# Calculations multdiv

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```					                       CALCULATION POLICY – MULTIPLICATION AND DIVISION

Multiplication                                           Division
Solve practical problems in a real or role play          Understand sharing as giving everyone the same
Foundation
context e.g.                                             amount e.g.
Stage                      How many shoe lace holes are there on this           6 grapes are shared equally between 2 people. How
Aim by end of               shoe?                                                many grapes does each one get?
year:                      Put 5 cherries on each cake. How many cherries
-All can count in           do you need?
2s, 5s and 10s
and solve practical     Oral counting in twos, fives and tens.
problems in a real
or role play            Count repeated groups of the same size.                  Solve practical problems in a real or role play
context.                                                                         context e.g.
-All understand                                                                     How many pairs of socks are there in the
sharing as giving                                                                    drawer? Can you cut the cake in half? How many
everyone the                                                                         pieces are there?
same amount and                                                                     Share objects into equal groups and count how
solve problems by                                                                    many in each group – e.g., ask three children to
sharing objects                                                                      share 6 sweets – can you share these sweets
into equal groups.                                                                   between you?

Observe number patterns in the environment – e.g., odd and even numbers on doors
Sing nursery rhymes with number patterns
Solve practical problems that involve combining       Understand sharing as giving everyone the same
Year 1
groups of 2, 5 and 10 e.g.                            amount e.g.
Aim by end of year:
-All can count in       How many fingers are there on 4 hands (draw round         6 grapes are shared equally between 2 people.
twos, fives and tens    own hands and numbers underneath)                          How many grapes does each one get?
and can derive                                                                    You have 12 wheels, how many cars can you
multiples of 2,5 and                                                               make? (draw a car to go with each group of 4
10.                                                                                wheels until 12 wheels have been used)
-All can solve real
problems involving
Count in 2s, 5s and 10s to derive the multiples of 2,5
combining groups.
-All understand         and 10.
sharing as giving
everyone the same                                                                Link to arrays.
amount and solve                                                                 Model number sentences in context.
problems by sharing
objects into equal
groups.

Understand multiplication as repeated addition e.g.      (See Framework – section 5 p49)
Year 2
There are 5 pencils in one packet, how many pencils      Understand division as Sharing equally
Aim by end of
in 4 packets?                                            E.g. 6 sweets are shared equally between 2 people.
year:
lllll lllll lllll lllll =                                How many sweets does each one get?
-Most know 2x,5x
5+5+5+5
and 10x tables
or
and be able to
4 lots of 5
derive division
or
facts.
4x5                                                      and as Grouping (this is repeated subtraction)
-Most understand
E.g. There are 15 apples in a box. How many bags of 5
multiplication as       This can also be shown as repeated jumps on a            apples can be filled? I.e. How many groups of 5 can you
repeated addition       number line (modelling on bead bar is useful image).     make from 15?
array. –                                                                                                                          arrays.
Most understand
the different                0         5         10              15      20      Grouping should also be modelled on a number line.
interpretations of                                                               Use prepared number lines and children draw own as
Understand multiplication as describing an array.
division.                                                                        appropriate
●●●●●
-In preparation                                                                  e.g. 8 children are put into teams of 2. How many teams are
● ● ● ● ● 5 x 4 = 20 (explained a 5 four times)
for repeated                                                                     there? (i.e. How many groups of 2 are there in 8?)
●●●●●
subtraction
●●●●●
approach for                                                                     0   2             4        6         8
4 x 5 = 20 (explained as 4 five times)
82=4

