# Whole School Written Calculation Policy

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"Whole School Written Calculation Policy"

```					                                                      Calculation Strategies – St. Bernadette’s R.C School.
NUMBER FACTS                                                         NURSERY                                                       REC
FS: Nursery and Reception:
    Nursery rhymes- number names                           Look at amounts and compare.                                Responds to the vocabulary involved in addition.
    Say number names in order.                             Children can look at an amount of objects and compare by    Number rhymes and games.
    Recognise numerals 0-9.                                saying there are more in one set and less in the other.
    Count reliably 10 objects.
    Order numbers to 10.                                                                                               Find 1 more/ 1 less.
    Match correct amount of objects to numerals.
Children find one more by using objects and adding 1
    Mental recall of number bonds.
KS1: Yr 1 and Yr2:                                                                                                          more to the group of up to 5 objects.
    Say number names to 100.                               Responds to the vocabulary involved in addition.
    Number bonds to 10/20/100.                             Number rhymes and games.                                    Sorting/rote count/ counting objects
    Count in 2’s/5’s/10’s.                                                                                             Mental counting using fingers/ objects.
    Count reliably 20 objects/ objects in sets of ten to   Count a groups of objects .
100.                                                   Children count a group of objects accurately.
    Order numbers on a number line/ 100 square.
    Partition 2 digit numbers.                                                                                         Look at amounts and compare.
    2x/5x/10x/3x/4x tables.                                                                                            Children can look at an amount of objects and
KS2 – Yr3 and Yr4:
Find 1 more/ 1 less.
Children find one more by using objects and adding 1 more   compare by saying there are more in one set and less
    Number bonds to 10/20/100.                                                                                         in the other through counting each amount.
    Read, write order numbers to 1000.                     to the group.
    Order numbers to 1000 on a number line.
    Partition 3/4 digit numbers.
Count two groups of objects together using
    Round to nearest 10/100/1000.
    Read and write proper fractions 3/7 and identify
objects.
equivalent fractions 6/8, 3/4.                                                                                     Children combine two groups of objects to make a total
    Recognise decimal facts.                                                                                           amount.
    3x/4x/6x/7x/8x/9x tables.
KS2 – Yr 5 and Yr6:                                                                                                         Count two groups of objects using pictures.
    Count and order numbers on a number line in                                                                        3 +2 = 5
whole and decimal steps extend beyond zero when
counting back.
    Say what each digit represents in decimals.
    Relate fractions to decimal/ simplify fractions by
cancelling common factors.
    Understand percentage as the number of parts in                                                                    Find 1 more/ 1 less.
every whole/ express one quantity as a percentage                                                                  Children find one more by using a number line up to
of another.                                                                                                        10.
    Find difference between positive and negative
integers.

CK/MD Strategy calculation policy
Year 1                                                    Year 2                                                   Year 3
Sorting/rote count/ counting objects
Mental counting using fingers objects.                      + = signs and missing numbers                               + = signs and missing numbers
Continue using a range of equations as in Year 1 but with   Continue using a range of equations as in Year 1 and
Count two groups of objects using pictures.                 appropriate, larger numbers.                                2 but with appropriate, larger numbers.
3 +2 = 5                                                    Extend to
14 + 5 = 10 + 
32 +  +  = 100 35 = 1 +  + 5

Partition into tens and ones and recombine                  Partition into tens and ones and recombine
Partition both numbers and recombine. Refine to
Finding 1 more and less than a number.                                                                                  partitioning the second number only e.g.
12 + 23 =
(10 +20) + (2+3)                                            36 + 53 = 53 + 30 + 6
Number lines (numbered)                                             = 30 + 5                                                     = 83 + 6
= 35                                                         = 89
7+4
refine to partitioning the second number only:
0    1    2   3   4     5    6   7   8   9   10   11   12                                                                                +30                   +6
23 + 12 = 23 + 10 + 2
Recording by - drawing jumps on prepared lines                      = 33 + 2
= 35
-       constructing own lines                                                                             53                             83           89
+10                   +2
( Teacher model number lines with missing
Add a near multiple of 10 to a two-digit number
numbers)                                                                                                                Continue as in Year 2 but with appropriate numbers
(Teachers model jottings appropriate for larger              23                               33            35          e.g. 35 + 19 is the same as 35 + 20 – 1.
