Mathematics Curriculum Intent

Mathematics Curriculum

Intent

The 2014 National Curriculum for Maths aims to ensure that all children:

• Become fluent in the fundamentals of Mathematics

• Are able to reason mathematically

• Can solve problems by applying their Mathematics

At Slaithwaite C. E. J. & I. School, these skills are embedded within Maths

lessons and developed consistently through progression over time. The

teaching and learning in each year group will work towards mastery of NC

skills and knowledge. Provision will be in place for children who require

additional support and also in lessons to deepen understanding for our greater

depth learners. We are committed to ensuring that all children are able to

recognise the importance of Maths in the wider world and that they are also

able to use their mathematical skills and knowledge confidently in their lives

in a range of different contexts. We want all our children to enjoy

Mathematics and to experience success in the subject, with the ability and

confidence to reason mathematically.

Implementation

Teachers create a positive attitude to mathematics learning within their

classrooms and reinforce an expectation that all children are capable of

achieving high standards in maths. Our whole school approach to the teaching

and learning of mathematics involves the following;

• Maths will be taught in planned and arranged blocks using the

NC framework. This is a strategy which enables progression

and full coverage of skills and knowledge.

• Each year group will focus on number and calculation topics

first so these skills are developed before being applied in

measurement or shape topics later in the year.

• Each year group will develop fluency in instant facts recall

through regularly planned activities. Key facts for each year

group (see programme key facts) will be taught, practised and

assessed. Throughout the year, these key facts will be

revisited to encourage a deeper recall. Provision will be in

place for children who require more support to learn key

facts.

• Each year group will develop standard calculation methods.

(see calculation policy for programme)These will be taught,

practised and assessed. As children become fluent and

accurate in these methods, timed assessments will be built in.

• Teaching and learning will use appropriate concrete

manipulatives and pictorial representations to support

conceptual understanding throughout school.

• Thorough planning of skills and knowledge to be taught will

lead to high quality modelling.

• Children will be supported through well planned activities to

allow them to practice skills and consolidate understanding.

• Activities will be differentiated to ensure appropriate

challenge for all learners.

• Fluency, reasoning and problem solving will be embedded into

all lessons and for all learners at the appropriate level.

• Good use of questioning in lessons will lead to the appropriate

support required and ongoing assessment of understanding.

• Children will be assessed regularly at the end of each unit.

This information will be used for further planning.

• Opportunities for age appropriate maths skills to be used in

cross curricular work will be embedded throughout the

curriculum.

Differentiation

We recognise that in all classes there are children of widely different

abilities in mathematics and we seek to provide suitable learning

opportunities for all children by matching the challenge of the task to the

ability of the child. Resources and support for individuals or groups can

allow all children to access the curriculum. Allowing the tasks to be of

different difficulties, differentiated questioning, scaffolding in problem

solving and open ended tasks, means we can allow all children to meet their

potential.

SEND

By maintaining an inclusive learning environment, we ensure that lessons

are tailored to suit the needs of the individuals in the class. Multi-sensory

approaches, including the use of computing, allow all children to access the

learning objectives. We aid children with both peer and adult support to

assist their learning.

Mastery and Greater Depth

Children can gain a greater level of understanding in mathematics due to

the open-ended nature of problem solving and the opportunities for

reasoning and discussion. Children who display mastery in mathematics and

work at greater depth can transfer and apply their mathematics knowledge

in different contexts, showing they make connections with other areas of

learning and retain the knowledge without difficulty. Children who are

greater depth in mathematics are encouraged to support their peers in

their learning by explaining their understanding, modelling their workings

and engaging in problem solving discussions.

Explicit curriculum links

Through this, where possible, we can make links to other areas of the

curriculum as well as teaching mathematics as a discrete subject.

• English – Children will develop understanding of mathematical vocabulary

and topic- specific language. Fluency in reading and the language of maths

will also be developed with age appropriate word problems. Speaking and

listening skills will also be important when discussing problems and

explaining thinking. This will be especially important in reasoning, as

children need to have a thorough understanding of mathematical language

to be able to explain their reasoning.

• Science – In science work, comprehensive maths skills are important.

When conducting experiments, scales need to be read accurately, data

needs to be collected precisely and results need to be presented in

various forms in tables, graphs and charts. Finally, results need to be

compared and analysed, leading to reasoned conclusions. Age appropriate

maths skills included in scientific work will develop opportunities for

maths to be used in real life experiences.

• Computing – children will develop their mathematical understanding

through computing topics such as programming, data collection formulas in

spreadsheets and shape work in graphics.

• Geography – children will develop shape and space skills in mapping work.

• Finance – (Y6) – calculation skills and real life problem solving will be

developed through this monetary work.

Impact

Our whole school approach to the teaching and learning of mathematics

successfully results in;

• Most children reaching end of year expectations. Progress is tracked

termly.

• Regular assessments lead to children being identified who need extra

support.

• Support group teaching and learning is matched to individual needs and

is flexible as to when and where support is needed.

• A well planned sequence of learning throughout the school allows

children to develop and refine their maths skills.

• Children independently their apply knowledge to a range of increasingly

complex problems.

• Children use reasoning skills with increasing confidence and accuracy.

Year 1 – Maths

Number – Number and Place Value

Pupils should be taught to:

• count to and across 100, forwards and backwards, beginning

with 0 or 1, or from any given number

• count, read and write numbers to 100 in numerals; count in

multiples of twos, fives and tens

• given a number, identify one more and one less

• identify and represent numbers using objects and pictorial

representations including the number line, and use the language

of: equal to, more than, less than (fewer), most, least

• read and write numbers from 1 to 20 in numerals and words.

Number – Addition and Subtraction


• read, write and interpret mathematical statements involving

addition (+), subtraction (–) and equals (=) signs

• represent and use number bonds and related subtraction facts

within 20

• add and subtract one-digit and two-digit numbers to 20,

including zero

• solve one-step problems that involve addition and subtraction,

using concrete objects and pictorial representations, and

missing number problems such as 7 = – 9.

Number – Multiplication and Division


• solve one-step problems involving multiplication and division, by

calculating the answer using concrete objects, pictorial

representations and arrays with the support of the teacher.

Number – Fractions


• recognise, find and name a half as one of two equal parts of an

object, shape or quantity

• recognise, find and name a quarter as one of four equal parts

of an object, shape or quantity.

