

as Numicon.

3 6 9 12

Counting in equal steps,

starting with 2s, 10s and 5s,

then progressing to 3s, 4s

and then 6s, 7s, 8s and 9s

Understanding how to count in

these steps is an important

foundation to learning

multiplication facts (tables).

100

90

80

70

60

50

40

30

20

10

0

Multiplication as repeated

addition

5 x 3 =

There are 5 cakes in a pack.

How many cakes in 3 packs?

Dots or tally marks are often

drawn in groups. This shows 3

groups of 5.

Sets the foundations for bar

model.

5 + 5 + 5

Number lines

This model illustrates how

multiplication relates to

repeated addition.

Pattern work on a 100 square

helps children begin to

recognise multiples and rules

of divisibility.

Using Numicon number line to

solve repeated addition

problems by laying pieces

upon track.

6 x 5 = 30

or

5 + 5 + 5 + 5 + 5 + 5 = 30

Arrays

Successful written methods

depend on visualising

multiplication as a rectangular

array. It also helps children to

understand why

3 X 4 = 4 X 3

Rectangular Arrays

The rectangular array gives a

good visual model for

multiplication. The area can be

found by repeated addition (in

this case 7+7+7+7+7).

Children should then commit

7 X 5 to memory and know

that it is the same as 5 X 7.

Area models like this

discourage the use of

repeated addition. The focus is

on the multiplication facts.

Mental multiplication using

arrays and partitioning to

multiply a two- digit number

by a one-digit number

An array illustrates the

distributive law of

multiplication i.e.

13 X 7 is the same as (10 X 7)

+ (3 X 7)

Please note that the squares

are used to ensure that

children have a secure mental

image of why the distributive

law works.

+ 70 + 21

10 x 7 3 x 7

0 70 91

Grid Method using place

value counters.

13 x 7 = 91

This can lead to the use of a

“blank rectangle/open arrays”

to illustrate

13 X 7 = (10 X 7) + (3 X 7)

Note the rectangle is drawn

to emphasise the

comparative size of the

numbers

Alternatively a number line

can be used

Bar Method for

multiplicative reasoning

Link to fractions

A computer game is £24 in

the sale. This is one quarter of

its original price. How much

did it cost before the sale?

Scaling:

How many jugs can you fill

with 10 litres?

Using the grid method to

multiply two- digit by one-

digit numbers

At first children will probably

need to partition into 10s

(example A).

It is important, if they are to

use a more compact method,

that they can multiply multiples

of 10 (example B).

i.e. 38 X 7 they must be able

to calculate 30 X 7 as well as

8 X 7.

Note the grid is drawn to

emphasise the comparative

size of the number.

38 X 7 is approximately 40 X 7 = 280

This will lead to a more formalised layout

Two-digit by two-digit

products using the grid

method

Extend to TO × TO, asking

children to estimate first.

Start by completing the grid.

The partial products in each

row are added, and then the

two sums at the end of each

row are added to find the total

product

Please note that at this

stage the grid is no longer

drawn to reflect the

respective size of the digits.

If a child shows signs of

insecurity return to

rectangular arrays to ensure

understanding

38 x 14

Three-digit by two-digit

products using the grid

method

Extend to HTO × TO asking

children to estimate first.

Ensure that children can

explain why this method

works and where the

numbers and the grid come

from

Place Value counters can

help children who are less

secure in their number facts.

138 x 24 =

The grid method works just as

satisfactorily with decimal

numbers as long as the

children can apply their

knowledge of multiplication

facts to decimal numbers.

38.5 x 24 =

It will be down to the class teacher as to whether they move onto the next stage with

their pupils. Children need to be confident with the grid method before this can be

considered.

Short multiplication

The recording is reduced

further, with carry digits

recorded below the line.

If, after practice, children

cannot use the compact

method without making

errors, they should return to

the expanded format of the

grid method

38 X 7 is approximately 40 X 7 = 280

3 8

X 7

2 6 6

5

The step here involves adding 210 and 50 mentally with only

the 5 in the 50 recorded. This highlights the need for children

to be able to add a multiple of 10 to a two- digit or three-digit

number mentally before they reach this stage.

Multiplying two-digit by two-

digit numbers includes the

working to emphasise the

link to the grid method

56 × 27 is approximately 60 × 30 = 1800.

5 6

X 2 7

4 2 (6 X 7)

3 5 0 (50 X 7)

1 2 0 (6 X 20)

1 0 0 0 (50 X 20)

1 5 1 2

1

Three-digit by two-digit

numbers

Continue to show working to

link to the grid method.

This expanded method is

cumbersome, with six

multiplications and a lengthy

addition of numbers with

different numbers of digits to

be carried out. There is plenty

of incentive for more confident

children to move on to a more

compact method.

