September 2014
Year 1
Westgate Academy: Calculation Policy
Addition
The + and = signs and missing numbers
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’.
Example
2 = 1+ 1
2+3=4+1
3=3
2+2+2=4+2
Missing numbers need to be placed in all possible places.
3+4=��=3+4
3+�=77=�+4
�+4=77=3+�
Use of prepared number lines and concrete objects
Children are encouraged to record by drawing jumps on
prepared lines.
Subtraction
The - and = signs and missing numbers
The notes opposite are relevant here.
7-3=��=7-3
7-�=44=�-3
Use of pictures, marks and concrete objects
Sam spent 4p. What was his change from 10p?
Number Lines
Example- Counting Back/Down
11 – 7
Example- Counting On/Up
The difference between 7 and 11
Children are encouraged to record by drawing jumps on
prepared lines and constructing their own lines.
Add one-digit and two-digit numbers to 20, including zero.
3+6=9
Subtract one-digit and two-digit numbers to 20, including zero.
9–3=6
Vocab
+
add, more, plus, and, make, altogether, total, equal to, equals,
double, most, count on, number line
Multiplication
Use of pictures and objects
There are 3 sweets in one bag. How many sweets are there in 5
bags?
equal to, take, take away, less, minus, subtract, leaves,
distance between, how many more, how many fewer / less
than, most, least, count back , how many left, how much less
is_?
Division
Use of pictures and objects or marks
Grouping
12 children get into teams of 4 to play a game. How many
teams are there?
Count in multiples of one, two, five and ten
Counting steps using bead string and on prepared number lines.
Year 1
Sharing
6 sweets are shared between 2 people. How many do they have
each?
Counting in multiples using a range of objects, e.g. pairs of legs
on animals; fingers in gloves etc.
Use of arrays
Counting in rows and columns
Vocab
So 6 = 2 + 2 +2 or 6 = 3 + 3
groups of, lots of, times, array, altogether, multiply, count
Make use of practical activities involving sharing, e.g.
distributing cards when playing a game, putting objects onto
plates, into cups, hoops
share, share equally, one each, two each…, group, groups of,
lots of, array
Addition
+ and = signs and missing numbers
Continue using a range of equations (See Year 1) but with
appropriate, larger numbers as specified in Year 2 requirements
and guidance, i.e. extend to 14 + 5 = 10 + � and 32 + � +� = 100
35 = 1 + � + 5.
Partition into tens and ones and recombine
12 + 23 = 10 + 2 + 20 + 3
= 30 + 5
= 35
Partitioning the second number only
23 + 12 = 23 + 10 + 2
= 33 + 2
= 35
Adding ten.
Example: Add 9 or 11 by adding 10 and adjusting by 1
35 + 9 = 44
Year 2
Using known addition facts to 20.
Recall and use addition facts to 20 fluently, and derive and use
related facts up to 100.
E.g. 3+7=10 therefore 30+70=100
Commutativity
Addition of two numbers can be done in any order
(commutative). The subtraction of two numbers cannot.
Inverse
Recognise the inverse relationship between addition and
subtraction and use this to check calculations.
E.g. 10+14=24 therefore 24-10=14
Using concrete objects, pictorial representations and mental
maths.
Add a two digit number and ones.
Add a two digit numbers and tens.
Add two digit numbers.
Add three one digit numbers.
Written methods:
Partitioned column method
Record addition in columns supporting place value in
preparation for formal written
methods. Dienes or cubes can be
used for support.
Use the partition (semi-compact)
column method to add two digit
Subtraction
The – and = signs and missing numbers
Continue using a range of equations (See Year 1) but with
appropriate numbers in relation to Year 2 requirements and
guidance, i.e. extend to 14 + 5 = 20 - �.
Find a small difference by counting
up (mental strategy)
42 – 39 = 3
Example: Subtract 9 or 11 & begin
to add/subtract 19 or 21
35 – 9 = 26
Use known number facts and
place value to subtract (Partition
second number only)
37 – 12 = 37 – 10 – 2
= 27 – 2
= 25
Using known subtraction facts up to 20.
Recall and use subtraction facts up to 20 fluently, and derive
and use related facts.
E.g. 8+5=3 therefore 80+50=30
Commutativity
Addition of two numbers can be done in any order
(commutative). The subtraction of two numbers cannot.
Inverse
Recognise the inverse relationship between addition and
subtraction and use this to check calculations.
