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Rothwell St. Mary’s Catholic Primary School Calculation Policy Supporting a Mastery Curriculum Mission Statement At St Mary’s Catholic Primary School, we ‘Grow together in Christ’ ‘Live and learn in God’s love’ by Developing the potential of every individual by providing the best education through experience of our Catholic, Christian Community within which all members can grow in faith. Policy Reviewed:

Rothwell St. Mary’s Catholic Primary School

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Page 1: Rothwell St. Mary’s Catholic Primary School

Rothwell St. Mary’s Catholic Primary School

Calculation Policy

Supporting a Mastery Curriculum

Mission Statement

At St Mary’s Catholic Primary School, we ‘Grow together in Christ’

‘Live and learn in God’s love’

by

Developing the potential of every individual by providing the best education through experience of our Catholic, Christian Community within

which all members can grow in faith.

Policy Reviewed:

Page 2: Rothwell St. Mary’s Catholic Primary School

Adding One More Than a Number:

Use of everyday objects, cubes

and counters to find one more than

any given number to 20

Build a numicon number track and

do a walk of one more

Use of pictorial representations to

count one more than a number

Use of a number track and a

counter or whiteboard pen to count

on a jump of one more than

Use of mental maths to count on from the biggest number one more

Adding Two Single Digit Numbers:

Early Years Addition

Pupils should be able to:

• Know one more than a number

• Using quantities and objects, they add two single-digit numbers and

count onto find the answer.

Page 3: Rothwell St. Mary’s Catholic Primary School

Number Bonds:

Year One Addition

Pupils should be able to:

• Read, write and interpret mathematical statements involving

addition

• Represent and use all number bonds within 20

• Add one-digit and two-digit numbers to 20, including 0

• Solve one-step problems that involve addition using concrete

objects and

• pictorial representations, and missing number problems

Page 4: Rothwell St. Mary’s Catholic Primary School

Adding One-Digit and Two-Digit:

Regrouping to Make Ten:

Page 5: Rothwell St. Mary’s Catholic Primary School

Missing Number Problems:

Year Two Addition

Pupils should be able to:

• 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 1s

• a two-digit number and 10s

• 2 two-digit numbers

• adding 3 one-digit numbers

• show that addition of 2 numbers can be done in any order

(commutative) and subtraction of 1 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

Page 6: Rothwell St. Mary’s Catholic Primary School

Adding a Two-Digit and One-Digit Number:

Adding Tens to a Number:

Base Ten

Page 7: Rothwell St. Mary’s Catholic Primary School

Adding Two Two-Digit Numbers:

No Exchanges:

With an Exchange:

Use of Base Ten to add.

Add together the ones first then

the tens.

Use of children’s drawings

of Base Ten/images of Base

Ten to support

understanding

Use of the partitioning

method to add

• Partition the 2-

digit numbers

• Arrange in a

column

• Add the ones

• Add the tens

• Recombine

Use of Base Ten to add.

Add together the ones

first then the tens.

32 + 25 = 57

Use of children’s drawings

of Base Ten /images of

Base Ten to support

understanding

Page 8: Rothwell St. Mary’s Catholic Primary School

Adding Three Single-Digit Numbers:

Year Three Addition

Pupils should be taught to:

Add numbers mentally, including:

• a three-digit number and 1s

• a three-digit number and 10s

• a three-digit number and 100s

• add numbers with up to 3 digits, using formal written methods of

columnar addition

Page 9: Rothwell St. Mary’s Catholic Primary School

Adding Mentally

Use of place value counters and base ten to support adding mentally

Adding Three-Digit Number

Use of concrete place

value counters and base

ten to support adding

Support pictorially through

drawings and pictures in books

Using the partitioning

method to add at first

before moving on to

columnar

Compact Columnar Addition – No exchange

Column method with base ten or place value counters 334 + 153 = 487

Children drawing pictures of base ten in the column method 334 + 153 = 487

Formal column method involving no exchange 334 + 153 = 487

✓ Line left after

calculation in case

of an exchange.

Page 10: Rothwell St. Mary’s Catholic Primary School

Compact Columnar Addition – With Exchange

Column method with

base ten or place value

counters

227 + 156 = 383

Children drawing pictures or

using support of pictures of

concrete objects in the

column method

Formal column method

involving exchanges

✓ Line left after

calculation in case of

an exchange.