Measurement


• compare, describe and solve practical problems for:

- lengths and heights [for example, long/short, longer/shorter,

tall/short, double/half]

- mass/weight [for example, heavy/light, heavier than, lighter

than]

- capacity and volume [for example, full/empty, more than, less

than, half, half full, quarter]

- time [for example, quicker, slower, earlier, later]

• measure and begin to record the following:

- lengths and heights

- mass/weight

- capacity and volume

- time (hours, minutes, seconds)

• recognise and know the value of different denominations of

coins and notes

• sequence events in chronological order using language [for

example, before and after, next, first, today, yesterday,

tomorrow, morning, afternoon and evening]

• recognise and use language relating to dates, including days of

the week, weeks, months and years

• tell the time to the hour and half past the hour and draw the

hands on a clock face to show these times.

Geometry – Properties of shapes


• recognise and name common 2-D and 3-D shapes, including:

- 2-D shapes [for example, rectangles (including squares),

circles and triangles]

- 3-D shapes [for example, cuboids (including cubes), pyramids

and spheres].

Geometry – Position and Direction


• describe position, direction and movement, including whole,

half, quarter and three-quarter turns.

Note: Please see appendices for Year 1 Termly Instant Recall Facts

Year 1 Calculations

Addition

In preparation for secure methods of calculation, children will develop instant recall of

the following facts during Year 1:

Children need to understand the concept of equality before using the ‘=’ sign.

Calculations should be written either side of the equality sign so that the sign is not

just interpreted as ‘the answer’.

2=1+1

2+3=4+1

Missing numbers need to be placed in all possible places.

3 + 4= =3 + 4

3 + = 7 7 == + 4

Number track / Number line ~ jumps of 1

(supported by models and images e.g. modelled using bead strings)

+1 +1 +1 +1 +1

18 19 20 21 22

18 + 5 = 23

Children will be introduced to the + and = signs where appropriate

Children should be encouraged to begin with the bigger number, this links to putting the

largest number in your head and counting on from there.

Remind the children that addition can be calculated with the numbers in any order. Give

examples where first number is smaller and encourage children to rewrite it.

5 + 18 = 23

18 + 5 = 23

Year 1 Calculations

Subtraction

In preparation for secure methods of calculation, children will develop instant

recall of the following facts during Year 1:

Missing number problems e.g.

7 = - 9 20 - = 9 - = 11 16 – 0 =

Use concrete objects and pictorial representations. If appropriate, progress

from using number lines with every number shown to number lines with

significant numbers shown.

Understand subtraction as take-away or counting back. Also understand

subtraction as counting on or finding the difference.

• Children can use counting back to subtract a 1-digit number from a 2-

digit number.

e.g. 13 – 5 = 8 can be modelled using bead strings as:

and using a number line as:

-1 -1 -1 -1 -1

8 9 10 11 12 13

• Subtract a multiple of 10 from a 2-digit number

(Use knowledge of counting back in 10s- 53,43,33,23… )

11 – 5

What is the difference between 11 and 5?

How many more is 11 than 5?

+6

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

The use of concrete apparatus and images is vital for modelling subtraction e.g.

bundles of straws, diennes apparatus, multi link cubes, bead strings.

Year 1 Calculations

Multiplication



Developing an understanding of multiplication is related to doubling and

combining groups of the same size (repeated addition). They use this

understanding to help them work out multiplication facts they cannot recall

quickly.

The use of models and images and practical resources is vital in developing this

understanding in young children: washing line; number line; bundles of straws;

bead strings; counters/cubes.

2+2+2+2+2= 10

2x5=10

2 multiplied by 5

5 pairs

5 hops of 2

• Problem solving with concrete apparatus (including money and measures).

• Use the vocabulary relating to multiplication: “pick up five, 4 times.”

• Use arrays to understand multiplication can be done in any order

(commutative law).

repeated addition +3 +3 +3 +3 +3 +3

+6 +6 +6

The top line shows 6 jumps of 3.

The bottom line shows 3 jumps of 6.

array 3 x 5 = 15 or 5 x 3 = 15

0 1 2 3 4 5

6 7 8 9 10 11

12 13 14 15 16 17

18

Year 1 Calculations

Division



Children must have secure counting skills ~ being able to confidently count in 2s,

5s and 10s.

Children should be given opportunities to reason about what they notice in

number patterns.

Children should be introduced to the division sign and that it can mean sharing

or grouping. Children should be given opportunities to group and share small

quantities ~ understanding the difference between the two concepts. Early

division begins with sharing in practical activities.

Sharing

The tray had 9 cakes in and they were shared out between Jamie, Kelly and

Tony. Each child had the same number of cakes. How many did they have each?

Jamie Kelly Tony

1 for Jamie, 1 for Kelly, 1 for Tony




So, 12 3 = 4

(12 buns shared between 3 children gives each child 4

buns)

The sharing concept of division readily leads into finding fractions of amounts

on a practical basis.

½ of 12 = 12 ÷ 2 = 6 (i.e. share 12 into 2 groups)

¼ of 12 = 12 ÷ 4 =3 (i.e. share 12 into 4 groups)

Grouping

Children should apply their counting skills to develop some understanding of

grouping.

The apples need putting into bags with 5 apples in each bag. Julie has 15 apples.

How many bags will she need?

So, 15 apples divided into groups of 5 = 3 bags 15 5 =3

In the early stages of division there should be a greater focus on the grouping

concept as this shows how division is the inverse of multiplication.

e.g. I know that 3 x 5 = 15 (3 groups of 5 equals 15)

so 15 5 = 3 (15 divided into groups of 5

equals 3)

Division can also be shown with an array (pictorial representation for division),

15 ÷ 3 = 5 There are 5 groups of 3

15 ÷5 = 3 There are 3 groups of 5

Year 2 – Maths



• count in steps of 2, 3, and 5 from 0, and in tens from any

number, forward and backward

• recognise the place value of each digit in a two-digit number

(tens, ones)

• identify, represent and estimate numbers using different

representations, including the number line

• compare and order numbers from 0 up to 100; use <, > and =

signs

• read and write numbers to at least 100 in numerals and in

words

• use place value and number facts to solve problems.



• solve problems with addition and subtraction:

- using concrete objects and pictorial representations,

including those involving numbers, quantities and measures

- applying their increasing knowledge of mental and written

methods

• recall and use addition and subtraction facts to 20 fluently,

and derive and use related facts up to 100

• add and subtract numbers using concrete objects, pictorial

representations, and mentally, including:

- a two-digit number and ones

- a two-digit number and tens

- two two-digit numbers

- adding three one-digit numbers

• show that addition of two numbers can be done in any order

(commutative) and subtraction of one number from another

cannot

• recognise and use the inverse relationship between addition

and subtraction and use this to check calculations and solve

missing number problems.