numbers)                                                    Mental strategy
+ = signs and missing numbers                                                                                           Pencil and paper procedures
35 + 9 = 44
35+10-1=44                                                  83 + 42 = 125
3+4=                   =3+4                                                                                                                             AA set
3+=7                   7=+4
+4=7                   7=3+                                                   +10                                      80   3                                83
+=7                   7=+                                                                                           +40   2                              + 42
Promoting covering up of operations and                                                                                 120   5 =125                            5
numbers.                                                                                                                                                      120
35                       44          45                                                         125
-1

CK/MD Strategy calculation policy
Year 4                                                    Year 5                                                    Year 6
+ = signs and missing numbers                            + = signs and missing numbers                                  + = signs and missing numbers
Continue using a range of equations as in Year 1 and     Continue using a range of equations as in Year 1 and 2 but     Continue using a range of equations as in Year 1 and
2 but with appropriate numbers.                          with appropriate numbers.                                      2 but with appropriate numbers.

Partition into tens and ones and recombine               Mental Strategy: Partition into HTU and recombine              Add the nearest multiple of 10, 100 or 1000, then
Either partition both numbers and recombine or           Either partition both numbers and recombine or partition the   adjust
partition the second number only e.g.                    second number only e.g.                                        Continue as in Year 2, 3, 4 and 5 but with appropriate
55 + 37 = 55 + 30 + 7                                    358 + 73 = 358 + 70 + 3                                        numbers including extending to adding 0.9, 1.9, 2.9
= 85 + 7                                                  = 428 + 3                                            etc
= 92                                                         = 431
Partition into hundreds, tens, ones and decimal                Partition into hundreds, tens, ones and decimal
+30                      +7          fractions and recombine                                        fractions and recombine
Either partition both numbers and recombine or partition the   See Year 5 example
second number only e.g.
92   35.8 + 7.3 = 35.8 + 7 + 0.3
55                                    85
= 42.8 + 0.3
= 43.1
+7                     +0.3

35.8                             42.8          43.1
Add the nearest multiple of 10, then adjust              Add or subtract the nearest multiple of 10 or 100, then
Continue as in Year 2 and 3 but with appropriate         adjust
numbers e.g. 63 + 29 is the same as 63 + 30 - 1          Continue as in Year 2, 3 and 4 but with appropriate numbers
e.g. 458 + 79 = is the same as 458 + 80 - 1

Pencil and paper procedures                              Pencil and paper procedures (returning to expanded             Pencil and paper procedures
358 + 73 = 431                                           methods if necessary).                                         Extend to numbers with any number of digits and
either            or                                      358                                                           decimals with 1 and 2 decimal places.
+ 73                                                           124.9 + 117.25 = 242.15
300      50 8                    358         358         431
11
+         70 3                +    73        + 73                                                                         124.9
300     120 11 = 431              11         431        Extend to numbers with at least four digits                    + 117.25
120         11                      3587 + 675 = 4262                                   242.15
11
300                     3587
431                    + 675                                                          Revert to expanded methods if the children
4262                                                          experience any difficulty.
111
Extend to decimals (either one or two decimal places,
Revert to expanded methods if the children experience any      refer to Year Five for mental method).
difficulty.

CK/MD Strategy calculation policy
Extend to decimals in the context of money (vertically)   Extend to decimals (same number of decimals places) and adding
£ 2.50 + £ 1.75 = £ 4.25                                  several numbers (with different numbers of digits).
£ 2.50                                                  Model negative numbers using a number line.
+ £ 1.75
£ 4.25
1

(Revert to expanded methods if the children
experience any difficulty.)

CK/MD Strategy calculation policy
Subtraction
FS / Year 1                                                      Year 2                                                 Year 3
FS- Nursery and Reception:                                  - = signs and missing numbers                               - = signs and missing numbers
Look at amounts and compare.                                Continue using a range of equations as in Year 1 but with
Children can look at an amount of objects and               appropriate numbers.                                        Continue using a range of equations as in Year and 2
but with appropriate numbers.
compare by saying there are less in one set of objects.     Extend to 14 + 5 = 20 - 

Responds to the vocabulary involved in addition.            Find a small difference by counting up
Number rhymes and games.                                    42 – 39 = 3                                                 Find a small difference by counting up
Continue as in Year 2 but with appropriate numbers
Find 1 less.                                                                                                            e.g. 102 – 97 = 5
Children find one less by using objects and taking 1                +1                         +2
object from the group/ children find 1 less to 10 using a
number line.