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CALCULATION POLICY – MULTIPLICATION AND DIVISION

calculating and        Relate to real life contexts. Make links between
recording when         arrays and number lines.                                 8 cakes are put into boxes of 4. How many boxes are there?
using more formal                                                               I.e. How many groups of 4 are there in 8?    84=2
written methods,
children should be                                                              0                4                       8
able to subtract                                                                84=2
10 from any                                                                     Count forwards and backwards.
number and begin                                                                Record simple mental divisions in a number sentence
to be able to                                                                   using the  and = signs.
subtract multiples                                                              e.g. ‘Share 18 between 2’ could be recorded as 18  2
of 10 (20/30 etc)      Derive and recall facts for 2x, 10x and 5x tables.       Explain methods and reasoning orally this includes
from any number.       Begin to know their 3x table.                            being able to interpret division number sentences
Also know how to manipulate number trios – e.g., 2, 6,   e.g. 20  4 could mean
12:                                                           If £20 is shared between 4 people how much
2 x 6 = 12                                                    would each get?
6 x 2 = 12                                                   There are 20 children and they sit in tables of
12 ÷ 6 = 2,                                                   4. How many tables will we need?
12 ÷ 2 = 6
Record simple mental multiplications in a number
sentence using x and = signs.
Recognise the use of symbols such as     □    or ∆ to
Recognise the use of symbols such as Δ or Ο to           stand for an unknown number e.g.
stand for unknown numbers e.g.                           12  2 =   □       □ = 12    2         □     2 =6
12   = 6          6 = 2             6 = 12  
6 x Δ = 12         Δ x 2 = 12
  ∆ = 10 etc
6x2=Δ              Δ x Ο = 12
20 = Δ x 5         20 = 4 x Δ     etc.
Begin to interpret situations as multiplications         Understand the relationship between multiplication
calculations and explain reasoning e.g.                  and division and therefore be able to derive division
    How many wheels are there on 3 cars?                facts for 2x, 5x and 10x tables.
    Katy’s box is 5 cm wide. Mary’s box is twice as     E.g. 5 x 10 =50 so 50  10 = 5
wide as Katy’s box. How wide is Mary’s box?             10 x 5 = 50       50  5 = 10 etc.
Understand multiplication as:                            (See Framework – section 5 p49)
Year 3
Understand the operation of division as
Aim by end of
 repeated addition                                       Sharing equally
year:
13 x 3                                                    Grouping
-All can derive
x10                                           As Y2, but use appropriate numbers
and recall facts
x1   x1   x1              also that
for 2, 3, 4, 5, 6
 Division is the inverse of multiplication.
and 10x tables.
0                           30 33 36 39                 Ensure that grouping continues to be modelled by
-All understand
adults and children on prepared and blank number
the three aspects
 describing an array                                    lines. E.g.
of multiplication
●●●●●●●●●●●●● 13 x 3                                     How many 5s make 35?
(repeated
●●●●●●●●●●●●● = 10 x 3 + 3 x 3
●●●●●●●●●●●●● = 30 + 9 = 39
describing an
0     5     10     15      20     25     30     35
array and scaling)
-All recognise all
3 x 13                                                   = Seven 5s make 35
multiples of 2, 5
= 3 x 10     +3x3
and 10 up to
= 30         +9                                          Count forwards or backwards
1000.
= 39
-All understand
Begin to develop informal ways of calculating and        Use practical and informal methods to support
division as
recording:       13 x 3                                  division of larger numbers to encourage chunking.
grouping or
13
sharing
52  4 = 13
-All solve division
calculations by
10 x3         3   x3                               x 10             x1    x1 x1
grouping on blank
number lines.
30             9
-All can round up
0                          40 44 48 52
or down after
39
division depending
 scaling
on the context
e.g. Make a tower 3 times taller then this.
-All can derive
Draw a line 4 times longer than this.
and recall

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CALCULATION POLICY – MULTIPLICATION AND DIVISION

multiplication and     Know 2x, 3x, 4x 5x, 6x, 10x times tables.                Record simple mental divisions in a number sentence
division facts for     Recognise multiples of 2, 5 and 10 up to 1000            using the  and = signs.
2, 3,4,5,6 and 10      Make links to multiplication square.                     e.g. ‘Divide 25 by 5’
times tables.          Be able to count in steps of 2,3,4,5, 6, 8 and 10.
Record mental multiplications in a number sentence       Interpret division number sentences
using x and = signs.                                      e.g. 24  4 could mean
If 24 tulips are shared equally between 4 plant pots,
Recognise the use of symbols such as Δ or Ο to           how many will be in each pot? or There are 55
stand for unknown numbers e.g.                           children and they are put in teams of 5. How many
6 x Δ = 18       Δ x 3 = 18                              teams can we make?
6 x 10 = Δ       Δ x Ο = 24                              64  2
20 = Δ x 5       20 = 4 x Δ       etc.                   ‘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.
To provide the children with skills for Y4 written       Recognise the use of symbols such
approaches, the objective ‘Use knowledge of number       as □ or ∆ to stand for an unknown number. E.g.
facts and place value to multiply or divide mentally’
16  4 = □      □ = 24  4
is important i.e.
    multiply a single digit by 1,10 or 100.             □ 3=6          35 □ = 7
    dvide a three digit multiple of 100 by 10 or 100.   8 □ = 2        8 = 16  □
    double any multiple of 5 up to 50.                  □÷∆=5
    halve any multiple of 10 to 100.
20 – 14 = □  5
    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)
Begin to develop informal ways of calculating and        Understand the concept of a remainder. E.g.
recording by partitioning and recombining. e.g.          How many lengths of 10 cms can you cut from 51 cm
17x5                                                     of tape? How many will be left?
10 x 5 = 50
7 x 5 = 35 50 + 35 = 85                                 0    10      20      30      40    50 51
Answer: 5 lengths and 1 cm left over.