✓ Exchange shown above

the line

Compact Columnar Addition – No Exchange

Children can draw a pictorial

representation of the columns and

place value counters 1222+2443 =3665

Formal column method involving no

exchanges

3512 + 232 = 3744 6321 + 2576 =8897

Year Four Addition

Pupils should be taught to:

• add numbers with up to 4 digits using the formal written methods

of columnar addition

Page 11: Rothwell St. Mary’s Catholic Primary School

Children can use or draw a pictorial

representation of the columns and

place value counters 2634 + 4517 = 7151

Compact Columnar Addition – With Exchange

Formal column method involving an exchange

3517 + 396 = 3913

Addition with Decimals

Children use coins to add

two decimal amounts

together

Example exemplifies regrouping £1. 46 + £2.45 = £3.91

Page 12: Rothwell St. Mary’s Catholic Primary School

Formal column method with

decimals in different contexts

including money

£ 7.36 + £ 2.41 = £9.77

The decimal point needs to be lined up like all the other place value columns It is important that children recognise that they are adding tenths and hundredths and that they understand they are adding part of a number not a whole number

Formal column method with

decimals in different contexts

including money £8.79 + £ 6.72 = £15.51

Children should use the column

method when adding tens of

thousands and hundreds of

thousands. As with previous years,

children begin by adding the ones,

then the tens etc

142365 + 39243= 181608

Children need to start using the

column method to add more than

two values

48216 + 37452 + 11367= 97035

Year Five Addition

Pupils should be taught to:

• Add whole numbers with more than 4 digits, including using formal

written methods (columnar addition)

Page 13: Rothwell St. Mary’s Catholic Primary School

Columnar Addition with Decimals

Zero (0) should be used as a place

holder to ensure that the numbers are

to the same decimal place

Zero is added to show there is no

value to add 23.3 + 16.48 = 39.78

It is important that children recognise

that they are adding tenths and

hundredths and that they understand

they are adding part of a number not

a whole number 19.01 + 3.65 + 0.7= 23.36

Columnar Addition with Decimals

Formal column method is used to

solve problems in the context of

measure, for examples, weight and

money

The decimal point needs to be lined

up like all of the other place value

columns

26.6 kg + 14.8 kg= 41.4 kg

Children use the column method to

add more than two values in the

context of measures

£19.01+ £3.65 + £ 0.70= £23.36

Year Six Addition

In year six children continue to practise column method for addition

for bigger numbers and decimal numbers up to three decimal

places

Page 14: Rothwell St. Mary’s Catholic Primary School

15.092 + 24.564= 39.656

Zero (0) should be used as a place

holder to ensure that the numbers

are to the same decimal place

Zero is added to show there is no

value to add

41.472 + 32. 8= 74.272

3.06 + 12.421+9.9= 25.381

Children use the column

method to add several

numbers with different numbers

of decimal places

Tenths, hundredths and

thousandths should be

correctly aligned including the

decimal point

23.361 + 9.08 + 59.77 + 1.3= 93.511

Children use the column

method to add several

numbers with different numbers

of decimal places

Tenths, hundredths and

thousandths should be

correctly aligned including the

decimal point

Page 15: Rothwell St. Mary’s Catholic Primary School

Finding One Less Than a Number

Children can use pegs to physically

remove to find one less than a

number

Subtracting Two Single-Digit

Early Years Subtraction

Pupils should be able to:

• Know one less than a number

• Using quantities and objects, they subtract two single-digit numbers

and count back to find the answer.

Page 16: Rothwell St. Mary’s Catholic Primary School

Subtract One and Two Digits.

Year One Subtraction

Pupils should be able to:

• Read, write and interpret mathematical statements involving

subtraction

• Represent and use all number bonds within 20

• Subtract one-digit and two-digit within 20, including 0

• Solve one-step problems that involve subtraction using concrete

objects and

• Use pictorial representations to solve missing number problems

Page 17: Rothwell St. Mary’s Catholic Primary School

Making 10

Page 18: Rothwell St. Mary’s Catholic Primary School

Missing Number Problems

Year Two Subtraction

Pupils should be able to:

• solve problems with 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

• subtract numbers using concrete objects, pictorial representations,

and mentally, including:

• a two-digit number and 1s

• a two-digit number and 10s

• 2 two-digit numbers

• show that subtraction is not commutative as addition is

• recognise and use the inverse relationship between addition and

subtraction and use this to check calculations and solve missing

number problems

Page 19: Rothwell St. Mary’s Catholic Primary School

Subtraction Two Digits and Ones.