E.g. 24-10=14 therefore 10+14=24
Using concrete objects, pictorial representations and mental
maths.
Subtract a two digit number and ones.
Subtract a two digit numbers and tens.
Subtract two digit numbers.
Written methods:
Partitioned column method
Record subtraction in columns supporting place value in
preparation for formal written methods.
Dienes or cubes can be used for
support.
Use the partition column method to add
two digit numbers where exchanging is
not required.
Extension: Use the partitioned column method to subtract two
digit number where exchanging is required. Dienes or cubes
can be used for support.
numbers that do not cross the tens
boundary.
Vocab
Extension: Use the partitioned column
method to add two digit number that do
cross the tens boundary.
add, more, plus, and, make, altogether, total, equal to, equals,
double, most, count on, number line, sum, tens, units,
partition, addition, column, tens boundary, inverse
equal to, take, take away, less, minus, subtract, leaves,
distance between, how many more, how many fewer / less
than, most, least, count back , how many left, how much less
is_? difference, count on, strategy, partition, tens, units,
inverse.
Multiplication
Division
The x and = signs and missing numbers
7x2=��=2x7
7 x � = 14 14 = � x 7
� x 2 = 14 14 = 2 x �
The ÷ and = signs and missing numbers
6÷2=��=6÷2
6÷�=33=6÷�
�÷2=33=�÷2
Mental Maths
Children should begin to recall multiplication facts for 2, 5 and
10 times tables through practice in counting and understanding
of the operation.
Mental Maths
Children should begin to recall division facts for 2, 5 and 10
times tables through practice in counting and understanding of
the operation.
Use materials, arrays, repeated addition
(including solving problems in context)
Arrays
Use materials, arrays, repeated addition (including solving
problems in context)
Arrays
Year 2
Or repeated addition
Use of sharing and grouping
Sharing
6 sweets are shared between 2 people.
How many do they have each?
Or apparatus
Grouping
There are 6 sweets. How many people can have 2 each? (How
many 2’s make
6?)
Partitioning
Written calculations
Write multiplication statements using the symbols x ÷ =
Commutativity
Multiplication of two numbers can be done in any order
(commutative). The division one number by another cannot.
Written calculations
Write multiplication statements using the symbols x ÷ =
Vocab
Commutativity
Multiplication of two numbers can be done in any order
(commutative). The division one number by another cannot.
Inverse
Recognise the inverse relationship between multiplication and
division and use this to check calculations.
E.g. 2x5=10 therefore 10÷5=2
groups of, lots of, times, array, altogether, multiply, count,
multiplied by, repeated addition, column, row, commutative,
sets of, equal groups, times as big as, once, twice, three
times...
Inverse
Recognise the inverse relationship between multiplication and
division and use this to check calculations.
E.g. 2x5=10 therefore 10÷5=2
Find and name fractions of length, shape and sets of objects
and quantities
Use of diagrams- count all equal parts to determine
denominator. Link to division into equal groups/parts.
share, share equally, one each, two each…, group, equal
groups of, lots of, array, divide, divided by, divided into,
division, grouping, number line, left, left over
Addition
The + and = signs and missing numbers
Continue using a range of equations as in Year 1 and Year 2 but
with appropriate larger numbers specified in the requirements
and guidance.
� + � = 96 16 + � = 31 – 9
Subtraction
The - and = signs and missing numbers
Continue using a range of equations as in Year 1 and Year 2 but
with appropriate larger numbers specified in the requirements
and guidance.
48 - � = 36
Progression in mental calculations with larger numbers
Calculate HTU + U
Calculate HTU + TU
Calculate HTU + HTU
Progress from no crossing of boundaries to crossing of boundary.
Find a small difference by counting up (mental calculations)
Continue from Year 2 but with appropriate numbers,
e.g. 102 – 97 = 5
Finding the difference between two numbers by counting up
(mental calculation)
Partition into tens and ones and recombine
Develop from Year 2- partitioning both numbers and
recombining. Refine to partitioning the second number only:
Add a near multiple of 10 to a two-digit number
Continue work from Year 2 but with appropriate numbers:
35 + 19 is the same as 35 + 20 – 1.
Year 3
Written methods:
Formal methods of columnar addition to add numbers with up
to three digits.
The partition (semi-compact) column method. Dienes or cubes
can be used for support.