Interpret situations as multiplication calculations      Understand the relationship between multiplication
and explain reasoning e.g.                               and division and therefore be able to derive division
    A baker puts 6 buns in each of 4 rows. How          facts for 2, 3, 4, 5 and 10x tables. Begin to know
many buns does she make?                            division facts for 6 and 8 x tables.
    Lee has 4 stickers. Ian has three times as many     e.g.    8 x 4 =32 so 32  4 = 8 etc.
as Lee. How many stickers does Ian have?            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.
Derive and recall multiplication facts up to 10 x 10     Understand the operation of division as:
Year 4
(including multiplication by 0 and 1).                       Grouping
Aim by end of
Be able to complete quickly.                                 Sharing
year:
e.g.                                                         The inverse of multiplication (and use this to
-All are confident
60 x 2 =                 x 4 = 160                            check results)
with the grid
8x      = 32         Δ x       = 120 etc
method way of
See Y2/3 examples
recording
Understand that division is the inverse of
multiplication and
multiplication and use this to check results.
are able to
Further develop informal written methods (see            EITHER REPEATED ADDITION METHOD
explain reasoning
Y2/3) e.g. partitioning                                  Continue to model grouping on prepared or blank
-All can derive
It is important that children are taught to always       number lines (and expect children to explain and
and recall
approximate first in order to get a sensible idea of     model it also) e.g.
multiplication
what the answer must be                                  72  5 = 14 remainder 2
facts up to 10 x
Begin with ‘teens’ numbers e.g. 13 x 8, then progress
10 (including
rapidly on to multiples of ten e.g. 23 x 8 (approx.      0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 72
multiplication by 0
and 1)
‘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,
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CALCULATION POLICY – MULTIPLICATION AND DIVISION

Partitioning                                            bead bar is excellent resource).
23 x 8                                 e.g. 72  5

20 x 8 = 160                  3 x 8 = 24                            10x5               x1 x1    x1 x1

0                           50 55 60 65 70 72

23 x 8 = 160 + 24 = 184                Answer: 14 r. 2
or
23 x 8 = (20 x 8) + (3 x 8) = 160 + 24 = 184            This can be written vertically.
72 5
or                                                      (10) 50
(see Framework - section 6 p66)                          ( 4) 20
23                                                 70
x 7                                                  + 2 (remainder)
20 x 8     160                                                  72
3x8        24                                          Answer: 14 r 2
184
OR REPEATED SUBTRACTION METHOD
and

Grid method (see Framework- Section 6 p66 –              0 2 7   12 17 22 27 32 37 42 47 52 57 62 67 72
Method A)
x   20    3
8   160   24      =184               ‘chunking’ ie.10 times the divisor is calculated in one
‘chunk’ because it is quicker and more efficient (do
23 x 8 = 184                                            not push children on to this without understanding,
23 x 8                                                      x1 x1     x1 x1            x 10
20 x 8 = 160
3 x 8 = 24      160 + 24 = 184                             0 2 7     12 17 22                        72

(See Framework – section 5 p68)

72 5
72
- 50        10 (10 groups of 5)
22
- 20         4 (4 groups of 5)
2        14

Children should be taught to approximate first to
gain a sensible idea of what the answer must be.
Progress to vertical expanded recording, multiplying    Record division calculations in a number sentence
by the most significant digit first. (see Framework –   where appropriate e.g.
Section 6 p66 - Method B)
How many lengths of 10 cm. Can you cut from 183
Record like this:
cm?
23 x 7
Could be recorded as 183  10
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
140                    16 1
161                      2