Subtracting Tens from a Number

Subtracting Two Two Digit Numbers

Use of Base Ten to

subtract Subtract the ones first then the tens

Use of children’s

drawings of base ten to

support understanding –

Children will physically

cross out.

Use of the partitioning

method to subtract

57 – 32 = 25 • Partition the 2-

digit numbers

Page 20: Rothwell St. Mary’s Catholic Primary School

• Arrange in a

column

• Subtract the ones

• Subtract the tens

combine

Use of base ten to

subtract

Subtract the ones first.

Must exchange in order

to subtract the ones.

Take a ten and add it to

the ones column.

Now subtract the ones,

then subtract the tens

Recombine

34 - 17=

Use of children’s

drawings of base ten to

support understanding

34 – 17 =

Children can draw or use

base ten to physically

cross out/draw when

subtracting.

Use of the partitioning

method to subtract

• Partition the 2-

digit numbers

• Arrange in a

column

• Regroup the tens

if cannot subtract

the ones

• Subtract the ones

• Subtract the tens

• Recombine

34 - 17 =

Page 21: Rothwell St. Mary’s Catholic Primary School

Using the Inverse

Children move away from counting

on/back to find the missing number to

rearranging the number sentence and

using the inverse

55 + ____ = 75

75 – 55 =

Then use known methods to solve

Children should understand

commutativity of addition when

using the inverse

_______ - 25 = 42

42 + 25 =

25 + 42 =

Page 22: Rothwell St. Mary’s Catholic Primary School

Adding Mentally

Use of place value counters and base ten to

support subtracting mentally –exchanging when

necessary

Year Three Subtraction

Pupils should be taught to:

• Subtract numbers mentally, including:

• a three-digit number and 1s

• a three-digit number and 10s

• a three-digit number and 100s

• Subtract numbers with up to 3 digits, using formal written methods of

columnar addition

• 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

Page 23: Rothwell St. Mary’s Catholic Primary School

Subtracting Three Digit Numbers

Use of concrete place

value counters and

base ten to support

subtraction

Partitioning base ten or

place value counters

Partitioning method 452- 237 =

Year Four Subtraction

Pupils should be taught to:

• Subtract numbers with up to 4 digits using the formal written

methods of columnar subtraction.

Page 24: Rothwell St. Mary’s Catholic Primary School

Compact Columnar Subtraction

Children can use concrete or draw a

pictorial representation of the

columns and place value counters.

Can physically cross out in books to

solve.

3667 – 2341 = 1326

Formal column method involving no

exchanges

3667 – 2341 =

5978 – 4523 =

Children should be able to represent

their understanding of addition and

subtraction within a bar model and a

part-part whole model.

Children should be able to explain

that they are finding a part when they

subtract, and they are finding a whole

or a total when adding.

Children can use or draw a pictorial representation of the columns and place

value counters

6421 – 3278 = 3143

Formal column method involving exchanges above

6421 – 3278 =

8442 – 2255 =

Page 25: Rothwell St. Mary’s Catholic Primary School

Reminding children of place value when exchanging –is this a ten or a one I’m

exchanging?

Subtraction with Decimals

Formal column method with decimals in different contexts including money

£ 3.56 - £ 2.45 = £1.11

The decimal point needs to be lined up like all the other place value columns

It is important that children recognise that they are subtracting tenths and

hundredths and that they understand they are subtracting part of a number

not a whole number

£2.51 - £ 1.45 = 1.06

Page 26: Rothwell St. Mary’s Catholic Primary School

Columnar Subtraction

Using previous imagery with place value

counters to support exchanging.