• recall and use multiplication and division facts for the 2, 5 and

10 multiplication tables, including recognising odd and even

numbers

• calculate mathematical statements for multiplication and

division within the multiplication tables and write them using

the multiplication (×), division (÷) and equals (=) signs

• show that multiplication of two numbers can be done in any

order (commutative) and division of one number by another

cannot

• solve problems involving multiplication and division, using

materials, arrays, repeated addition, mental methods, and

multiplication and division facts, including problems in contexts.



• recognise, find, name and write fractions 1

3 ,

1

4 ,

2

4 and

3

4 of a

length, shape, set of objects or quantity

• write simple fractions for example, 1

2 of 6 = 3 and recognise the

equivalence of 2

4 and

1

2.

Measurement


• choose and use appropriate standard units to estimate and

measure length/height in any direction (m/cm); mass (kg/g);

temperature (°C); capacity (litres/ml) to the nearest

appropriate unit, using rulers, scales, thermometers and

measuring vessels

• compare and order lengths, mass, volume/capacity and record

the results using >, < and =

• recognise and use symbols for pounds (£) and pence (p);

combine amounts to make a particular value

• find different combinations of coins that equal the same

amounts of money

• solve simple problems in a practical context involving addition

and subtraction of money of the same unit, including giving

change

• compare and sequence intervals of time

• tell and write the time to five minutes, including quarter

past/to the hour and draw the hands on a clock face to show

these times

• know the number of minutes in an hour and the number of

hours in a day.



• identify and describe the properties of 2-D shapes, including

the number of sides and line symmetry in a vertical line

• identify and describe the properties of 3-D shapes, including

the number of edges, vertices and faces

• identify 2-D shapes on the surface of 3-D shapes, [for

example, a circle on a cylinder and a triangle on a pyramid]

• compare and sort common 2-D and 3-D shapes and everyday

objects.



• order and arrange combinations of mathematical objects in

patterns and sequences

• use mathematical vocabulary to describe position, direction and

movement, including movement in a straight line and

distinguishing between rotation as a turn and in terms of right

angles for quarter, half and three-quarter turns (clockwise and

anticlockwise).

Statistics


• interpret and construct simple pictograms, tally charts, block

diagrams and simple tables

• ask and answer simple questions by counting the number of

objects in each category and sorting the categories by quantity

• ask and answer questions about totalling and comparing

categorical data.


Year 2 Calculations

Addition

In preparation for secure methods of calculation, children will develop instant recall of

the following facts during Year 2:

14 + 5 = 10 + 32 + + = 100 35 = 1 + + 5

It is valuable to use a range of representations (also see Y1). Continue to use number

lines to develop understanding of following concepts.

The first written method for adding is to count on using a number line (see

Year1).

Children should be encouraged to begin with the bigger number, this links to putting the

largest number in your head and counting on from there.

Remind the children that addition can be calculated with the numbers in any order.

24 + 35 =

Turn the calculation round so that the bigger number is first (35 + 24 = )

Draw a blank number line with 35 at the beginning.

35 45 55 59

+10 +10 +4

Say: add the 2 tens, 35 + 10 = 45

45 + 10 = 55

add on the 4 units 55 + 4 = 59

Remind the children that the answer is at the bottom of the line and needs to be

written after the equals sign in the written calculation.

The steps in addition often bridge through a multiple of 10 e.g. children should be able

to partition the 7 to relate adding the 2 and then the 5.

8 + 7 = 15

8 10 15

+2 +5

e.g add 9 by adding 10 and adjusting by 1

35 +9 =44

35 44 -1 45

+10

From counting on using a number line, this then leads on to the method of partitioning

the numbers into parts (tens and units), adding the parts, and then recombining to find

the total.

e.g. 45 + 13 Partition the numbers into tens and units:

40 + 5

+ 10 + 3

50 + 8 = 58

We say: Add the units together: 5 + 3 = 8

Add the tens together: 40 + 10 = 50

Recombine the numbers to give the total:

50 + 8 = 58

Use diennes apparatus to provide a model and image to support in the explanation of

this written method.

Year 2 Calculations

Subtraction




52 – 8 = - 20 = 25 22 = - 21 6 + + 3 = 11

It is valuable to use a range of representations (also see Y1). Continue to use

number lines to model take-away and difference. e.g.

39 40 42

+1 +2

42- 39

Difference between 42 and 39.

How many more to go from 39 to 42?

Bridging 10- using number bonds of 10 knowledge.

-2

-10

25 27 37

Using counting back in multiples of 10 knowledge.

The link between the two may be supported with an example such as the one

below, subtracting a 2-digit number from a 2-digit number using the more

refined method of counting on.

e.g. There are 74 sweets in a jar, 56 are eaten by the children. How many

sweets are left in the jar?

56 60 70 74

+4 +10 +4

74 – 56 = 18

We say: Draw a number line with the smaller number at the

beginning and the larger number at the end.

Count on to the next multiple of 10 after 56 (60).

Draw the jump on the number line and write +4

above the jump.

Count on to the multiple of 10 below 74 (70).

Draw the jump on the number line and write +10

above the jump.

Count on to 74 (+4)

Total the numbers at the top of the jumps (4+10+4=18)

Recording subtraction and subtraction in expanded columns can support

understanding of the quantity aspect for place value and prepare for efficient

written methods with larger numbers. In order to gain secure mathematical

understanding, the children need to work with practical apparatus before they

move on to more traditional methods of subtraction. e.g.

45 – 20 =

45 – 24 =

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Year 2 Calculations

Multiplication



Learning and recalling multiplication tables begins in KS1.

It is essential that all children know their multiplication tables and associated

facts thoroughly.

e.g. I know that 6 x 5 = 30 so I know that 5 x 6 = 30

60 x 5 = 300 50 x 6 = 300

30 5 = 6 30 6 = 5 etc

Tables are learned first by rote and then randomly.

Children also learn the corresponding division facts for multiplication tables.

Children learn up to the twelfth multiple of each multiplication table, up to and

including the twelve times table.

Y1 Count on & back in 2s, 5s & 10s

Know by heart & know corresponding division facts

2x 3x 4x 5x 6x 7x 8x 9x 10x 11x 12x

Y2

Y3

Y4 Y5 Y6 Consolidate all multiplication tables and associated facts

Activities in the classroom will build time tables practice. Also extra practice

for homework and weekly testing will consolidate instant recall.

Missing number problems

• Expressing multiplication as a number sentence using x

• Using their understanding of inverse and practical resources to solve

missing number problems:

7 x 2 = = 2 x 7

7 x = 14 = x 7

X 2 = 14 14 = 2 x

X = 14 14 = x

Mental methods

• Develop understanding of multiplication using array and number lines (see

Year 1). Include multiplications not in the 2,5, or 10 times tables.

