Moseley C of E Primary School
Maths Calculation Policy
MOSELEY C OF E PRIMARY SCHOOL
CALCULATIONS POLICY
Progression towards a standard method of calculation
Mission Statement:
Our policy will address the needs of all “our” pupils as stated in our Mission Statement
(2007) below.
Our successful Christian school offers a wide range of exciting and educational
opportunities to enhance skills, talents and creativity.
The school community
appreciates and accepts others, and celebrates the achievements of all. We have
supportive and trusting relationships with God and all his children. As a result, we take
responsibility and welcome absolutely everyone into a caring and safe environment, where
we are all guided to work together.
The Aims of School:
To Be A Community Where:
1.
Our Christian ethos encompasses all aspects of school life where every individual is
respected.
2.
All school staff, governors and parents work in partnership for the benefit for all
pupils.
3.
Teachers and support staff enable all pupils to achieve their full potential as
independent life-long learners.
4.
Pupils experience a broad, balanced and enriched curriculum which promotes challenge,
enabling everyone to make a positive contribution towards their own achievements.
5.
We foster strong links with the community and encourage children to be responsible
citizens.
6
We encourage initiative within a happy, healthy and safe environment where all
achievement is valued and celebrated.
Introduction
The Primary Framework provides a structured and systematic approach to the teaching of
calculation. There is considerable emphasis on teaching mental calculation methods. Up to
the age of 9 (end of Year 4) informal written recording is practised regularly and is an
important part of learning and understanding.
More formal written methods follow when a child is able to use a wide range of mental
strategies (sometimes before the end of Year 4 if children/a child are secure with informal
methods). Moseley C of E Primary School has developed a consistent approach to the teaching
of written calculations in order to establish continuity and progression through out the
school.
Aims
Children should be able to choose an efficient method; mental, written or calculator
appropriate, to the given task. By the end of Year 6, children working at Level 4 and above
will have been taught, and be secure with, a compact standard method for each operation.
General Progression






Establish mental methods based on a good understanding of place value
Use of informal jottings to aid metal calculations
Develop use of an empty number line to help mental imagery and aid recording
Use of partitioning and recombining to aid informal methods
Introduce expanded written methods
Develop expanded written methods into compact standard written form.
Before carrying out a calculation, children should be encouraged to consider:





Can I do it in my head? (using rounding, adjustment)
The size of an approximate answer (estimation)
Could I do jottings to keep track of the calculation?
Do I need to use an expanded or compact written method?
(Children may not refer to these names but will understand the methods)
When are children ready for written calculations?
Addition and subtraction





Do they know addition and subtraction facts to 20?
Do they understand place value and can they partition numbers?
Can they add three single digit numbers mentally?
Can they add and subtract any pair of two digit numbers mentally?
Can they explain their mental strategies orally and record them using informal jottings?
Multiplication and division







Do they know the 2,3,4,5 and 10 times tables?
Do they know the result of multiplying by 1 and 0?
Do they understand 0 as a place holder?
Can they multiply two and three digit numbers by 10 and 100?
Can they double and halve two digit numbers mentally?
Can they use multiplication facts they know to derive mentally other multiplication facts
that they do not know?
Can they explain their mental strategies orally and record them using informal jottings?
Vocabulary
The correct terminology should be used when referring to the value of digits to support
children’s understanding of place value. E.g. 68 + 47 should be read ‘sixty add forty’ not ‘six
add four’.
Addition and Subtraction
Foundation
Stage
Aim by end of
year:
- All can move
(count on or
back) up to 10
spaces on a
number track.
-Some can add
two 1 digit
numbers showing
method used.
-All can subtract
small numbers by
taking away using
apparatus.
-Some can
discuss
difference
mathematically
.
Addition
Subtraction
Make own marks or tallies to record numbers.
Begin to relate addition to combining two groups of
objects and counting on.
Adult to model number sentences in context.
Begin to relate subtraction to taking objects away
from a group and counting what is left. Find own way
of recording for subtraction e.g. cross-outs.
Begin to record numbers and number sentences,
when ready.
3 + 2 = 5
Select two groups of objects to make a given total
e.g. Find dominoes with 6 dots on.
Adults scribe number sentences.
◦
2+4=6
2
3
4
1+5=6
5
6
7
8
9
10
Use a number track to find one more than a
number.
Say the number one more than when playing a
board game.
Experience addition as counting on, e.g. rolling a
dice and moving along a number track when playing
snakes and ladders.
Children to work practically with bead bars and
bead strings.
Number tracks and number lines to be available for
children to use in free flow activities.
Find own way of recording for addition. Using
pictures, symbols, apparatus e.g.
5
Experience subtraction in the context of counting
back along a number track
e.g. jumping backwards two jumps along a floor
number track game.
Adults model use of number tracks and number lines.
4+2=6
3 and 2
7–2=5
Children record number sentences related to
practical work, when ready.
Adults model use of number tracks and number
lines.
1
Adults to model recording. (After practical work, in
context and in conjunction with apparatus).
3
2
5
Sing nursery rhymes and simple songs.
1
2
3
4
5
6
7
8
9
10
6–2=4
Use a number track to find one less than a number.
Children to work practically with bead bars and bead
strings.
Number tracks and number lines to be available for
children to use in free flow activities.
Start to develop the concept of difference by
comparing objects by the number in two sets or in
the context of measures and saying if they are the
same or different e.g.