Subtract mentally a ‘near multiple of 10’ to or from a twodigit number, extending to three digit numbers
Continue as in Year 2 but with appropriate numbers
e.g. 78 – 49 is the same as 78 – 50 + 1
Progression in mental calculations with larger numbers
Calculate HTU - U
Calculate HTU - T
Calculate HTU - H
Progress from no crossing of boundaries to crossing of
boundary.
Complementary addition
84 – 56 = 28
Written methods:
Partitioned column method
Record subtraction in columns supporting place value in
preparation for formal written methods.
Dienes or cubes can be used for
support.
Extension: The column (compact) method.
When the understanding of the above method is
secure then the column (compact) method can be
taught. Use apparatus to support.
Use the partition column method to add
two digit numbers where exchanging is
not required.
Extension: Extend to decimals in the context of
money
Use the partitioned column method to subtract two digit
number where exchanging is required. Dienes or cubes can be
used for support.
The expanded method should be used if children experience
persisting difficulties.
Vocab
Extend addition to decimals (same number of decimals places)
and adding several numbers (with different numbers of digits).
add, more, plus, and, make, altogether, total, equal to, equals,
double, most, count on, number line, sum, tens, units,
partition, plus, addition, column, tens boundary, hundreds
boundary, increase, vertical, ‘carry‘, expanded, compact,
inverse
Once
pupils are secure with the
understanding of
‟exchanging‟, they can use
the partitioned column
method to subtract any 2
and 3-digit numbers.
equal to, take, take away, less, minus, subtract, leaves,
distance between, how many more, how many fewer / less
than, most, least, count back , how many left, how much less
is_? difference, count on, strategy, partition, tens, units
exchange, decrease, hundreds, value, digit, inverse
Multiplication
The x and = signs and missing numbers
Continue using a range of equations as in Year 2 but with
appropriate numbers in relation to the requirements and
guidance.
13 x � = 65
� x � = 24
Mental Maths
Children should begin to recall multiplication facts for 2, 4 and
8 times tables through doubling.
Develop efficient mental methods to solve a range of problems
e.g using commutativity (4 × 12 × 5 = 4 × 5 × 12 = 20 × 12 = 240)
Year 3
Using concrete objects, pictorial representations and mental
maths.
Work out multiplication facts not known by repeated addition or
other taught mental strategies (e.g. by commutative law,
working out near multiples and adjusting, using doubling etc.)
Strategies to support this are repeated addition using a number
line, bead bars and arrays:
Written methods: TU x U
Informal written methods
Use known facts x3, x4, x8 (Year 3 expectations) and x2, x5 and
x10 (Year 2 expectations).
Formal written methods
When children are secure with the
informal written methods then they can
progress onto the formal written methods.
Always teach this method alongside the
informal method to ensure understanding.
Pupils could be asked to work out a given
calculation using the grid, and then
compare it to the column method. What
are the similarities and differences? Unpick the steps and show
how it reduces the steps.
Vocab
Inverse
Continue to recognise the inverse relationship between
multiplication and division and use this to check calculations.
groups of, lots of, times, array, altogether, multiply, count,
multiplied by, repeated addition, column, row, commutative,
sets of, equal groups, times, _times as big as, once, twice, three
times..., partition, grid method, multiple, product, tens, units,
value
Division
The ÷ and = signs and missing numbers
Continue using a range of equations as in Year 2 but with
appropriate numbers in relation to the requirements and
guidance.
� ÷ 6= 4
Mental Maths
Children should begin to recall division facts for 2, 4 and 8
times tables.
Develop efficient mental methods to solve a range of problems
e.g using associativity (3 x 2 = 6, 6 ÷ 3 = 2 and 2= 6 ÷ 3)
Written methods TU ÷ U
Short multiplication should be used when dividing a 2 digit
number by a one digit number. Ensure that each of the
methods below are secure before moving on.
Grouping on a number line
Children continue to work out unknown division facts by
grouping on a number line from zero. They are also now taught
the concept of remainders, as in
the example. This should be
introduced practically and with
arrays, as well as being translated
to a number line. Children should
work towards calculating some
basic division facts with remainders mentally for the 2s, 3s, 4s,
5s, 8s and 10s, ready for ‘carrying’ remainders across within the
short division method.
Short division- with no remainders in the answer.