• Begin to develop understanding of multiplication as scaling (3 times

bigger/taller)

• Doubling numbers up to 10+10

• Using known doubles to work out double 2 digit numbers ( double 15 =

double 10 + double 5)

• A strategy to help children learn multiplication tables facts from counting

is to say or show the child a multiplication fact such as: 6 x 2 =

Ask the child to put up six fingers and count each of the six fingers in twos.

Six lots of 2 is 12.

Also with 7 x 10 =

Ask the child to put up seven fingers and count each of the fingers in tens.

Seven lots of 10 is 70.

It is important for children to know that 10 x 7 will give the same answer

as 7 x 10, let them show this with their fingers.

repeated addition +3 +3 +3 +3 +3 +3

+6 +6 +6

The top line shows 6 jumps of 3.

The bottom line shows 3 jumps of 6.

array 3 x 5 = 15 or 5 x 3 = 15

0 1 2 3 4 5

6 7 8 9 10 11

12 13 14 15 16 17

18

Use jottings to develop an understanding of doubling 2 digit numbers.

16

10 6

x2 x2

20 12

32

Year 2 Calculations

Division



÷ 2, ÷ 5, ÷10

÷ = signs and missing numbers

6 ÷ 2 = = 6 ÷ 2

6 ÷ = 3 3 = 6 ÷

÷ 2 = 3 3 = ÷ 2

÷ = 3 3 = ÷

Know and understand sharing and grouping ~ introducing the children to the ÷

sign.

Children should continue to use grouping and sharing for division using practical

apparatus, arrays and pictorial representations.

Support children to understand how multiplication and division are inverse. Look

at an array ~ what do you see?

Year 3 – Maths



• count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100

more or less than a given number

• recognise the place value of each digit in a three-digit number

(hundreds, tens, ones)

• compare and order numbers up to 1000


representations

• read and write numbers up to 1000 in numerals and in words

• solve number problems and practical problems involving these

ideas.



• add and subtract numbers mentally, including:

- a three-digit number and ones

- a three-digit number and tens

- a three-digit number and hundreds

• add and subtract numbers with up to three digits, using formal

written methods of columnar addition and subtraction

• estimate the answer to a calculation and use inverse operations

to check answers

• solve problems, including missing number problems, using

number facts, place value, and more complex addition and

subtraction



• recall and use multiplication and division facts for the 3, 4 and

8 multiplication tables

• write and calculate mathematical statements for multiplication

and division using the multiplication tables that they know,

including for two-digit numbers times one-digit numbers, using

mental and progressing to formal written methods

• solve problems, including missing number problems, involving

multiplication and division, including positive integer scaling

problems and correspondence problems in which n objects are

connected to m objects.



• count up and down in tenths; recognise that tenths arise from

dividing an object into 10 equal parts and in dividing one-digit

numbers or quantities by 10

• recognise, find and write fractions of a discrete set of

objects: unit fractions and non-unit fractions with small

denominators

• recognise and use fractions as numbers: unit fractions and non-

unit fractions with small denominators

• recognise and show, using diagrams, equivalent fractions with

small denominators

• add and subtract fractions with the same denominator within

one whole [for example, 5

7 +

1

7 =

6

7 ]

• compare and order unit fractions, and fractions with the same

denominators

• solve problems that involve all of the above.

Measurement


• measure, compare, add and subtract: lengths (m/cm/mm); mass

(kg/g); volume/capacity (l/ml)

• measure the perimeter of simple 2-D shapes

• add and subtract amounts of money to give change, using both

£ and p in practical contexts

• tell and write the time from an analogue clock, including using

Roman numerals from I to XII, and 12-hour and 24-hour clocks

• estimate and read time with increasing accuracy to the nearest

minute; record and compare time in terms of seconds, minutes

and hours; use vocabulary such as o’clock, a.m./p.m., morning,

afternoon, noon and midnight

• know the number of seconds in a minute and the number of

days in each month, year and leap year

• compare durations of events [for example to calculate the time

taken by particular events or tasks].



• draw 2-D shapes and make 3-D shapes using modelling

materials; recognise 3-D shapes in different orientations and

describe them

• recognise angles as a property of shape or a description of a

turn

• identify right angles, recognise that two right angles make a

half-turn, three make three quarters of a turn and four a

complete turn; identify whether angles are greater than or less

than a right angle

• identify horizontal and vertical lines and pairs of perpendicular

and parallel lines.

Statistics


• interpret and present data using bar charts, pictograms and

tables

• solve one-step and two-step questions [for example, ‘How many

more?’ and ‘How many fewer?’] using information presented in

scaled bar charts and pictograms and tables


Year 3 Calculations

Addition



Missing number problems using a range of equations as in Year 1 and 2 but with

appropriate, larger numbers.

Partition both numbers and recombine.

Count on by partitioning the second number only e.g.

247 + 125 = 247 + 100 + 20 + 5

= 347 + 20 + 5

= 367 + 5

= 372

Children need to be secure adding multiples of 100 and 10 to any three digit

number including those that are not multiples of 10.

(These notes are to aid explaining this method-children should not necessarily

be expected to record this method- could use informal jottings to support

mental calculations.)

See Year 2 ~ children need to be secure with partitioning and recombining to

find a total. This method can then lead to a more compact method. Continue

to work on this expanded method of column addition modelled with place value

counters (diennes could be used for those who need a more concrete

representation).

e.g. 436 + 252 Partition the numbers: H T U

400 + 30 + 6

+ 200 + 50 + 2

600 + 80 + 8= 688

Where the numbers to be totalled are too difficult to add mentally, an

additional calculation can be made:

e.g. 458 + 387 Partition the numbers: H T U

400 + 50 + 8

+ 300 + 80 + 7

700 + 130 + 15

To find the total, partition the numbers:

H T U

700 + 0 + 0

100 + 30 + 0

+ 10 + 5

800 + 40 + 5 = 845

Set out all column addition on squared paper, to support understanding of place

value.

Vertical addition (carrying) is only used when a child has a very sound

understanding of the mathematics involved in the previous methods.

a) 625 add the units,

+ 48 five add eight is thirteen

3 one ten under the tens column and 1 3 in the units column.

b) 625 add the tens, twenty add forty is

+ 48 sixty, plus ten underneath, seventy.

7 3 put the seventy in the tens column. 1

c) 625 add the hundreds, six hundreds.

+ 48 put the six hundreds in the hundreds

673 column. 1

This is how the calculation would look in a child’s book:

625

+ 48

673 1

This carrying method can also be used with larger numbers:

587

+ 475

1062 1 1

This formal written method of addition, including carrying should be used by children

when they are secure in steps towards written method.