number of sweets in different size jars.
or

when playing with cars make two rows and
discuss that the row of 12 cars is longer than
the row of 8 cars. “Can you make them the same
length? How?”
Sing nursery rhymes, involving something being
taken away in each verse e.g. 5 little men in a flying
saucer.
Solve practical problems in a real or role play
context and talk about own ideas, methods and
solutions.
Year 1
Aim by end of
year:
-All can add two
1 digit numbers
-Some can add a
1 digit number to
a 2 digit number
Showing method
used.
-All can count
back on a number
line to subtract 1
digit numbers
from a 1 or 2
digit number.
-Some can count
on when the
difference is
small.
E.g. Sarah wants 3 grapes and you want 4 grapes.
How many grapes do I need altogether?
Relate addition to combining two groups and
counting on and record in a number sentence using +
and = signs.
Record addition by:
- showing jumps on prepared number lines
- drawing own number line
e.g. 6 + 5 = 11
6
7
8
9
10
Solve practical problems in a real or role play
context and talk about own ideas, methods and
solutions
e.g. In a play shop put 10 pennies in a purse, pay for
something and say how much money they have left
Relate subtraction to taking away by counting back
and as counting on and record in a number sentence
using the – and = signs.
Record simple subtraction in a number sentence
using the – and = signs e.g.
There were 8 cakes on a plate. Mary ate 3 of them.
How many were left?
11
8–3=5
Addition
Subtraction
Using the empty number line to add 10 to a single
digit number.
e.g. 8 + 10 = 18
+10
Use objects to develop idea that the number of
objects started with and those taken away can be
represented by a subtraction calculation.
8
18
Use a number line to add a pair of single digit
numbers to bridge through 10 e.g.
8 + 5 = 13
Model this
strategy.
2 3
+2
+3
8
10
13
(see Framework – section 5 p.40)
Represent number line calculations in a number
sentence
e.g.
+1
+5
Shows 9 + 1 + 5 = 15
or
9 + 6 = 15
Bridge through a multiple of 10 e.g. add a single
digit to a teen’s number bridging through 20.
18 + 5 = 23
9
2
10
18
Or record as:
18 + 5 = 18 + 2 + 3
= 20 + 3
= 23
+3
20
1 2 3
23
4
5
6
7 8
9 10 11 12
What is the difference between 5 and 12?
(counting on) – marked line
1 2 3 4
5
6
7 8 9 10 11 12
What is the difference between 5 and 12? (counting
on) – empty line
5
15
3
+2
Use a marked or empty number line to count back
(take away) or to count on (find the difference) e.g.
12 – 7 (counting back) - marked line
12
Children need to begin to understand when it is
sensible to count back e.g. 18 – 5
13
14
15
16
17
18
And when it is sensible to count on e.g. 18 – 13
13
14
15
16
17
18
Say the number that is 1 less than any given number
or 10 less than a multiple of 10.
Say the number that is one more than any given
number and ten more than a multiple of ten.
Add 9 by adding 10 and subtracting 1.
Find the difference between two numbers by
comparing them using apparatus or on number lines
e.g. What is the difference between 4 and 7?
17 + 9
With cubes:
+ 10
17
26
-1
Partition numbers using place value cards
1
7
10
Aim by end of
year:
-All can add 1
digit number to a
2 digit number.
-Some can add
two 2 digit
numbers showing
method used.
-All can use a
number line to
subtract 2 digit
numbers
-Some can
subtract numbers
that cross 100.
or on two number lines:
4
7
17
=
10
+
7
And use calculator to confirm that numbers such as
57 are made up of 50 and 7 to develop their
understanding of place value.
Year 2
How many
more?
27
7
or on one number line:
4
7
Be able to complete number sentences where a
missing number is shown by a symbol e.g.
5+2= ∆
∆ =5+2
5+∆=7
7=∆+2
∆ + 2 =7
7=2 +∆
etc.
Generate equivalent calculations for given numbers
and record e.g. 6 =2 + 4 = 1 + 5 = 3 + 3
Be able to complete number sentences where a
missing number is shown by a symbol e.g.
6-2=∆
∆ =6-2
6-∆=4
4=∆-2
∆ -2=4
4=О-∆
etc.
Addition
Subtraction
Derive and recall pairs of numbers with a total of
10 and addition facts for totals to at least 5.
Solve simple problems explaining methods and
reasoning orally or in pictures in the context of
measures or money.
Use the language of addition accurately. Read 19 +
15 = 34 as nineteen add fifteen equals 34. Decide
the best strategy for addition: put the larger
number first and count on; look for numbers that
total 10 or 20; partition and recombine.
Use prepared number lines then progress on to
drawing own empty number lines to: e.g.
Solve simple problems involving subtraction in the
context of measure or money explaining reasoning
orally or in pictures
e.g. This bottle holds 5 cups of water but this bottle
holds 7 cups. How much more is in the bigger bottle?