Once children are secure with division as grouping and
demonstrate this using number lines,
arrays etc., short division for larger 2-digit
numbers should be introduced, initially
with carefully selected examples requiring
no calculating of remainders at all. Start by
introducing the layout of short division by
comparing it to an array.
Remind children of correct place value, that 96 is equal to 90
and 6, but in short division, pose:
- How many 3s in 9? = 3, and record it
above the 9 tens.
- How many 3s in 6? = 2, and record it
above the 6 units.
Short division- remainders within the answer but no
remainders in the final answer.
Once children demonstrate a full understanding of remainders,
and also the short division method taught, they can be taught
how to use the method when remainders occur within the
calculation (e.g. 96†4), and be taught
to „carry‟ the remainder onto the next
digit. If needed, children should use
the number line to work out individual
division facts that occur which they
are not yet able to recall mentally.
share, share equally, one each, two each…, group, equal
groups of, lots of, array, divide, divided by, divided into,
division, grouping, number line, left, left over, inverse, short
division, ‗carry‘, remainder, multiple
Addition
The + and = signs and missing numbers
Continue using a range of equations as in Key Stage 1 and Year 3
but with appropriate numbers.
98 = 46 + �
Subtraction
The – and = signs and missing numbers
Continue using a range of equations as in Key Stage 1 and Year
3 but with appropriate numbers.
� – 24= 37 - �
Mental method to progress on from Y3 by using increasingly
large numbers.
Mental method to progress on from Y3 by using increasingly
large numbers.
Partition into hundreds, tens and ones and recombine
Either partition both numbers and recombine or partition the
second number only e.g.
358 + 73 = 358 + 70 + 3
= 428 + 3
= 431
Differences
Find a difference by counting up, e.g. 8006 – 2993 = 5013.
This can be modelled on an empty number line.
Use known number facts and place value to subtract
6.1 – 0.4 = 5.7
Year 4
Add or subtract the nearest multiple of 10 or 100, then
adjust
Continue as in Year 2, 3 and 4 but with appropriate numbers e.g.
458 + 79 = is the same as 458 + 80 – 1
Written methods:
Addition of numbers with at up to four digits using formal
method of columnar addition
Introduce the compact column addition method by asking
children to add the two given numbers together using the
method that they are familiar with (expanded column
addition—see Y3). Teacher models the compact method with
carrying, asking children to discuss similarities and differences
and establish how it is carried out.
Written methods:
Subtraction with up to four digits using formal method of
columnar subtraction.
Recap the semi- compact column subtraction method from Y3
using larger numbers.
When children are secure move on to the compact column
subtraction method.
The formal, efficient method of columnar addition will involve
crossing of boundaries (at the tens, hundreds and/or
thousands). Take a systematic approach to teaching this looking
at crossing each boundary in turn before mixed practice. Revert
to expanded method if children experience difficulties.
Vocab
Use and apply this method to
money and measurement values by
extending addition to decimals
(same number of decimals places)
and adding several numbers (with
different numbers of digits).
add, more, plus, and, make, altogether, total, equal to, equals,
double, most, count on, number line, sum, tens, units,
partition, plus, addition, column, tens boundary, hundreds
boundary, increase, vertical, ‘carry’, expanded, compact,
thousands, hundreds, digits, inverse
To introduce the compact method, ask children to perform a
subtraction calculation with the familiar partitioned column
subtraction then display
the compact version for
the calculation they have
done. Ask pupils to
consider how it relates to
the method they know,
what is similar and what is
different, to develop an
understanding of it.
Give plenty of opportunities to apply this to money and
measures.
Extension: Extend subtraction to decimals (same number of
decimals places) and adding several numbers (with different
numbers of digits)
equal to, take, take away, less, minus, subtract, leaves,
distance be-tween, how many more, how many fewer / less
than, most, least, count back , how many left, how much less
is_? difference, count on, strategy, partition, tens, units
exchange, decrease, hundreds, value, digit, inverse.
Multiplication
The x and = signs and missing numbers
Continue using a range of equations but with appropriate
numbers for Year 4.
3� x 7 = 266
� x � = 420
Mental methods
Recall multiplication facts up to 12 x 12
Division
The ÷ and = signs and missing numbers
Continue using a range of equations but with appropriate
numbers for Year 4.
Mental methods
Recall related division facts up to 12 x 12
Use place value, known and derived facts to multiply and divide
mentally, including: multiplying and dividing by 10 and 100 and
1.