Year 3 Calculations

Subtraction




= 43 – 27 145 - = 138 274 – 30 = 245 - = 195

532 – 200 = 364 – 153 =

Mental methods should continue to develop, supported by a range of models and

images, including the number line. Children should make choices about whether

to use complementary subtraction or counting back, depending on the numbers

involved.

Introduce expanded column subtraction with no decomposition, modelled with

place value counters (dienes could be used for those who need more concrete

representation).

98-35= 63 9 0 8

- 3 0 5

6 0 3

For some children this will lead to exchanging, modelled using place value

counters (or dienes).

Beginning to introduce decomposition.

Set this method out on squared paper.

Subtracting a number where the units digit to be subtracted, is bigger than the

other units digit so 1 ten has to be exchanged for 10 units. At this stage the

calculation needs to be written in vertically. Some children may begin to use a

formal columnar algorithm, initially introduced alongside the expanded method.

The formal method should be seen as a more streamlined version of the

expanded method, not a new method.

T U 3 1

4 5

-2 9

1 6

Initially use examples where units number is too big, therefore decomposition is

from 10s column.

We say: 5 take away 9 we can’t do

change 1 ten into units

add to the units column which now equals 15

the tens column is now 30

15 take away 9 equals 6

3 tens take away 2 tens equals 10

1 ten add 6 equals 16

H T U 2 1 1 3 2

- - 2 7

1 0 5

Move onto 3 digit numbers (decomposition still in 10s column).

Both of these methods need to be supported practically to introduce

exchanging tens into units, using base ten apparatus such as Dienes rods and

cubes or 10p and 1p coins.

Year 3 Calculations

Multiplication




Continue with a range of equations as in Year 2 but with appropriate numbers.

Mental methods

• Doubling 2 digit numbers using partitioning.

• Demonstrating multiplication on a number line – jumping in larger groups.

• 13 x 4 = 10 groups of 4 + 3 groups of 4

• Develop written methods using understanding of visual images.

10 8

3 30 24

18 x 3

Use knowledge of place value to explain that 18 x 3

is the same as 10 x 3 and 8 x 3.

Begin to use written method to multiply two digit by one digit number. At first

use expanded brackets method. When secure move to short method.

2 7

x 7

4 9 (7x7)

+ 1 4 0 (7x20)

1 8 9

Year 3 Calculations

Division



÷ 3, ÷ 4, ÷18


Continue using a range of equations as in Year 2 but with appropriate numbers.

Grouping

How many 6’s are in 30?

30 ÷ 6 can be modelled as:

+6 +6 +6 +6 +6

0 6 12 18 24 30

Becoming more efficient using a numberline

Children need to be able to partition the dividend in different ways.

48 ÷ 4 =

+40 +8

10 groups 2 groups

Remainders

49 ÷ 4 = 12 r1

+40 +8 +1

10 groups 2 groups

Sharing ~ 49 shared between 4. How many left over?

Grouping ~ How many 4s make 49? How many are left over?

Place value counters can be used to support children apply their knowledge of

grouping.

For example: 60 ÷ 10 = How many groups of 10 in 60?

600 ÷ 100 = How many groups of 100 in 600

Year 4 – Maths



• count in multiples of 6, 7, 9, 25 and 1000

• find 1000 more or less than a given number

• count backwards through zero to include negative numbers

• recognise the place value of each digit in a four-digit number

(thousands, hundreds, tens, and ones)

• order and compare numbers beyond 1000


representations

• round any number to the nearest 10, 100 or 1000

• solve number and practical problems that involve all of the

above and with increasingly large positive numbers

• read Roman numerals to 100 (I to C) and know that over time,

the numeral system changed to include the concept of zero and

place value.



• add and subtract numbers with up to 4 digits using the formal

written methods of columnar addition and subtraction where

appropriate

• estimate and use inverse operations to check answers to a

calculation

• solve addition and subtraction two-step problems in contexts,

deciding which operations and methods to use and why.



• recall multiplication and division facts for multiplication

tables up to 12 × 12

• use place value, known and derived facts to multiply and

divide mentally, including: multiplying by 0 and 1; dividing by

1; multiplying together three numbers

• recognise and use factor pairs and commutativity in mental

calculations

• multiply two-digit and three-digit numbers by a one-digit

number using formal written layout

• solve problems involving multiplying and adding, including

using the distributive law to multiply two-digit numbers by

one digit, integer scaling problems and harder

correspondence problems such as n objects are connected

to m objects.

Number – Fractions (including decimals)


• recognise and show, using diagrams, families of common

equivalent fractions

• count up and down in hundredths; recognise that hundredths

arise when dividing an object by one hundred and dividing

tenths by ten.

• solve problems involving increasingly harder fractions to

calculate quantities, and fractions to divide quantities,

including non-unit fractions where the answer is a whole

number

• add and subtract fractions with the same denominator

• recognise and write decimal equivalents of any number of

tenths or hundredths

• recognise and write decimal equivalents to 1

4 ,

1

2 ,

3

4

• find the effect of dividing a one- or two-digit number by 10

and 100, identifying the value of the digits in the answer as

ones, tenths and hundredths

• round decimals with one decimal place to the nearest whole

number

• compare numbers with the same number of decimal places up to

two decimal places

• solve simple measure and money problems involving fractions

and decimals to two decimal places

Measurement


• Convert between different units of measure [for example,

kilometre to metre; hour to minute]

• measure and calculate the perimeter of a rectilinear figure

(including squares) in centimetres and metres

• find the area of rectilinear shapes by counting squares

• estimate, compare and calculate different measures, including

money in pounds and pence

• read, write and convert time between analogue and digital 12-

and 24-hour clocks

• solve problems involving converting from hours to minutes;

minutes to seconds; years to months; weeks to days.



• compare and classify geometric shapes, including quadrilaterals

and triangles, based on their properties and sizes

• identify acute and obtuse angles and compare and order angles

up to two right angles by size

• identify lines of symmetry in 2-D shapes presented in

different orientations

• complete a simple symmetric figure with respect to a specific

line of symmetry.



• describe positions on a 2-D grid as coordinates in the first

quadrant

• describe movements between positions as translations of a

given unit to the left/right and up/down

• plot specified points and draw sides to complete a given

polygon.

Statistics


• interpret and present discrete and continuous data using

appropriate graphical methods, including bar charts and time

graphs

• solve comparison, sum and difference problems using

information presented in bar charts, pictograms, tables and

other graphs


Year 4 Calculations

Addition



Missing number / digit problems- continue to develop using larger numbers.


images, including the number line.

As Year 3, use expanded column addition modelled with place value counters,

progressing to calculations with 4 digit numbers.