23

count in tens 23 + 20
+10
+10
33
count in multiples of ten
+20
27
Use marked, partly marked or empty number lines to
count back (take away) or to count on (find the
difference) – as Y1. Understand when it is sensible
to count back and when to count on. e.g.

93 – 5 (count back) 93 - 88 (count on)
88
43
27 + 20
Use number lines or jottings to count back.
47
number line 45 + 13 =
+10
+3
93
76 – 15
To add tens and units by partition second number
(not crossing the tens or hundreds barrier) using
different methods of recording:

Use language of subtraction accurately. Read 16 – 4
= 12 as sixteen subtract 4 equals twelve.
-5
61
-10
66
76
Record in number sentences : 76 – 10 = 66
66 – 5 = 61
Bridge through multiple of 10 when counting back.
45
55
Record in number sentences
45 +10 = 55 55 + 3 = 58

-4
Lead to partitioning
- second number only.
35 + 20 + 3
55 + 3 = 58
using drawing
= 50
35 + 23
=8

71 – 25
not using number line, partitioning both
numbers
35 + 23
30 + 20 = 50
5+ 3=8
50 + 8 = 58

58
50 + 8 = 58
46
+4
51
71
Subtract 1 or 10 from any given number.
Relate finding a difference to subtraction.
Understand difference is the same as subtraction
and work out small differences by counting on.
Count on to the nearest 10.
3
16
50
-20
Record in number sentences: 71 -20 = 51
51 – 1 = 50
50 – 4 = 46
Bridge through a multiple of 10, explaining
method
16 + 7 = 23
4
-1
23 – 18 = 5
+2
+3
18
20
23
Develop into calculations that count on in three
jumps.
+3
20
23
or record as
16 + 7 = 16 + 4 + 3
= 20 + 3
= 23
91 – 65 (counting on)
+5
65
+20
70
+1
90
= 26
91
Addition
Subtraction
Add 1 or 10 to any given number.
Add 19 or 21 by adding 10 and adjusting.
e.g. 27 + 19 = 27 + 20 -1
= 47 -1
= 46
Using partitioning (second number only)
-not crossing 10
-crossing 10
48 – 23 = 48 – 20 – 3
73 – 25 = 73 -20 - 5
= 28 – 3
= 53 - 5
= 25
= 48
Or using empty number line
Subtract 9 or 19, by subtracting 10 or 20 and
adjusting.
E.g.
+20
27
46
-1
45 – 9 = 45 – 10 +1
= 35 +1
47
= 36
0r using empty number line
-10
35
36
45
+1
Use knowledge of facts to identify missing numbers
in sentences.
9 + ∆ = 13
∆+ 4 = 13
∆ + ◊ = 13
40 +  = 100
 +200 = 400 etc
Extend to 3 numbers:
and:
5 + ∆ + 4 = 13
13 + 5 = ∆ + 10
50 + ∆ + 3 = 73
12 + ∆ = 14 + 4 etc
Use knowledge of facts to identify missing numbers
in number sentences.
13 - ∆ = 9
∆-4 =9
∆ - ◊= 9 etc
Extend to:
13 + 5 = ∆ - 10 etc
Year 3
Aim by end of
year:
-All children add
two 2 digit
numbers.
-Some can add 2
and 3 digit
numbers, showing
method used.
-All children
should be able to
use a method to
subtract 2 and
3-digit numbers.
-Some should be
able to use
expanded
decomposition as
shown.
13 = ∆+ ◊+ 3 etc
Generate equivalent calculations for a given
number. e.g. 20
20 = 10 + 10 = 11 + 9 etc
Derive and recall all addition facts for each number
to at least 10, all pairs which total 20 and multiples
of 10 with totals up to 100.
Solve problems involving addition in contexts of
measures or pounds and pence explaining methods
and reasoning orally and where appropriate in
pictures and writing.
Use of mathematical vocabulary is more precise.
Develop methods for adding two digit and three
digit numbers by partitioning second number only.
246 + 87
246 + 80 + 7 or 246 + 7 + 80
356 + 427 = 356 + (400 + 20 + 7)
First step:
356 + 400 =756
756 + 20 = 776
776 + 7 = 783
Solve problems involving subtraction in contexts of
measures or pounds and pence explaining methods
and reasoning orally and where appropriate in
pictures and writing
e.g. In the sales my coat was reduced from £15.50
to £12.99. What was the difference in price?
Use of mathematical vocabulary is more precise.
Use a number line to count back alongside an
informal written method.
246 -47
leading to:
= 756 + 20 +7
= 776 + 7
= 783
-7
199
-40
206
246
246 – 40 = 206
206 - 7 = 199
Use knowledge of place value and partitioning of
three digit numbers to develop written methods
for addition of two and three digit numbers using
expanded methods of recording.
375 + 67
300
+
70
5
60
7
300 130
Expanded decomposition (see Framework – section 5
p45)
E.g. 81 – 57
leading to:
81
- 57
70
81 and 1 = 70 and 11
50 and 7 = 50 and 7
20 and 4
1
80 1
50 7
20 4 = 24
= 24
12 = 442
Addition
67
+ 24
80
11
91
Begin to record calculations in preparation for an
efficient standard method.
83
+ 42
120
5
125
Subtraction
Add most significant
digits first.
Add mentally from top.
This leads onto most
significant digits first.
Count up when the difference is small
(complementary addition) (Framework - Section 5
p45)
e.g. 216 -187
+13
Bridge through a multiple of 10 to add, explaining
method e.g.
68 + 7
2
5
= 68 + 2 + 5
= 70 + 5
= 75
187
+16
200
216
- 187
13 to make 200
= 29
216
16 to make 216
29
Add 1, 10 or 100 to any given number.
Add a near multiple of 10 to a two digit number and
show on a number line e.g.
45 + 28
+30
45
73
-2
75
Subtract 1, 10 or 100 from any given number.
Subtract a near multiple of 10 from a 2-digit
number, explaining the method used
e.g. 96 – 39 = 96 – 40 +1
= 56 +1
= 57
or
-40
56
Apply understanding of inverse relationship
between addition and subtraction to generate pairs
of statements to find unknowns in number
sentences.
4 + ∆ = 33
33 – 4 =
Use knowledge of number facts to find unknowns.
347 + ∆ = 447
Use 3 numbers e.g.
10 + ∆ + 50 = 100
∆ + ◊ + O = 100
Recall pairs of numbers with totals of 100 and
addition facts for totals to at least 20.
Solve problems explaining methods and reasoning
orally and where appropriate in pictures and
writing, in the context of measures money and
time.
Year 4
Aim by end of
year:
-All can use an
efficient written
method to add
and subtract 2
and 3 digit whole
numbers and
£.p.
but continue to
use counting up
method where
appropriate.
Note: ‘compact’
method is not
appropriate for
adding two 2-digit
numbers – this is a
mental method.
Use symbols and missing numbers:Continue to develop as in Y1, 2 and 3 but with
appropriate numbers. Develop use of empty number
lines, partitioning and other informal recording
methods developed in Y1,2 and 3 to support and
explain calculations where appropriate e.g.