Using known facts- extend this to multiplying three digit
numbers (mental maths)
Use place value, known facts and derived facts to multiply
mentally, e.g. multiply by 1, 10, 100, by 0, or to multiply 3
numbers. E.g. 200 x 3 x 4= 2400 can be derived from 3 x 4=12
and 12 x 2= 24.
Using known facts- extend this to dividing three digit numbers
(mental maths)
Pupils practise mental methods and extend this to three-digit
numbers to derive facts, for example 200 × 3 = 600 so 600 ÷ 3 =
200
Inverse (mental and written methods)
Continue to recognise the inverse relationship between
multiplication and division and use this to check calculations.
Inverse (mental and written methods)
Continue to recognise the inverse relationship between
multiplication and division and use this to check calculations.
Partition- distributive law (mental and written methods)
23 x 4 = 92
23 x 4 = (20 x 4) + (3 x 4)
= (80) + (12)
= 92
Written methods
Remainders
Introduce the concept of remainders.
E.g. 16 ÷ 3 = 5 r1
Sharing – There are 16 sweets shared between 3, how many
left over?
Year 4
Written methods: TU x U and HTU x U
Informal written methods - developing the grid method
Grouping – How many 3s make 16, how many left over?
Formal written methods
When children are secure with the informal written methods
then they can progress onto the formal written methods.
Always teach this method alongside
the informal method to ensure
understanding.
Vocab
Pupils could be asked to work out a
given calculation using the grid, and
then compare it to the column
method. What are the similarities
and differences? Unpick the steps
and show how it reduces the steps.
groups of, lots of, times, array, altogether, multiply, count,
multiplied by, repeated addition, array, column, row,
commutative, groups of, sets of, lots of, equal groups, times,
multiply, times as big as, once, twice, three times... partition,
grid method, total, multiple, product, sets of, inverse
Short division- remainders within the answer but no
remainders in the final answer. TU÷U
Once children demonstrate a full understanding of remainders,
and also the short division method taught, they can be taught
how to use the method when remainders occur within the
calculation (e.g. 96†4), and be taught to
„carry‟ the remainder onto the next
digit. If needed, children should use the
number line to work out individual
division facts that occur which they are
not yet able to recall mentally.
Short division- remainders within the answer but no
remainders in the final answer. HTU÷U
Pupils move onto dividing numbers with
up to 3-digits by a single digit, however
problems and calculations provided
should not result in a final answer with
remainder at this stage.
Extension
Children who exceed this expectation may progress onto short
division with remainders (see Y5 division).
share, share equally, one each, two each…, group, equal
groups of, lots of, array, divide, divided by, divided into,
division, grouping, number line, left, left over, inverse, short
division, „carry‟, remainder, multiple, divisible by, factor
Addition
Subtraction
The + and = signs and missing numbers
Continue using a range of equations as in Key Stage 1 and Year 4
but with appropriate numbers.
36 + � = 71 - 24
The – and = signs and missing numbers
Continue using a range of equations as in Key Stage 1 and Year
3 but with appropriate numbers.
236+ � = 37 - 124
Mental method to progress on from Y4 by using increasingly
large numbers.
Mental method to progress on from Y4 by using increasingly
large numbers.
Mental strategies.
Add numbers mentally with increasingly large numbers, using
and practising a range of mental strategies e.g. add the nearest
multiple of 10, 100, 100 and adjust; use near doubles, inverse,
partitioning and re-combining; using number bonds.
Differences
Find a difference by counting up, e.g. 9006 – 2893 = 6113.
This can be modelled on an empty number line.
Use known number facts and place value to subtract
6.9 – 1.4 = 5.5
Use rounding to check answers and accuracy.
Year 5
Addition of numbers with at least four digits using formal
method of columnar addition
Recap the compact column
method for addition which
was introduced in Y4. Use this
method to add numbers with
at least 4 digits.
Addition of numbers with at least four digits using formal
method of columnar addition- linked to money and measures
(with the same number of decimal places)
The decimal point should be aligned
in the same way as the other place
value columns, and must be in the
same column in the answer.
Addition of numbers with at least four digits using formal
method of columnar addition- linked
to money and measures (with a
different number of decimal places).
Empty decimal places can be filled with
zero to show the place value in each
column. Say “1 hundredths add 0
hundredths‟ to reinforce place value
Vocab
Addition of numbers with at least four digits using formal
method of columnar addition- adding
more than two values.