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CALCULATION POLICY – MULTIPLICATION AND DIVISION

Interpret situations as multiplication calculations      Explain methods and reasoning orally and in writing,
and explain reasoning e.g.                               including whether to round up or down after division
      There are 6 eggs in a box. How many in 45         (involving remainders) depending on the context
boxes? (single step problem)                      (using pencil and paper jottings or mental
      There are 4 stacks of plates. Three stacks have   strategies). e.g.
15 plates each. One stack has 5 plates. How       320   = 80          240  6 = 
many plates are there altogether? (multi- step       30 = 8           (25   ) + 2 = 7
problem)                                          (  5) – 2 = 3
Recall quickly multiplication facts up to                Understand the different aspects of division and
Year 5
10 x 10, including multiplication by 0 and 1.            use as appropriate. (see Y2/3/4 examples)
Aim by end of
Complete written questions e.g.
year:
160 x 2 =              x 2 = 290
-All use an
0.9 x  = 6.3          Δ x  = 1600 etc
efficient and
Understand that division is the inverse of
appropriate
multiplication and use this to check results.
written method
Continue to teach children to approximate answers        Continue to develop method of recording division
for multiplication
first.                                                   from Year 4 progressing to
-All recall quickly
(See Framework Section 6 p 67)                           HTU  U, ‘chunking’ 20x and 30x the divisor, where
multiplication
Continue to use informal methods of recording to         appropriate.
facts up to 10 x
support and explain mental methods where the             This can be modelled on a blank number line e.g.
10 and use them
numbers are appropriate.                                 256  7
to multiply pairs
It is important to ensure that children continue to     REPEATED ADDITION METHOD
of multiples of 10
use informal methods of recording to support and                  20x7               10x7           5x7         1x7   r.4
and 100.
explain their mental methods where the numbers are
-All quickly derive                                                             0                     140            210         245   252    256
appropriate
the corresponding                                                               = 36 r 4
i.e. they do not use formal recording where it is
division facts.
inappropriate. E.g. 47 x 5
- All can use the                                                               leading to:
40 x 5 = 200
‘chunking’ method
7 x 5 = 35           200 + 35 = 235                        140 (20)
division (using
20/30x the                                                                            70 (10)
Begin with the ‘grid’ method. E.g. 72 x 38                   210
divisor, if
ans. approx. 70 x 40 = 2800                                    42 (6)
appropriate) and
the schools’                                                                        252
x          70        2                                      4 (remainder)
chosen method of
30   2100       60           2160                    256
recording with
8    560       16           576 +               Answer: 36 r.3
HTU  U
2736
calculations. -
Those who cannot                                                                WHEN READY MOVE FROM REPEATED
Only progress to compact recording for children
are able to use                                                                 ADDITION TO REPEATED SUBTRACTION.
for whom it is appropriate. It is important to
10x the divisor.       show links to the grid method.
-All can explain                                                                        r4       x6          x10                   x20
(see Framework – section 6 p67)
methods and                         72                               72
reasoning and                                                                       0        4        46               116                         256
x 38                             x 38
whether to round        30 x 70 2100                    72 x 30 2160            (see Framework – section 6 p69)
up or down after        30 x 2      60      leading to   72 x 8    576
8 x 70     560                           2736
on context.             8x2         16                             1            256  7           256
2736                                                          - 140         (20)
1
116
- 70          (10)
46
-     42         (6)
4