146 +29
+30
146

175
-1
176
548 + 235
548 + 235 = 548 + 200 + 30 + 5
= 748 + 30 + 5
= 778 + 5
= 783
57
96
+1
Apply the understanding of the inverse relationship
between addition and subtraction to generate pairs
of statements to find unknowns in number
sentences.
∆ - 15 = 19
19 – 15 =∆
Use knowledge of number facts to find unknown
numbers.
∆ - ◊= 19
20 - ∆ - ◊= 5
etc
Solve one and two step problems involving
subtraction in contexts of measures money and time,
explain methods and reasoning orally in pictures and
writing
e.g. The bus left school at 8.30 and arrived at the
museum at 10.15. How long was the journey?
Continue to use counting up (complimentary addition)
method, with informal notes or jottings, when
appropriate e.g.
When subtracting from multiples of 100 or
1000

Finding a small difference by counting up
e.g. 5003 – 4996 =7. (can be modelled using an
empty number line or jottings)
+4
+3
=7

4996
5000
5003
 To support or explain mental calculations
e.g. 754 – 86 =
+ 14 + 600 + 54 = 668
+14
86
+600
100
+54
700
754
Addition
Subtraction
Begin expanded method, adding least significant
digit first
Explaining the subtraction of the nearest multiple of
10 and adjusting (see Y2/3 examples)
625
205
358
+ 48
+ 176
+ 973
13
11
11
60
70
120
600
300
1200
673
381
1331
If children find
this difficult go
back to first
stage (see Y3)
Teach expanded decomposition leading to compact
decomposition. (see Framework – section 6 p50)
-
754
86
-
= 700 and 40 and 14
80 and 6
This leads to preparing for ‘carrying’ below the line
(compact recording).
(see Framework – Section 6 p48)
To tens
to hundreds
tens and hundreds
625
783
367
+ 48
+ 42
+ 85
673
825
452
1
11
1
Cross out the
digit that has
been carried,
once it has been
added in.
Extend to decimals as appropriate e.g. money
knowing that the decimal points should line up
under each other.
Year 5
Aim by end of
year:
-Most children
are able to use
compact method
for addition and
compact
decomposition for
subtraction, when
appropriate,
(numbers up to
10,000 and
decimals) but
should continue
to use counting
up method,
where
appropriate.
Note: ‘compact’
method is not
appropriate for
adding two 2-digit
numbers – this is a
mental method.
= 700 and 50 and 4
80 and 6
= 600 and 140 and 14
80 and 6
Leading to:
754
- 86
600
= 700
600
1
50 4
80 6
60 8
= 668
= 668
Leading to:
7 '5 8
- 8 6
668
Extend to decimals as appropriate e.g. money
knowing that the decimal points should line up under
each other.
Use knowledge of addition facts and place value to
derive sums of pairs of multiples of 10, 100 or
1000.
Solve problems explaining methods and reasoning.
Solve problems explaining methods and reasoning.
Use symbols and missing numbers:Continue to develop as in Y1, 2, 3 and 4 but with
appropriate number.s
Continue to use counting up (complimentary addition)
method, with empty number lines, when appropriate
e.g.
Develop use of empty number lines, partitioning and
other informal recording methods to support and
explain calculations where appropriate (including
decimals).
125.64 + 56.7
125.64 + 50 + 6 + .7
175.64 + 6 + .7
181.64 + .7
182.34
50
6
0.7
When subtracting from multiples of 100 or 1000
Finding a small difference by counting up, or when
bridging across a boundary by a small amount.
e.g. 8006 – 2993 = 5013. (can be modelled using an
empty number line or jottings)
+7
+5000
+6
2993