Empty decimal places can be filled
with zero to show the place value in
each column. Say “6 tenths add 7
tenths‟ to reinforce place value.
add, more, plus, and, make, altogether, total, equal to, equals,
double, most, count on, number line, sum, tens, units,
partition, plus, addition, column, tens boundary, hundreds
boundary, increase, ‘carry’, expanded, compact, vertical,
thousands, hundreds, digits, inverse & decimal places, decimal
point, tenths, hundredths, thousandths
Written methods:
Subtraction with at least four digits using formal method of
columnar subtraction.
Recap this if children are not secure with the compact column
method for subtraction.
Subtraction with at least four digits using the Compact column
method for subtraction- with exchanging.
Recap the compact column
method for subtraction
which was introduced in Y4.
Use this method to subtract
numbers with at least 4 digits
Subtraction with at least four digits using the Compact column
method for subtraction- with decimals (linked to money and
measures)
Subtract with decimal
values, including
mixtures of integers
and decimals, aligning
the decimal point.
Create lots of
opportunities for
subtracting and finding
differences with money and measures.
Extension- subtracting decimals with different number of
decimal places (see Year 6)
equal to, take, take away, less, minus, subtract, leaves,
distance between, how many more, how many fewer / less
than, most, least, count back , how many left, how much less
is_? difference, count on, strategy, partition, tens, units
exchange, decrease, hundreds, value, digit, inverse, tenths,
hundredths, decimal point, decimal
Multiplication
The x and = signs and missing numbers
Continue using a range of equations but with appropriate
numbers for Year 5.
3�5 x � = 2070
The ÷ and = signs and missing numbers
Continue using a range of equations but with appropriate
numbers for Year 5.
� ÷ 6 = 23 r1
Mental methods
Recall multiplication facts up to 12 x 12
Mental methods
Recall multiplication and division facts for all numbers up to 12
x 12.
Multiply and divide numbers mentally, drawing upon known
facts.
Multiply and divide whole numbers and those involving
decimals by 10, 100 and 1000.
Perform mental calculations, including with mixed operations
and large numbers.
Approximating
Children need to be taught to approximate first, e.g. for 72 x 38,
they will use rounding: 72 x 38 is approximately 70 x 40 = 2800,
and use the approximation to check the reasonableness of their
answer against.
Written methods: By the end of Year 5 children should be able
to multiply- THTU x U and THTU x TU
Short multiplication for multiplying by a single digit.
Pupils could be asked to work out a given calculation using the
grid, and then compare it to the column method. What are the
similarities and differences? Unpick the steps and show how it
reduces the steps. Move from the grid method to the short
method for multiplication- teach side by side.
Year 5
Division
Long multiplication for multiplying by 2 digits.
The grid method (informal method) should be used to introduce
long multiplication (formal method), as the relationship can be
seen in the answers in each row.
18 x 3 on the 1st row
(8 x 3 = 24, carrying the 2 for twenty, then „1‟ x 3).
18 x 10 on the 2nd row. Put a zero in units first, then say 8 x 1,
and 1 x 1.
Move towards more complex numbers.
Type of answer
Interpret non-integer answers to division by expressing results
in different ways according to the context, including with
remainders, as fractions, as decimals or by rounding (e.g. 98 ÷ 4
= 24 r 2 = 24½ = 24.5 ≈ 25).
Inverse (mental and written methods)
Continue to recognise the inverse relationship between
multiplication and division and use this to check calculations.
Short division with remainders: Now that pupils are introduced
to examples that give rise to remainder answers, division needs
to have a real life problem solving context, where pupils
consider the meaning of the remainder and how to express it,
i.e. as a fraction, a decimal, or as a rounded number or value,
depending upon the context of the problem.
The answer to 5309 ÷ 8 could be expressed as 663 and five
eighths, 663 r 5, as a decimal, or rounded as appropriate to the
problem involved.
Include money and measure contexts.