Columnar Subtraction with Decimals

Year Five Subtraction

Pupils should be taught to:

• Subtract whole numbers with more than 4 digits, including using

formal written methods (columnar subtractions)

Page 27: Rothwell St. Mary’s Catholic Primary School

Columnar Subtraction with Decimals in a Range of Contexts

Formal column method is used to solve problems in the context of measure, for

examples, weight and money. The decimal point needs to be lined up like all

of the other place value columns

Columnar Subtraction with Decimals

Year Six Subtraction

In year six children continue to practise column method for

subtraction for bigger numbers and decimal numbers up to three

decimal places

Page 28: Rothwell St. Mary’s Catholic Primary School

Columnar Subtraction to One Million

No exchanges

With exchanges

Page 29: Rothwell St. Mary’s Catholic Primary School

Making Equal Groups

Use of everyday objects, cubes and counters to put them into equal groups

and then counting on in ones. If children are secure could write as 2 + 2 + 2

Doubling

Early Years Multiplication

Pupils should be able to:

• Can solve problems involving doubling

There should be an emphasis on number exploration within EYFS.

Page 30: Rothwell St. Mary’s Catholic Primary School

Counting in Multiples

Repeated Addition

Year 1 Multiplication

Pupils should be able to:

• solve one-step problems involving multiplication by calculating

the answer using concrete objects, pictorial representations

and arrays with the support of the teacher.

Page 31: Rothwell St. Mary’s Catholic Primary School

Arrays

Commutative Relationship

Numbered Number Line

Mental Maths

To count on in back in multiples of 2s, 10s and 5s to solve multiplication

problems as well as being able to recognise the multiplication symbol.

To make connections between arrays, number patterns and counting in 2s 5s,

and 10s. Ex Multiples of 5 end in 5 and 0

Page 32: Rothwell St. Mary’s Catholic Primary School

Count in Multiples

Mentally counting on in multiples. Children should use pattern spotting to

support their understanding of multiples.

‘Multiples of 5 end in 0 and 5 only. They are even and odd numbers.’

‘48 cannot be a multiple of 5 because it doesn’t end in a 0 or 5’

Year 2 Multiplication

Pupils should be able to:

• recall and use multiplication facts for the 2, 5 and 10

multiplication tables, including recognising odd and even

numbers

• calculate mathematical statements for multiplication within the

multiplication tables and write them using the multiplication

(×) and equals (=) signs

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

order (commutative)

• solve problems involving multiplication, using materials, arrays,

repeated addition, mental methods, and multiplication facts,

including problems in contexts

Page 33: Rothwell St. Mary’s Catholic Primary School

Repeated Addition

Arrays

Commutative Relationship

Page 34: Rothwell St. Mary’s Catholic Primary School

Number Line

Bar Model

Mental Maths

Solving Problems in Context

Page 35: Rothwell St. Mary’s Catholic Primary School

Count in Multiples

Use of pictorials to support counting

on in multiples

24

8 groups of 3 is 24

Mentally counting on in multiples. Children should use pattern spotting to

support their understanding of multiples.

0, 5, 10, 15, …

‘Multiples of 4 end in 0,2,4,6,8. They are even numbers.’

‘53 cannot be a multiple of 8 because it’s not an even number’

Year 3 Multiplication

Pupils should be able to:

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

8 multiplication tables

• write and calculate mathematical statements for multiplication

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

Page 36: Rothwell St. Mary’s Catholic Primary School

Number Line

Bar Model

Grid Method

Base Ten

The two-digit number is partitioned horizontally

with the tens digit coming first. The number is

represented by the base ten 18 x 3=

18 x 3 =

• Partition the number

into tens and ones

• Multiply the pairs of

numbers

• Record the answer in

the grid

• Recombine to find the

answers

Page 37: Rothwell St. Mary’s Catholic Primary School

Grid Method 2 Digit by 1 Digit

Expanded short 2 digit by 1 digit Short 2 digit by 1 digit

Year 4 Multiplication

Pupils should be able to:

• Count in multiples and solve problems within 0,1, 6, 7, 9, 11

and 12 times tables

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

number using formal written layout

• Continue on with skill development from Y3

Page 38: Rothwell St. Mary’s Catholic Primary School

Grid Method Three Digit by One Digit

Short Multiplication

77 x 9= 23 x 6 =

658 x 8=

Year 5 Multiplication

Pupils should be able to:

• 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

Page 39: Rothwell St. Mary’s Catholic Primary School

Expanded long Multiplication

Long Multiplication

TO x TO= 24 x 16=

Page 40: Rothwell St. Mary’s Catholic Primary School

Short Multiplication

Practise and consolidation of multiplying a number by a one digit may be

needed in year six so that children can confidently use the short method of

multiplication to solve:

to x o=

hto x o=

th h t o x o=

Please refer to previous year’s guidance for short multiplication exemplification Long Multiplication

Children consolidate using long

multiplication for multiplying a number

up to four digits by two-digit number

124 x 26=

ThHTO x TO 2951 x 17

Year 6 Multiplication

Pupils should be able to:

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

whole number using the formal written method of long

multiplication

Page 41: Rothwell St. Mary’s Catholic Primary School

Fair Sharing

Allowing children to explore what is

fair sharing but also what is not

Children can experience real life problems. “We have 6 sweets. How will be

share them equally so Benny and Samni have the same”?