125.64
175.64
181.64
182.34
1.8
-
3000
8000 8006
Using known number facts and place value to
subtract e.g. 4.1 – 1.8 = 2.3
+0.2
+2.0
+0.1
2.0
4.0
4.1
to support or explain mental calculations
to support or explain the subtraction of the
nearest multiple of 10 or 100 then adjust e.g.
4005 – 1997 = 4005 – 2000 +3
= 2005 +3
= 2008
Addition
Subtraction
Use compact (‘carrying’) method.
See (see Framework – section 6 p49 – Method C)
587
3587
+ 475
+ 675
1062
4262
Continue to develop compact decomposition with
different numbers of digits and decimals.
Note: Children should understand the importance of
lining up units digits under units digits, tens under
tens etc.
11
111
HTU + HTU then ThHTU + ThHTU
Children may need to return to expanded method
when first carrying out addition of decimals - least
significant digits first.
Ensure that children know the importance of ‘lining
up’ the decimal points particularly when adding
mixed amounts e.g. 16.4 m. + 7.68 m.
16.4
+ 7. 68
2 4 . 0 8m.
4
3
5 '7 6 4 .' 0
- 821. 6
4 942. 4
Children may need to return to expanded method
when first carrying out subtraction involving decimal
numbers. This reinforces understanding of place
value, particularly with decimals.
1 1
Year 6
Aim by the end
of Year 6:
-All children
should be able to
use carrying
method for
addition and
decomposition
method for
subtraction,
accurately and
reliably – when
appropriate but
should be able
use counting up
method, with
jottings, where
appropriate.
Note: ‘compact’
method is not
appropriate for
adding and
subtracting two 2digit numbers – this
is a mental method
Solve problems, explaining methods and reasoning
orally and in writing.
Solve problems, explaining methods and reasoning
orally and in writing.
Use symbols and missing numbers:Continue to develop as in earlier years but with
appropriate numbers (including decimals)
Develop use of empty number lines, partitioning and
other informal recording methods developed in
earlier years to support and explain calculations
where appropriate (including decimals).
Use compact (‘carrying’) method. As Y5, extend
method to any number of digits and decimal places
Use symbols and missing numbers:Continue to develop as in earlier years but with
appropriate numbers (including decimals)
Develop use of empty number lines, partitioning and
other informal recording methods developed in
earlier years to support and explain calculations
where appropriate (including decimals).
Continue to use complimentary addition, using an
empty number line, informal notes or jottings when
appropriate with appropriate numbers e.g.
For those children who have not mastered compact
method (see Framework – section 6 p49 Method C)
or are unable to use it reliably, use expanded
method, but teach again when appropriate.
 0.5 – 0.31
+0.09
= + 0.09 + 0.1 = 0.19
+0.1
0.31
0.40
0.50
 Subtracting the nearest multiple of 10,100, 1000
 Subtracting from any multiple of 1000, 10,000
Solve problems explaining methods and reasoning
orally and in writing.
etc i.e. where using decomposition would be very
complicated.
Continue to develop compact decomposition with
different numbers of digits and decimals.
Note: Children should understand the importance of
lining up digits.
Multiplication and Division
Year 3
Aim by end of
year:
-All can derive
and recall facts
for 2, 3, 4, 5, 6
and 10x tables.
-All understand
the three aspects
of multiplication
(repeated
addition,
describing an
array and scaling)
-All recognise all
multiples of 2, 5
and 10 up to
1000.
-All understand
division as
grouping or
sharing
-All solve division
calculations by
grouping on blank
number lines.
-All can round up
or down after
division depending
on the context
-All can derive
and recall
multiplication and
division facts for
2, 3,4,5,6 and
10 times tables.
Understand multiplication as:
 repeated addition
13 x 3
x10
x1
0
x1
x1
30 33 36 39
 describing an array
●●●●●●●●●●●●● 13 x 3
●●●●●●●●●●●●● = 10 x 3 + 3 x 3
●●●●●●●●●●●●● = 30 + 9 = 39
0
3 x 13
= 3 x 10
+3x3
= 30
+9
= 39
Begin to develop informal ways of calculating and
recording:
13 x 3
13
10 x3
3
30
9
(See Framework – section 5 p49)
Understand the operation of division as
 Sharing equally
 Grouping
As Y2, but use appropriate numbers
also that
 Division is the inverse of multiplication.
Ensure that grouping continues to be modelled by
adults and children on prepared and blank number
lines. E.g.
How many 5s make 35?
10
15
20
25
30
35
= Seven 5s make 35
Count forwards or backwards
Use practical and informal methods to support
division of larger numbers to encourage chunking.
52  4 = 13
x3
39
5
x 10
0
x1
x1 x1
40 44 48 52
 scaling
e.g. Make a tower 3 times taller then this.
Draw a line 4 times longer than this.
Know 2x, 3x, 4x 5x, 6x, 10x times tables.
Recognise multiples of 2, 5 and 10 up to 1000
Make links to multiplication square.
Be able to count in steps of 2,3,4,5, 6, 8 and 10.
Record mental multiplications in a number sentence
using x and = signs.
Recognise the use of symbols such as Δ or Ο to
stand for unknown numbers e.g.
6 x Δ = 18
Δ x 3 = 18
6 x 10 = Δ
Δ x Ο = 24
20 = Δ x 5
20 = 4 x Δ
etc.
To provide the children with skills for Y4 written
approaches, the objective ‘Use knowledge of number
facts and place value to multiply or divide mentally’
is important i.e.