Extension 1- If children feel confident the progress onto short
division with decimals (see Year 6 division)
Vocab
Extension 2- If children are confident and accurate then
introduce long division for pupils who are ready to divide any
number by a 2-digit number (e.g. 2678 ÷ 19). (See Year 6
division)
groups of, lots of, times, array, altogether, multiply, count,
multiplied by, repeated addition, column, row, commutative,
sets of, equal groups, _times as big as, once, twice, three
times..., partition, grid method, total, multiple, product,
inverse, square, factor, integer, decimal, short/long multiplication, ‘carry‘
share, share equally, one each, two each…, group, equal
groups of, lots of, array, divide, divided by, divided into,
division, grouping, number line, left, left over, inverse, short
division, ‘carry’, remainder, multiple, divisible by, factor,
inverse, quotient, prime number, prime factors, composite
number (non-prime)
Addition
The + and = signs and missing numbers
Continue using a range of equations as in Key Stage 1 and Year 4
but with appropriate numbers.
798 = 346 + �
Subtraction
The – and = signs and missing numbers
Continue using a range of equations as in Key Stage 1 and Year
3 but with appropriate numbers.
�-2.14 = 3.7- �
Mental method to progress on from Y5 by using increasingly
large numbers.
Mental method to progress on from Y5 by using increasingly
large numbers.
Mental strategies.
Add numbers mentally with increasingly large numbers, using
and practising a range of mental strategies e.g. add the nearest
multiple of 10, 100, 100 and adjust; use near doubles, inverse,
partitioning and re-combining; using number bonds.
Pupils should be able to apply their knowledge of a range of
mental strategies, mental recall skills, and informal and formal
written methods when selecting the most appropriate method
to work out subtraction problems.
Use rounding to check answers and accuracy.
Differences
Find a difference by counting up, e.g. 9006 – 2893 = 6113.
This can be modelled on an empty number line.
Addition of numbers with four digits (or more) using formal
method of columnar addition- see Year 5.
Use known number facts and place value to subtract
6.9 – 3.4 = 3.5
Year 6
Addition of numbers with four digits (or more) using formal
method of columnar addition- linked to money and measures
(with the same number of decimal places)- see Year 5
Addition of numbers with four digits (or more) using formal
method of columnar addition- linked to money and measures
(with a different number of decimal
places)
Empty decimal places can be filled with
zero to show the place value in each
column. Say “1 hundredths add 0
hundredths‟ to reinforce place value
Addition of numbers with four digits (or more) using formal
method of columnar addition- adding more than two values.
Adding several numbers with different numbers of decimal
places (including money and measures):
- Tenths, hundredths and thousandths should be correctly
aligned, with the decimal point lined
up vertically including in the answer
row.
- Zeros could be added into any
empty decimal places, to show there
is no value to add.
- Say “9 thousandths add 8
thousandths and 1 thousandth and
one thousandth”.
Vocab
Addition of numbers with more than four digits using formal
method of columnar addition.
Subtraction with four digits (or
more) using the compact
column method for
subtraction- with exchanging.
Using the compact
column method to
subtract more complex
integers
Compact column method for subtraction- with decimals
(linked to money and measures) Subtract with decimal values,
including mixtures of
integers and decimals,
aligning the decimal
point. Create lots of
opportunities for
subtracting and finding
differences with
money and measures.
Using the compact column method to subtract money
and measures, including decimals with different
numbers of decimal places. Empty decimal places can be
Addition of several numbers with more
than four digits using formal method of
columnar addition
filled with zero to
show the place
value in each
column.
add, more, plus, and, make, altogether, total, equal to, equals,
double, most, count on, number line, sum, tens, units,
partition, plus, addition, column, tens boundary, hundreds
boundary, increase, ‘carry’, expanded, compact, vertical,
thousands, hundreds, digits, inverse, decimal places, decimal
point, tenths, hundredths, thousandths
equal to, take, take away, less, minus, subtract, leaves,
distance between, how many more, how many fewer / less
than, most, least, count back , how many left, how much less
is_? difference, count on, strategy, partition, tens, units
exchange, decrease, hundreds, value, digit, inverse, tenths,
hundredths, decimal point, decimal
Multiplication
The x and = signs and missing numbers
Continue using a range of equations but with appropriate
numbers for Year 6.
2� x 52 = 1512
Division
The ÷ and = signs and missing numbers
Continue using a range of equations but with appropriate
numbers for Year 6.
432 ÷ � = 28 r12
Mental methods
Recall multiplication facts up to 12 x 12
Perform mental calculations with mixed operations and large
numbers.
Mental methods- As Year 5.
Type of answer- As Year 5
Inverse (mental and written methods)- As Year 5
Brackets
Pupils explore the order of operations using brackets.