Early Years Division

Pupils should be able to:

• Understanding the concept of a fair share

Year 1 Division

Pupils should be able to:

• Solve one-step problems involving division, by calculating the

answer using concrete objects, pictorial representations and

arrays with the support of the teacher.

Page 42: Rothwell St. Mary’s Catholic Primary School

Sharing

Grouping

Page 43: Rothwell St. Mary’s Catholic Primary School

Sharing

Sharing with Remainders

Children use concrete objects to

understand the concept of

remainders. The idea that sometimes

there cannot be a fair share.

Children can use pictorials within their

books to solve division sentences

through sharing out between 2, 5 and

10 equally.

Year 2 Division

Pupils should be able to:

• Recall and use division facts for the 2, 5 and 10 multiplication

tables, including recognising odd and even numbers

• Calculate mathematical statements for division within the

multiplication tables and write them using the division (÷) and

equals (=) signs

• Show that division of one number by another cannot

• Solve problems involving division, using materials, arrays,

repeated addition, mental methods, and multiplication and

division facts, including problems in contexts.

Page 44: Rothwell St. Mary’s Catholic Primary School

Grouping with Arrays

Page 45: Rothwell St. Mary’s Catholic Primary School

Grouping with Numicon

Bar Model Grouping

Number Line Repeated Addition

Page 46: Rothwell St. Mary’s Catholic Primary School

Number Line Repeated Subtraction

Repeated Subtraction

Year 3 Division

Pupils should be able to:

• Recall and use division facts for the 3, 4 and 8 multiplication

tables

• Write and calculate mathematical statements for 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

Page 47: Rothwell St. Mary’s Catholic Primary School

Chunking

Children can use place value counters

as well as drawings to support this

method conceptually.

Children should be encouraged to

write down the related time tables

facts to support them with the

formal method of chunking.

Page 48: Rothwell St. Mary’s Catholic Primary School

Chunking

Children should consolidate

chunking before moving on to the

more formal short division TO x O

HTO x O

Year 4 Division

Pupils should be able to:

• Recall multiplication and division facts for multiplication tables

up to 12 × 12

• Use place value, known and derived facts to divide mentally,

including: multiplying by 0 and 1; dividing by 1; multiplying

together 3 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

Page 49: Rothwell St. Mary’s Catholic Primary School

Formal Short

Children should understand short

division as grouping. Start by using

concrete resources such as place

value counters 615 ÷ 5 = 213

Children should consolidate chunking

before moving on to the more formal

short division

Once children have solved both

concretely and pictorially they can

use the formal short division as

exemplified.

Year 4 pupils can do this with both

HT x O and HTO X O as well as working

out with remainders.

Page 50: Rothwell St. Mary’s Catholic Primary School

Formal Short

Children should understand short

division as grouping. Start by using

concrete resources such as place

value counters and pictorial methods

to solve

5648 ÷ 4 = 1412

Children can do the same when

working out remainders

2753 ÷ 2 = 1376 r1

Year 5 Division

Pupils should be able to:

• 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

• Divide whole numbers and those involving decimals by 10,

100 and 1,000

• Solve problems involving division, including using their

knowledge

• Solve problems involving addition, subtraction, multiplication

and division and a combination of these.

Page 51: Rothwell St. Mary’s Catholic Primary School

Formal Short Division

ThHTO X TO

Year 6 Division

Pupils should be able to:

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

using the formal written method of short division

• Where appropriate for the context 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

• Solve problems involving division

• Use written division methods in cases where the answer has

up to two decimal place

Page 52: Rothwell St. Mary’s Catholic Primary School

Long Division

Page 53: Rothwell St. Mary’s Catholic Primary School