multiply a single digit by 1,10 or 100.

dvide a three digit multiple of 100 by 10 or 100.

double any multiple of 5 up to 50.

halve any multiple of 10 to 100.

multiply a 2-digit multiple of 10 up to 50, by 2,
3, 4, 5 or 10.

multiply a 2-digit number by 2, 3, 4 or 5 without
crossing tens boundary ( e.g. 23 x 3 using
partitioning)
Record simple mental divisions in a number
sentence using the  and = signs.
e.g. ‘Divide 25 by 5’
Interpret division number sentences
e.g. 24  4 could mean
If 24 tulips are shared equally between 4 plant
pots, how many will be in each pot? or There are
55 children and they are put in teams of 5. How
many teams can we make?
64  2
‘I halved 60 to get 30, then halved 4 to get 2, then
I recombined the numbers to get 32.’
Round up or down after division, according to the
context.
Recognise the use of symbols such
□ or ∆ to stand for an unknown number. E.g.
16  4 = □
□ = 24  4
□ 3=6
35 □ = 7
8 □ = 2
8 = 16  □
□÷∆=5
20 – 14 = □  5
as
Begin to develop informal ways of calculating and
recording by partitioning and recombining. e.g.
17x5
10 x 5 = 50
7 x 5 = 35 50 + 35 = 85
Understand the concept of a remainder. E.g.
How many lengths of 10 cms can you cut from 51
cm of tape? How many will be left?
0
10
20
over.
Interpret situations as multiplication calculations
and explain reasoning e.g.

A baker puts 6 buns in each of 4 rows. How
many buns does she make?

Lee has 4 stickers. Ian has three times as many
as Lee. How many stickers does Ian have?
Year 4
Aim by end of
year:
-All are confident
with the grid
method way of
recording
multiplication and
are able to
explain reasoning
-All can derive
and recall
multiplication
facts up to 10 x
10 (including
multiplication by 0
and 1)
Derive and recall multiplication facts up to 10 x 10
(including multiplication by 0 and 1).
Be able to complete quickly.
e.g.
60 x 2 =
8x
= 32
x 4 = 160
Δ x
Understand the relationship between multiplication
and division and therefore be able to derive
division facts for 2, 3, 4, 5 and 10x tables. Begin
to know division facts for 6 and 8 x tables.
e.g.
8 x 4 =32 so 32  4 = 8 etc.
In preparation for repeated subtraction approach
for calculating and recording when using more
formal written methods, children should be
competent at subtracting multiples of 10 from any
number e.g. 117 – 20/30 etc.
Understand the operation of division as:

Grouping

Sharing

The inverse of multiplication (and use this to
check results)
See Y2/3 examples
= 120 etc
Understand that division is the inverse of
multiplication and use this to check results.
Further develop informal written methods (see
Y2/3) e.g. partitioning
It is important that children are taught to always
approximate first in order to get a sensible idea of
what the answer must be
Begin with ‘teens’ numbers e.g. 13 x 8, then progress
rapidly on to multiples of ten e.g. 23 x 8 (approx.
answer - between 160 and 200)
Partitioning
23 x 8
20 x 8 = 160
30
40
50 51
Answer: 5 lengths and 1 cm left
EITHER REPEATED ADDITION METHOD
Continue to model grouping on prepared or blank
number lines (and expect children to explain and
model it also) e.g.
72  5 = 14 remainder 2
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 72
leading to:
‘chunking’ ie.10 times the divisor is calculated in
one ‘chunk’ because it is quicker and more efficient
(do not push children on to this without
understanding, bead bar is excellent resource).
e.g. 72  5
10x5
3 x 8 = 24
0
72
23 x 8 = 160 + 24 = 184
or
23 x 8 = (20 x 8) + (3 x 8) = 160 + 24 = 184
x1 x1
x1 x1
50 55 60 65 70
Answer: 14 r. 2
or
(see Framework - section 6 p66)
23
x 7
20 x 8
160
3x8
24
184
This can be written vertically.
72 5
(10) 50
( 4) 20
70
+ 2 (remainder)
72
Answer: 14 r 2
and
OR REPEATED SUBTRACTION METHOD
Grid method (see Framework- Section 6 p66 –
Method A)
0 2 7
12 17 22 27 32 37 42 47 52 57 62 67 72
x
8
20
160
3
24
leading to:
=184
23 x 8 = 184
23 x 8
20 x 8 = 160
3 x 8 = 24
‘chunking’ ie.10 times the divisor is calculated in
one ‘chunk’ because it is quicker and more efficient
(do not push children on to this without
understanding, bead bar is excellent resource).
x1 x1
160 + 24 = 184
0 2 7
x1 x1
x 10
12 17 22
72
leading to:
(See Framework – section 5 p68)
72 5
72
- 50
22
- 20
2
Answer: 14 r.2
Progress to vertical expanded recording, multiplying
by the most significant digit first. (see Framework
– Section 6 p66 - Method B)
Record like this:
23 x 7
approx. ans. – bit larger than 140
23
x 7
140 (20 x 7)
21 ( 3 x 7)
161
When appropriate, still using expanded recording,
begin to record the least significant digit first, in
order to prepare children for teaching the ‘Compact
Standard Method i.e.
23
x 7
23
21
leading to
x7
140
16 1
161
2
Year 5
Aim by end of
year:
-All use an
efficient and
appropriate
written method
for multiplication
-All recall quickly
multiplication
facts up to 10 x
10 and use them
to multiply pairs
Interpret situations as multiplication calculations
and explain reasoning e.g.

There are 6 eggs in a box. How many in 45
boxes? (single step problem)

There are 4 stacks of plates. Three stacks
have 15 plates each. One stack has 5 plates.
How many plates are there altogether? (multistep problem)
Recall quickly multiplication facts up to
10 x 10, including multiplication by 0 and 1.
Complete written questions e.g.
160 x 2 = 
 x 2 = 290
0.9 x  = 6.3
Δ x  = 1600 etc
Understand that division is the inverse of
multiplication and use this to check results.
Continue to teach children to approximate answers
first.
(See Framework Section 6 p 67)
Continue to use informal methods of recording to
support and explain mental methods where the
numbers are appropriate.
It is important to ensure that children continue to
10 (10 groups of 5)
4 (4 groups of 5)
14
Children should be taught to approximate first to
gain a sensible idea of what the answer must be.
Record division calculations in a number sentence
where appropriate e.g.
How many lengths of 10 cm. Can you cut from 183
cm?
Could be recorded as 183  10
Explain methods and reasoning orally and in
writing, including whether to round up or down
after division (involving remainders) depending on
the context (using pencil and paper jottings or
mental strategies). e.g.
320   = 80
240  6 = 
  30 = 8
(25   ) + 2 = 7
(  5) – 2 = 3
Understand the different aspects of division and
use as appropriate. (see Y2/3/4 examples)
Continue to develop method of recording division
from Year 4 progressing to
HTU  U, ‘chunking’ 20x and 30x the divisor, where
appropriate.
This can be modelled on a blank number line e.g.
256  7
REPEATED ADDITION METHOD
of multiples of 10
and 100.
-All quickly derive
the corresponding
division facts.
- All can use the
‘chunking’ method
division (using
20/30x the
divisor, if
appropriate) and
the schools’
chosen method of
recording with
HTU  U
calculations. Those who cannot
are able to use
10x the divisor.
-All can explain
methods and
reasoning and
whether to round
up or down after
division depending
on context.
use informal methods of recording to support and
explain their mental methods where the numbers are
appropriate
i.e. they do not use formal recording where it is
inappropriate. E.g. 47 x 5
40 x 5 = 200
7 x 5 = 35
200 + 35 = 235
Begin with the ‘grid’ method. E.g. 72 x 38
ans. approx. 70 x 40 = 2800
x
70
2100
560
30
8
2
60
16
2160
576 +
2736
Only progress to compact recording for children
for whom it is appropriate. It is important to
show links to the grid method.
(see Framework – section 6 p67)
72
72
x 38
x 38
30 x 70 2100
72 x 30 2160
30 x 2
60
leading to
72 x 8
576
8 x 70
560
2736
8x2
16
1
2736
1
20x7
10x7
0
140
= 36 r 4
5x7
210
1x7
245
252
r.4
256
leading to:
140 (20)
70 (10)
210
42 (6)
252
4 (remainder)
256
Answer: 36 r.3
WHEN READY MOVE FROM REPEATED
ADDITION TO REPEATED SUBTRACTION.
r4
0
256
x6
4
x10
46
x20
116
(see Framework – section 6 p69)
leading to:
256  7
256
- 140
116
- 70
46
42
4
Answer: 36 r.4
(20)
(10)
(6)
leading to:
256  7
-
Answer: 36 r 4
Children should be taught to approximate first to
gain a sensible idea of what the answer must be
Interpret situations as multiplication calculations
and explain reasoning e. g.

I think of a number, then divide it by 15. The
answer is 20. What was my number?