E.g. 2 + 1 x 3= 5 and (2+1) x 3 = 9
Year 6
Written methods
- Use short multiplication to multiply numbers with more than
4-digits by a single digit; to multiply money and measures, and
to multiply decimals with up to 2d.p. by a single digit.
- Use long multiplication to multiply numbers with at least 4
digits by a 2-digit number.
- Use the grid method to support the teaching of these
methods.
Move towards more complex numbers.
Written methods
By the end of Year 6 pupils should be able to divide at least 4
digits by both single-digit and 2-digit numbers (including
decimal numbers and quantities).
Short division, for dividing by a single digit.
Short division with remainders: Pupils should continue to use
this method, but with numbers to at least 4 digits, and
understand how to express remainders as fractions, decimals,
whole number remainders, or rounded numbers. Real life
problem solving contexts
need to be the starting point,
where pupils have to
consider the most
appropriate way to express
the remainder.
Calculating a decimal remainder: In this example, rather than
expressing the remainder as r 1, a decimal point is added after
the units because there is still a remainder, and the one
remainder is carried onto zeros after the decimal point (to
show there was no
decimal value in the
original number). Keep
dividing to an
appropriate degree of
accuracy for the
problem being solved.
Introduce long division by chunking for dividing by 2 digits.
Vocab
Multiply decimals with up to 2d.p by a single digit. Line up the
decimal points in the question and the answer. Remind children
that the single digit belongs in the units column. This works well
for multiplying money (£.p) and other measures.
groups of, lots of, times, array, altogether, multiply, count,
multiplied by, repeated addition, array, column, row,
commutative, sets of, equal groups, times as big as, once,
twice, three times... partition, grid method, total, multiple,
product, inverse, square, factor, integer, decimal, short / long
multiplication, „carry‟, tenths, hundredths, decimal
Find out ‘How many 36s are in 972?’ by subtracting ‘chunks’ of
36, until zero is reached (or until there is a remainder).
Teach pupils to write a ‘useful list’ first at the side that will help
them decide what chunks to use, e.g.:
‘Useful’ list: 1x = 36
10x = 360
100x = 3600
Introduce the method in a
simple way by limiting the
choice of chunks to Can we
use 10 lots? Can use 100 lots?
As children become confident
with the process, encourage
more efficient chunks to get to
the answer more quickly (e.g.
20x, 5x), and expand on their
‘useful’ lists.
Where remainders occur,
pupils should express them as fractions, decimals or use
rounding, depending upon the problem.
share, share equally, one each, two each…, group, equal
groups of, lots of, array, divide, divided by, divided into,
division, grouping, number line, left, left over, inverse, short
division, ‘carry’, remainder, multiple, divisible by, factor,
inverse, quotient, prime number, prime factors, composite
number (non-prime), common factor
Useful Calculation Links
Year 1
Addition
Year 2
Multiplication
Year 3
Addition
Subtraction
Multiplication
Year 4
Subtraction
Year 5 and 6
Subtraction
Multiplication
Useful Links
https://www.youtube.com/watch?v=OkW1Y11tGxw&list=PLQqF8sn28L9wjDm8uJEJcRCDDoY6raPE_
https://www.youtube.com/watch?v=YPWmOVt8vgw&list=PLQqF8sn28L9yj34NpXK7Yffze7ZoXTiix
https://www.youtube.com/watch?v=VGkjjVfnGYI&list=PLQqF8sn28L9yj34NpXK7Yffze7ZoXTiix&index=2
http://www.teachertube.com/viewVideo.php?video_id=24325
https://www.youtube.com/watch?v=RCCLseBLBSo
https://www.youtube.com/watch?v=dP8NlFLZzOg
https://www.youtube.com/watch?v=qyTRtoqYi7Q&list=PLQqF8sn28L9yj34NpXK7Yffze7ZoXTiix
https://www.youtube.com/watch?v=RCCLseBLBSo
https://www.youtube.com/watch?v=dP8NlFLZzOg
https://www.youtube.com/watch?v=3ihxp2mqnhs
https://www.youtube.com/watch?v=3ihxp2mqnhs
https://www.youtube.com/watch?v=5ppOF53x_q0&list=PLQqF8sn28L9yj34NpXK7Yffze7ZoXTiix
https://www.youtube.com/watch?v=t_bnlB2KRL4
https://www.youtube.com/watch?v=BcIjRLZzMaw&list=PLQqF8sn28L9wjDm8uJEJcRCDDoY6raPE_&index=2