286

x29

54 (6 X 9)

720 (80 X 9)

1800 (200 X 9)

120 (6 X 20)

1600 (80 X 20)

4000 (200 X 20)

8294

2

If secure with the expanded method, and children are making very few errors, then they

can move on to the compact method. This is at the discretion of the class teacher.

Compact method for TO x

TO and HTO x TO

2 3 1 2 3

x 1 2 x 1 2

4 6 ( 2 x 23) 2 4 6 (2 x 123)

2 3 0 (10 x 23) 1 2 3 0 (10 x 123)

2 7 6 1 4 7 6

Division

(Incorporate bar model to pictorial representations)

Division by sharing

Practical sharing along with

more pictures and jottings.

6 strawberries shared between

2 children. How many eggs do

they get each? 62 =

Sharing should only be used briefly as a precursor to grouping, which is a more

preferable method and should be moved onto as soon as possible. Solving division by

grouping strengthens mental calculation strategies.

Division by grouping

4 apples are packed in a

basket. How many baskets

can you fill with 12 apples?

124 =

Practical grouping with 12 objects, grouped into 4s. Dots or

tally marks can be split up into groups.

E.g. draw 12 dots representing apples and grouping into 4s to

find how many groups. 124 =3

I had 10 fish treats shared

between 5 fish.

10 5 = 2

Two boys shared

20 bananas.

How many did

they get each?

20 2 = 10

Numicon number line

How many 5s are in 20?

Number lines (Repeated +)

Counting on in equal steps

based on adding multiples up

to the number to be

divided.Counting back in

equal steps based on

subtracting multiples from the

number to be divided

Note: Counting on is a

powerful tool for mental

calculation but does not

lead onto written calculation

for division

A chocolate bar costs 3p. How many can I purchase for 15p?

Using an array to divide

Children can build upon what

they have learnt about arrays

in multiplication, it is vital that

links between multiplication

and division are made in a

visual way.

Bar model linked to fractions

and division

12 dots arranged into rows of 3

123=

There are 4 rows/groups so the

answer is 4

Ben has 32 sweets. He gives away 3/4 of them to his brother.

How many sweets does his brother get?

Miss Pearce took 2/5 of her wages out of the bank. She then spent 1/4 of the money she had taken out

on a jumper . Her wages were £140.

How much was the jumper and how much money does she still have in the bank?

Finding remainders using

Numicon.

37 ÷ 5 = 7 r2

Counting on by chunking

This method is based on

adding multiples of the divisor,

or ‘chunks’. Initially children

add several chunks, but with

practice they should look for

the biggest multiples of the

divisor that they can find to

add.

Chunking is useful for

reminding children of the link

between division and repeated

addition.

100 7 =

10 x 7 = 70 4 x7 = 28

0 70 98

Answer 14 remainder 2

As you record the division, ask: ‘How

many sixes in 100?’ as well as ‘What

is 100 divided by 6?’

10 4

Initially children add several

chunks, but with practice they

should look for the biggest

multiples of the divisor that

they can find to add.

Children need to recognise

that chunking is inefficient if

too many additions have to

be carried out. Encourage

them to reduce the number

of steps and move them on

quickly to finding the largest

possible multiples.

Answer 33 remainder 2

As you record the division, ask ‘How many sixes in 200?’ as

well as ‘What is 200 divided by 6?’ Leading to - 200 6

10x6=60 10x6 = 60 10x6=60 1x6 1 x6 1x6

0 60

120 180 186 192 198

30 x 6 = 180 3 x 6 = 18

0 180 198

How many 6’s in 200?

200 divided by 6

33 with a remainder of 2

10 10 10 1 1 1

30 3

Bus shelter method using

place value counters.

Bus shelter method for

when dividing by a 1-

digit number

Children should first be

introduced to this method by

working through calculations

where there are no

remainders.

Children should then solve

calculations with remainders.

Children can look at putting

remainders into decimals

using this method.

For example: 693 ÷ 3 =

For example: 937÷ 3 =

312 r 1

3 937

For example: 937÷ 3 =

312 .33 (2d.p)

3 937 .1 0 1 0

Use of bar model for ratio, proportion and percentage calculations

Long division

The next step is to tackle HTO

÷ TO, which for most children

will be in Year 6, where

appropriate.

How many packs of 24 can we make from 560 biscuits?

Start by multiplying 24 by multiples of 10 to get an

estimate. As 24 × 20 = 480 and 24 × 30 = 720, we

know the answer lies between 20 and 30 packs. We start

by subtracting 480 from 560.

23 r 8

5 6 0

4 8 0 (20 packs taken)

8 0

7 2 (3 packs taken)

8 (8 remainder)

2 4