Extend to numbers with at least 4 digits.

2634

+ 4517

7151 1 1

Children should be able to make the choice of reverting to expanded methods if

experiencing any difficulty.

Extend to up to two places of decimals (same number of decimal places) and

adding several numbers (with different numbers of digits).

1 6 2

7 2 . 8 7 3

+ 5 4 . 6 + 8

1 2 7 . 4 2 4 3 1 1 1 1

Year 4 Calculations

Subtraction




456 + = 710 1 7 + 6 m=200 60 + 99 + = 340 200- 90 -80 =

225 - = 150 - - 25 = 67 3450 – 1000= - 2000 = 900



Once the children have a secure understanding that the remaining tens are

changed to units then the decomposition method can be developed for larger

numbers and numbers where decomposition is required in the hundreds,

thousands etc. 4 1 5 3 2

- 2 9 1

2 4 1

Also where more than one decomposition is required.

7 13 1

8 4 3 9

- 5 6 4 8

2 7 9 1

We say: 5 take away 9 we can’t do

change 1 ten into units and add to the units column

the tens column is now 70

15 take away 9 equals 6

7 tens take away 4 tens equals 3 tens

30 add 6 equals 36

This method can then be used to:

• Subtract two 2-digit numbers

• Subtract two 3-digit numbers

• Subtract numbers with decimals in context

(e.g. money)

• Subtract 4/5-digit numbers

• Subtract 4/5-digit numbers with decimals

Year 4 Calculations

Multiplication





Also include equations with missing digits.

2 x 5 = 160

Mental methods

• Counting in multiples of 6,7,9,25 and 1000, and steps of 1/100.

• Solving practical problems where children need to scale up.

• Relate to known number facts e.g. how tall would a 25cm sunflower be if

it grew 6 times taller?

• Multiplying by 10 and 100:

Multiplying by 10

To ensure that the children have a secure understanding of what they are doing

when they multiply by 10, we: explain that we are using place value.

We say:

▪ move each digit one place to the left

65 x 10=

H T U

6 5

6 5 0

We say:

▪ the six tens become six hundreds.

▪ five units become five tens.

▪ put a zero in the units column to hold the place value.

Multiplying by 100

To ensure that the children have a secure understanding of what they are doing

when they multiply by 100, we say:

▪ move each digit two places to the left.

65 x 100=

Th H T U

6 5

6 5 0 0

We say:

▪ the six tens become six thousands.

▪ five units become five hundreds.

▪ put a zero in the tens column and the units column

to hold the place value.

Continue with method from Year 3 but now developing with • three digits by one digit

Use expanded bracket method at first, then move to short method when secure.

3 2 8

x 6

1 2 (6x2)

+ 4 8 0 (6x80)

1 8 0 0 (6x300)

2 2 9 2

• four digits by one digit

Some children may be ready for long multiplication of two digit by two digit.

Use brackets to support this method.

3 8 2

x 6

2 2 9 2

4 1

Year 4 Calculations

Division


recall of the following facts during Year 4/5:

÷ 6, ÷ 9, ÷11, ÷ 7, ÷12


Continue using a range of equations as in Year 2/3 but with appropriate

numbers.

Sharing, grouping and using a number line

Children will continue to explore division as sharing and grouping, and to

represent calculations on a number line until they have a secure understanding.

By Year 5, the children should be encouraged to stop using the number line.

Children should progress in their use of written division calculations:

Towards a written method

We can use multiplication facts that we already know to work out bigger

division calculations using short division of a 2-digit number divided by a

1-digit number with whole numbers.

e.g.

2 3

3 6 9

We say: How many 3s go into 6?

How many 3s go into 9?

so 69 ÷ 3 = 23

Leading to:

2 6 1 3 7 8

We say: How many 3s in 7? 2 remainder 1. Add the 1 in front of the next

number. So 8 becomes 18.

How many 3s in 18?

so 78 ÷ 3 = 26

Leading to short division of a 2-digit number divided by a 1-digit number where

there is a remainder.

2 6 r1 1 3 7 9

Leading to:

• Using the short division method to divide a 4/5 digit number by a 1 digit

number with no remainder

• Using the short division to divide a 4/5 digit number by a 1 digit number

where there is a remainder

Year 5 – Maths



• read, write, order and compare numbers to at least 1 000 000

and determine the value of each digit

• count forwards or backwards in steps of powers of 10 for any

given number up to 1 000 000

• interpret negative numbers in context, count forwards and

backwards with positive and negative whole numbers, including

through zero

• round any number up to 1 000 000 to the nearest 10, 100,

1000, 10 000 and 100 000

• solve number problems and practical problems that involve all

of the above

• read Roman numerals to 1000 (M) and recognise years written

in Roman numerals.



• add and subtract whole numbers with more than 4 digits,

including using formal written methods (columnar addition and

subtraction)

• add and subtract numbers mentally with increasingly large

numbers

• use rounding to check answers to calculations and determine, in

the context of a problem, levels of accuracy

• solve addition and subtraction multi-step problems in contexts,

deciding which operations and methods to use and why.



• identify multiples and factors, including finding all factor pairs

of a number, and common factors of two numbers

• know and use the vocabulary of prime numbers, prime factors

and composite (nonprime) numbers

• establish whether a number up to 100 is prime and recall prime

numbers up to 19

• multiply numbers up to 4 digits by a one- or two-digit number

using a formal written method, including long multiplication for

two-digit numbers

• multiply and divide numbers mentally drawing upon known facts

• divide numbers up to 4 digits by a one-digit number using the

formal written method of short division and interpret

remainders appropriately for the context

• multiply and divide whole numbers and those involving decimals

by 10, 100 and 1000

• recognise and use square numbers and cube numbers, and the

notation for squared (²) and cubed (³)

• solve problems involving multiplication and division including

using their knowledge of factors and multiples, squares and

cubes

• solve problems involving addition, subtraction, multiplication

and division and a combination of these, including

understanding the meaning of the equals sign

• solve problems involving multiplication and division, including

scaling by simple fractions and problems involving simple rates

Number – Fractions (including decimals and percentages)


• compare and order fractions whose denominators are all

multiples of the same number

• identify, name and write equivalent fractions of a given

fraction, represented visually, including tenths and hundredths

• recognise mixed numbers and improper fractions and convert

from one form to the other and write mathematical

statements > 1 as a mixed number [for example, 2

5 +

4

5 =

6

5 = 1

1

5 ]

• add and subtract fractions with the same denominator and

denominators that are multiples of the same number

• multiply proper fractions and mixed numbers by whole

numbers, supported by materials and diagrams

• read and write decimal numbers as fractions [for example, 0.71

= 71

100 ]

• recognise and use thousandths and relate them to tenths,

hundredths and decimal equivalents

• round decimals with two decimal places to the nearest whole

number and to one decimal place

• read, write, order and compare numbers with up to three

decimal places

• solve problems involving number up to three decimal places

• recognise the per cent symbol (%) and understand that per

cent relates to ‘number of parts per hundred’, and write

percentages as a fraction with denominator 100, and as a

decimal

• solve problems which require knowing percentage and decimal

equivalents of 1

2 ,

1

4 ,

1

5 ,

2

5 ,

4

5 and those fractions with a

denominator of a multiple of 10 or 25.