There are 8 shelves of books. Six of the
shelves hold 25 books each. Two of the shelves
have 35 books each. How many books are there
altogether on the shelves?
Extend to simple decimals, with one decimal place,
multiplied by a single digit. Approximate first. E.g.
4.9 x 3 is approx. 5x3 = 15
4.9 x 3
x
4
0.9
3
12
2.7
12 + 2.7 =14.7
256
210 ( 30)
46
42 (6)
4
Children should be taught to approximate first to
gain a sensible idea of what the answer must be.
Explain methods and reasoning orally and in
writing, including whether to round up or down
after division (involving remainders) depending on
the context.
Complete written questions (using pencil and paper
jottings or mental strategies). E.g.
54   = 18
186  6 = 
leading to 4.9
x 3
14.7
  40 = 12
(125  ) + 2 = 27
(   5) – 22 = 30
2
Year 6
Aim by end of
year:
-All use an
efficient and
appropriate
method for
multiplication.
-All use
knowledge of
place value and
multiplication fats
to 10 x 10 to
derive related
multiplication and
division facts
involving decimals.
- All can use an
appropriate
method for short
division for any
numbers, including
decimals.
-All can explain
methods and
reasoning and
whether to round
up or down after
division depending
on context.
-All use
knowledge of
place value and
multiplication
facts up to
10x10 to derive
related
multiplication and
division facts
involving decimals
e.g., 0.8 x 7,
4.8 ÷ 6
Use knowledge of place value and multiplication
facts to 10 x 10 to derive related multiplication and
division facts involving decimals.
Complete written questions e.g.
0.7 x 20 = 
 x 20 = 8000
4 x  = 3.6
Δ x  = 2.4 etc
Understand that division is the inverse of
multiplication and use this to check results
Continue to teach children to approximate answers
first.
(See Framework – Section 6 p67)
Continue to use partitioning ‘grid’ or expanded
methods if appropriate (see y4/5)
It is important to ensure that children continue to
use informal methods of recording to support and
explain their mental methods where the numbers are
appropriate i.e. they do not use formal recording
where it is inappropriate
e.g. 8.6 x 7
(approx. as: between 56 and 63)
Understand the different aspects of division and
use as appropriate. (see Y2/3 examples)
8 x 7 = 56
0.6 x 7 = 4.2
56 + 4.2 = 60.2
Continue to use ‘grid’ method if it is more reliable
and better understood.
372 x 24
x
300
70
2
= 7440
20
6000
1400
40
= 1488 +
4
1200
280
8
8928
leading to:
372
x 24
6000 (300 x 20)
1400 (70 x 20)
40
(2 x 20)
1200 (300 x 4)
280
(70 x 4)
8
(2 x 4)
8928
360 (10)
+ 360 (10)
720
+ 180 (5)
900
+ 72 (2)
972
+ 5 (remainder)
977
Answer: 27 remainder 5
leading to:
(see framework – Section 6 p67)
372
x 24
7740 (372 x 20)
1488
(372 x 4)
8928
Interpret situations as multiplication calculations
and explain reasoning e.g.

There are 35 rows of chairs. There are 28
chairs in each row. How many chairs are there
altogether?

There is space in a multi-storey car park for 17
rows of 30 cars on each of 4 floors. How many
cars can park?

960 marbles are put into 16 bags. There is the
same number of marbles in each bag. How many
marbles are there in 3 of these bags?
Extend to decimals, with up to 2-decimal places,
Continue to develop method of recording division
from Year 5, ‘chunking’ multiples of 10x the divisor
(20/30x etc) – see year 5 examples.
Develop the compact method for short division if
appropriate (see Y5).
Teach long division (HTU  TU) using ‘chunking’
method that school prefers i.e. ‘repeated
subtraction’ or ‘counting on’ method.
Children should approximate answers first e.g.
REPEATED ADDITION
977  36 is approximately 1000  40 = 25
REPEATED SUBTRACTION (see Framework –
section 6 p69)
977
- 360
(10)
617
- 360
10
257
- 180
5
77
- 72
2
5
27
Answer: 27 remainder 5
When appropriate develop an efficient standard
method (see Framework - section 6 p 69) e.g.
972  36
_____
27
36) 972
36) 9 7 2
- 720
20
-720
252
252
- 252
7
- 252
0
0
Answer: 27
Extend to decimals with up to 2 decimal places as
multiplied by a single digit e.g.
4.92 x 3 (answer approx: 15)
x
3
4
12
0.9
2.7
0.02
0.06
= 12 +2.7 + 0.06 = 14.76
appropriate and using school’s chosen method of
recording i.e. ‘chunking’ or compact short division.
Complete written questions e.g.
= 14.76
9.9   = 1.1
6.3  7 = 
  5 = 0.8
(100   ) + 5 = 7.5
(  25) – 22 = 30
Leading to:
(Framework – section 6 p67)
x
4.92
3
12.00
2.70
0.06
( 4x 3)
(0.9 x 3)
(0.2 x 3)
This Policy has been created by Miss E Weedon (Co-ordinator for Numeracy) in April
2010, in consultation with staff and governors, and will be reviewed in line with the
school’s Policy review programme in April 2012.