Rothwell St. Mary’s Catholic Primary School
Transcript of 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:
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.
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
Adding One-Digit and Two-Digit:
Regrouping to Make Ten:
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
Adding a Two-Digit and One-Digit Number:
Adding Tens to a Number:
Base Ten
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
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
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.
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
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
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)
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
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
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.
•
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
Making 10
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
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
• 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 =
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 =
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
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.
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 =
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
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)
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
Columnar Subtraction to One Million
No exchanges
With exchanges
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.
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.
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
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
Repeated Addition
Arrays
Commutative Relationship
Number Line
Bar Model
Mental Maths
Solving Problems in Context
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
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
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
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
Expanded long Multiplication
Long Multiplication
TO x TO= 24 x 16=
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
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.
Sharing
Grouping
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.
Grouping with Arrays
Grouping with Numicon
Bar Model Grouping
Number Line Repeated Addition
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
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.
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
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.
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.
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
Long Division