Measurement


• convert between different units of metric measure (for

example, kilometre and metre; centimetre and metre;

centimetre and millimetre; gram and kilogram; litre and

millilitre)

• understand and use approximate equivalences between metric

units and common imperial units such as inches, pounds and

pints measure and calculate the perimeter of composite

rectilinear shapes in centimetres and metres

• calculate and compare the area of rectangles (including

squares), and including using standard units, square

centimetres (cm² ) and square metres (m² ) and estimate the

area of irregular shapes

• estimate volume [for example, using 1 cm³ blocks to build

cuboids (including cubes)] and capacity [for example, using

water]

• solve problems involving converting between units of time

• use all four operations to solve problems involving measure [for

example, length, mass, volume, money] using decimal notation,

including scaling.



• identify 3-D shapes, including cubes and other cuboids, from 2-

D representations

• know angles are measured in degrees: estimate and compare

acute, obtuse and reflex angles

• draw given angles, and measure them in degrees (°)

• identify:

- angles at a point and one whole turn (total 360° )

- angles at a point on a straight line and 1

2 a turn (total 180°)

• other multiples of 90° use the properties of rectangles to

deduce related facts and find missing lengths and angles

• distinguish between regular and irregular polygons based on

reasoning about equal sides and angles.



• identify, describe and represent the position of a shape

following a reflection or translation, using the appropriate

language, and know that the shape has not changed.

Statistics


• solve comparison, sum and difference problems using

information presented in a line graph

• complete, read and interpret information in tables, including

timetables.


Year 5 Calculations

Addition



Missing number / digit problems- including decimals


images, including the number line. Children should practise with increasingly

large numbers to aid fluency.

e.g. 12462 + 2300 = 14762

Children need to be secure in rounding and encouraged to use this method to

check for accuracy when solving problems.

Continue to develop this formal written method using larger than 4 digit

numbers and decimals. Begin with numbers of same decimal places.

As Year 4, progressing when understanding of the expanded method is secure,

children will move on to the formal columnar method for whole numbers and

decimal numbers as an efficient written algorithm.

1 7 2 . 8 3

+ 5 4 . 6 8

2 2 7 . 5 1 1 1 1

Then move onto numbers with different number of decimal places. Teach

children to fill in gaps with 0s.

1 5 9 . 5 1 5 9 . 5 0

+ 2 3 . 2 7 + 2 3 . 2 7

Year 5 Calculations

Subtraction



Missing number / digit problems- including decimals.

6.45 = 6 + 0.4 + 119 - = 86 1 000 000 - = 999 000

600 000 + + 1000 = 671 000 12 462 – 2 300 =



5 1 2 1

6 2 3 2

- 4 8 1 4

1 4 1 8

Use examples of numbers where exchange has to move across more than one

column. 3 9 9 1 4 0 0 2

- 2 9 8 6

1 0 1 6

Progress to calculating with decimals, including those with different numbers of

decimal places. 6 1 7 1 1 7 2 . 8 3

- 5 4 . 6 8

1 1 8 . 1 5

4 1

1 5 9 . 5 0

- 2 3 . 2 7

1 3 6 . 2 3

Year 5 Calculations

Multiplication





Also include equations with missing digits.

2 x 5 = 60 28 x = 280

2 x 3 = 72 1 x 5 = 75

Mental methods

• x by 10, 100,100 using the moving digits

• Use practical resources and jottings to explore equivalent statements e.g.

4 x 35 = 2 x 2 x 35

• Recall prime numbers up to 19 and identify prime numbers up to 100 (with

reasoning)

• Solve practical problems where children need to scale up

• Relate to known number facts

• Identify factor pairs for numbers

Continue to develop short multiplication (use expanded version for any children

who need support).

3 7

X 2 3

2 1 (3x7)

9 0 (3x30)

1 4 0 (20x7)

6 0 0 (20x30)

8 5 1

In short method teach children to place 0 in units column when multiplying by

power of 10.

3 7

x 2 3

1 1 1

2

7 4 0

11

8 5 1

Year 5 Calculations

Division


recall of the following facts during Year 4/5:

÷ 6, ÷ 9, ÷11, ÷ 7, ÷12


Continue using a range of equations as in Year 2/3 but with appropriate

numbers.

Sharing, grouping and using a number line

Children will continue to explore division as sharing and grouping, and to

represent calculations on a number line until they have a secure understanding.

By Year 5, the children should be encouraged to stop using the number line.

Children should progress in their use of written division calculations:

Towards a written method

We can use multiplication facts that we already know to work out bigger

division calculations using short division of a 2-digit number divided by a

1-digit number with whole numbers.

e.g.

2 3

3 6 9

We say: How many 3s go into 6?

How many 3s go into 9?

so 69 ÷ 3 = 23

Leading to:

2 6 1 3 7 8

We say: How many 3s in 7? 2 remainder 1. Add the 1 in front of the next

number. So 8 becomes 18.

How many 3s in 18?

so 78 ÷ 3 = 26

Leading to short division of a 2-digit number divided by a 1-digit number where

there is a remainder.