256  7               256
-   210 ( 30)
46
-    42 (6)
4

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CALCULATION POLICY – MULTIPLICATION AND DIVISION

Children should be taught to approximate first to       Children should be taught to approximate first to
gain a sensible idea of what the answer must be         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,      Explain methods and reasoning orally and in writing,
multiplied by a single digit. Approximate first. E.g.   including whether to round up or down after division
4.9 x 3 is approx. 5x3 = 15                             (involving remainders) depending on the context.
Complete written questions (using pencil and paper
4.9 x 3
jottings or mental strategies). E.g.
x    4      0.9
3    12     2.7     12 + 2.7 =14.7
54   = 18             186  6 = 
  40 = 12
(125  ) + 2 = 27     (   5) – 22 = 30
x 3
14.7
2
Use knowledge of place value and multiplication facts   Understand the different aspects of division and
Year 6
to 10 x 10 to derive related multiplication and         use as appropriate. (see Y2/3 examples)
Aim by end of
division facts involving decimals.
year:
Complete written questions e.g.
-All use an
0.7 x 20 =         x 20 = 8000
efficient and
4 x  = 3.6       Δ x  = 2.4 etc
appropriate
Understand that division is the inverse of
method for
multiplication and use this to check results
multiplication.
Continue to teach children to approximate answers       Continue to develop method of recording division
-All use
first.                                                  from Year 5, ‘chunking’ multiples of 10x the divisor
knowledge of
(See Framework – Section 6 p67)                         (20/30x etc) – see year 5 examples.
place value and
Continue to use partitioning ‘grid’ or expanded
multiplication fats
methods if appropriate (see y4/5)                       Develop the compact method for short division if
to 10 x 10 to
It is important to ensure that children continue to     appropriate (see Y5).
derive related
use informal methods of recording to support and        Teach long division (HTU  TU) using ‘chunking’
multiplication and
explain their mental methods where the numbers are      method that school prefers i.e. ‘repeated
division facts
appropriate i.e. they do not use formal recording       subtraction’ or ‘counting on’ method.
involving decimals.
where it is inappropriate                               Children should approximate answers first e.g.
- All can use an
e.g. 8.6 x 7
(approx. as: between 56 and 63)
method for short                                                               977  36 is approximately 1000  40 = 25
division for any
8 x 7 = 56                                                  360 (10)
numbers, including
0.6 x 7 = 4.2       56 + 4.2 = 60.2                      + 360 (10)
decimals.
Continue to use ‘grid’ method if it is more reliable        720
-All can explain
and better understood.                                    + 180 (5)
methods and
372 x 24                                                    900
reasoning and
x       300        70          2                        + 72 (2)
whether to round
20     6000     1400          40       = 7440             972
up or down after
4    1200       280          8       = 1488 +          + 5 (remainder)
division depending
8928             977
-All use                             372
knowledge of                      x 24                                         REPEATED SUBTRACTION (see Framework –
place value and                    6000 (300 x 20)                             section 6 p69)
multiplication                     1400 (70 x 20)                                   977
facts up to 10x10                     40     (2 x 20)                             - 360       (10)
to derive related                   1200 (300 x 4)                                  617
multiplication and                   280     (70 x 4)                            - 360         10
division facts                         8      (2 x 4)                               257
involving decimals                  8928                                         - 180          5
e.g., 0.8 x 7,                                                                       77
4.8 ÷ 6                leading to:                                               - 72           2
5        27

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CALCULATION POLICY – MULTIPLICATION AND DIVISION

(see framework – Section 6 p67)
372
x    24
7740 (372 x 20)
1488      (372 x 4)
8928
Interpret situations as multiplication calculations     When appropriate develop an efficient standard
and explain reasoning e.g.                              method (see Framework - section 6 p 69) e.g.
    There are 35 rows of chairs. There are 28
chairs in each row. How many chairs are there      972  36
altogether?                                            _____                        27
    There is space in a multi-storey car park for 17     36) 972                   36) 9 7 2
rows of 30 cars on each of 4 floors. How many          - 720        20            -720
cars can park?                                            252                      252
    960 marbles are put into 16 bags. There is the          - 252        7           - 252
same number of marbles in each bag. How many                0                           0
marbles are there in 3 of these bags?              Answer: 27
Extend to decimals, with up to 2-decimal places,        Extend to decimals with up to 2 decimal places as
multiplied by a single digit e.g.                       appropriate and using school’s chosen method of
4.92 x 3 (answer approx: 15)                            recording i.e. ‘chunking’ or compact short division.
Complete written questions e.g.
x         4       0.9     0.02
3        12       2.7     0.06        = 14.76
9.9   = 1.1        6.3  7 = 
  5 = 0.8
= 12 +2.7 + 0.06 = 14.76                                (100   ) + 5 = 7.5       (  25) – 22 = 30

(Framework – section 6 p67)

4.92
x       3
12.00   ( 4x 3)
2.70     (0.9 x 3)
0.06     (0.2 x 3)

Page 7                                     May 2009

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