2 6 r1 1 3 7 9

Leading to:

• Using the short division method to divide a 4/5 digit number by a 1 digit

number with no remainder

• Using the short division to divide a 4/5 digit number by a 1 digit number

where there is a remainder

Year 6 – Maths



• read, write, order and compare numbers up to 10,000,000 and

determine the value of each digit

• round any whole number to a required degree of accuracy

• use negative numbers in context, and calculate intervals across

zero

Number – Addition, Subtraction, Multiplication and Division


• multiply multi-digit numbers up to 4 digits by a two-digit whole

number using the formal written method of long multiplication

• divide numbers up to 4 digits by a two-digit whole number using

the formal written method of long division, and interpret

remainders as whole number remainders, fractions, or by

rounding, as appropriate for the context

• divide numbers up to 4 digits by a two-digit number using the

formal written method of short division where appropriate,

interpreting remainders according to the context

• perform mental calculations, including with mixed operations

and large numbers

• identify common factors, common multiples and prime numbers

• use their knowledge of the order of operations to carry out

calculations involving the four operations

• solve addition and subtraction multi-step problems in contexts,

deciding which operations and methods to use and why

Number – Fractions (including decimals and percentages)


• use common factors to simplify fractions; use common

multiples to express fractions in the same denomination

• compare and order fractions, including fractions >1

• add and subtract fractions with different denominators and

mixed numbers, using the concept of equivalent fractions

• multiply simple pairs of proper fractions, writing the answer in

its simplest form [for example, ¼ x ½ = 1

8]

• divide proper fractions by whole numbers [for example, 1

3 ÷ 2 =

1

6]

• associate a fraction with division and calculate decimal

fractions equivalents [for example, 0.375] for a simple fraction

[for example, 3

8 ]

• identify the value of each digit in numbers given to three

decimal places and multiply and divide numbers by 10, 100 and

1000 giving answers up to three decimal places

• multiply one-digit numbers with up to two decimal places by

whole numbers

• use written division methods in cases where the answer has up

to two decimal places

• solve problems which require answers to be rounded to

specified degrees of accuracy

• recall and use equivalences between simple fractions, decimals

and percentages, including in different contexts

Ratio and Proportion

• solve problems involving the relative sizes of two quantities

where missing values can be found by using integer

multiplication and division facts

• solve problems involving the calculation of percentages [for

example, of measures, and such as 15% of 360] and the use of

percentages for comparison

• solve problems involving similar shapes where the scale factor

is known or can be found

• solve problems involving unequal sharing and grouping using

knowledge of fractions and multiples

Algebra


• use simple formulae

• generate and describe linear number sequences

• express missing number problems algebraically

• find pairs of numbers that satisfy an equation with two

unknowns

• enumerate possibilities of combinations of two variables

Measurement


• solve problems involving the calculation and conversion of units

of measure, using decimal notation up to three decimal places

where appropriate

• use, read, write and convert between standard units,

converting measurements of length, mass, volume and time

from a smaller unit of measure to a larger unit, and vice versa,

using decimal notation to up to three decimal places

• convert between miles and kilometres

• recognise that shapes with the same areas can have different

perimeters and vice versa

• recognise when it is possible to use formulae for area and

volume of shapes

• calculate the area of parallelograms and triangles

• calculate, estimate and compare volume of cubes and cuboids

using standard units, including cubic centimetres (cm³) and

cubic metres (m³), and extending to other units [for example,

mm³ and km³]



• draw 2-D shapes using given dimensions and angles

• recognise, describe and build simple 3-D shapes, including

making nets

• compare and classify geometric shapes based on their

properties and sizes and find unknown angles in any triangles,

quadrilaterals, and regular polygons

• illustrate and name parts of circle, including radius, diameter

and circumference and know that the diameter is twice the

radius

• recognise angles where they meet at a point, are on a straight

line, or are vertically opposite, and find missing angles



• describe positions on the full coordinate grid (all four

quadrants)

• draw and translate simple shapes on the coordinate plane, and

reflect them in the axes

Statistics


• interpret and construct pie charts and line graphs and use

these to solve problems

• calculate and interpret the mean as an average


Year 6 Calculations

Addition

Missing number / digit problems- including decimals and negative numbers.

- 15 = 6

21 - = -5

Mental methods should be confident when working mentally.

As Year 5, progressing to larger numbers, including multi-step problems, aiming

for both conceptual understanding and procedural fluency with columnar method

to be secured.

Continue calculating with decimals, including those with different numbers of

decimal places.

Children need to be able to perform written addition accurately and efficiently

in preparation for Year 6 calculation SATs paper.

Teachers should ensure that pupils have the opportunity to apply their

knowledge in a variety of contexts and problems (exploring cross curricular

links) to deepen their understanding and develop mastery.

Year 6 Calculations

Subtraction

Missing number / digit problems including algebra – including decimals and

negative numbers.

10 + = 26 -

10 000 000 = 9 000 100 +

7 – 2 x 3 = ; (7-2) x 3 = ; ( - 2 ) x 3 = 15

If a = 34 what is the value of a+a

If b = 64 what could c =

2b = 2c + b

Mental methods should be confident to use mental methods where appropriate.

As Year 5, progressing to larger numbers, aiming for both conceptual

understanding and procedural fluency with decomposition to be secured.

Continue calculating with decimals, including those with different numbers of

decimal places.

Children need to be able to perform written subtraction accurately and

efficiently in preparation for Year 6 calculation paper.

Year 6 Calculations

Multiplication




4 x 7 = 301 3 x 6 = 138

2 x 5 = 60 2 x 3 = 72

6 x 5 x 4 = 284 x 47 =

20.61 x 10 = 34.9 x 6 =

319 x 6 =


Also include equations with missing digits and encourage children to explain

their thinking behind the calculation.

Mental methods

• Identifying common factors and multiples of given numbers

• Solving practical problems where children need to scale up

• Relate to known number facts

Continue to refine and deepen understanding of written methods including

fluency for using long multiplication. Children need to be efficient with this

method for up to four digits by two digits, including decimals.

3 . 5 1 x 4 . 9 = 1 7 . 1 9 9

3 5 1

x 4 9

3 1 5 9

1 4 0 4 0

1 7 1 9 9

Replace decimal point in answer. Estimate first so avoid error when placing it.

ie. 4 x 5 = 20, so answer must be 17

Year 6 Calculations

Division


56 ÷ 8 = 248 ÷ 5 = 98.4 ÷ 100 = 2751 ÷ 21 =

Continue using a range of equations but with appropriate numbers and be able to

explain the thinking behind their calculation.

Quotients should be expressed as decimals and fractions.

Formal written method ~ short division

We continue by dividing a 4 digit number by a 1 digit number using the short

division method.

1504 ÷ 8 = 0 1 8 8

8 1 7 6

1 5 0 4

1994 ÷ 8 = 0 2 4 9 .2 5

8 1 3 7 2 4

1 9 9 4 . 0 0

In calculations with a remainder show how to give the answer as a fraction and a

decimal.

249 R 2 = 249 2/8 = 249 1/4 = 249.25

We then move onto dividing up to 4 digit numbers by 2 digit numbers using the

short division method supported by jottings, such as the first few numbers in

the multiplication table of the divisor.

0 2 4 6 5 7

12 2 9 5 2

0 1 5 7 . 6 8 11 9

15 2 3 6 4 . 0

Write down multiples in a list to help you mentally work out divisions and

remainders.

12

24

36

48

60

72 15

30

45

60

75

90

105

120

Documents

Mathematics Curriculum Intent