Practical/Pictures / marks
Sam spent 4p. What was his change from 10p?
39          40                           42

Mental Strategy: Subtract 9 or 11. Begin to                 Mental Strategy: Subtract a ‘near multiple of 10’ to
add/subtract 19 or 21                                       or from a two-digit number
YEAR 1:                                                     35 – 9 = 26 / 35-10+1=
Practical/Pictures / marks                                                                                              Continue as in Year 2 but with appropriate numbers
Sam spent 4p. What was his change from 10p?
+1                                                 e.g. 78 – 49 is the same as 78 – 50 + 1

25               26                     35
-10
Number lines (numbered)                                     Use known number facts and place value to subtract          Use known number facts and place value to
(partition second number only)                              subtract
11 – 7                                                    37 – 12 = 37 – 10 – 2
(Counting back)                                                       = 27 – 2                                          Continue as in Year 2 but with appropriate numbers
e.g. 97 – 15 = 82
= 25
0   1   2    3    4   5   6   7     8   9   10   11   12
25                    27                      37
82              87                        97

The difference between 7 and 11
(Counting up)                                                          -2                       -10                               -5                 -10

CK/MD Strategy calculation policy
Find a small difference by counting up: bridging 10.
0    1   2   3    4   5    6    7   8   9   10    11   12
84 – 66 = 18. Use as a checking strategy, to find
change etc.
Recording by - drawing jumps on prepared lines
- constructing own lines
+ 10
+4                            +4
(Teachers model jottings appropriate for larger
numbers)
66           70              80        84
- = signs and missing numbers
7-3=              =7-3
7-=4              4=-3                                    Expanded written method (no decomposition).
76 – 54=
-3=4              4=7-
-=4              4=-                                      70          6
- 50          4
20          2 = 22            (extend to HTU for more able)

Expanded written method (decomposition)
91 - 79 =

80        10+
90        1
-       70        9
10         2 = 12 (extend to HTU for more able)

Compact written method.
(AA ONLY)

8             1
9            1
-        7            9
1            2    (exchange once, then twice).

CK/MD Strategy calculation policy
Subtraction
Year 4                                                       Year 5                                                                 Year 6

- = signs and missing numbers                              - = signs and missing numbers                                      - = signs and missing numbers
Continue using a range of equations as in Year 1 and 2     Continue using a range of equations as in Year 1 and 2             Continue using a range of equations as in Year 1 and 2
but with appropriate numbers.                              but with appropriate numbers.                                      but with appropriate numbers.

Mental Strategy: Find a small difference by counting       Mental Strategy :Find a difference by counting                     Mental Strategy :Find a difference by counting
e.g. 8005 – 6996 = 1009                                    e.g. 8054 – 6986 = 1068                                            e.g. 0.5 – 0.31 = 0.19
This can be modelled on an empty number line               This can be modelled on an empty number line                       This can be modelled on an empty number line

+14                +1000                 +54                                                     +0.1
+1000                                                                                                                      +0.09
+4                                     +5

0.31                0.4                 0.5
6986           7000                        8000           8054
6996      7000                      8000          8005

Mental Strategy: Subtract the nearest multiple of
Mental strategy: Subtract the nearest multiple of 10,      Mental Strategy: Subtract the nearest multiple of 10
10, 100 or 1000, then adjust
Continue as in Year 2, 3, 4 and 5 but with appropriate
Continue as in Year 2 and 3 but with appropriate           Continue as in Year 2, 3 and 4 but with appropriate
numbers.
numbers.                                                   numbers.
Mental Strategy: Use known number facts and
Mental strategy: Use known number facts and place          Mental strategy: Use known number facts and place
place value to subtract
value to subtract                                          value to subtract
Continue as year 5
92 – 15 = 67                                               6.1 – 0.4 = 5.7
77               82                        92
5.7                   6.0                           6.1

-0.3                 -0.1
Expanded written method (decomposition)
-5                  -10
Revert to this method to review understanding of
Expanded written method (decomposition)                            compact method.
Expanded written method (no decomposition).
76 – 54=                                                    261 - 179 =                                                        262 - 179 =

70        6                                                                                                                      100            100 +50        10+
100            100 +50       10+
- 50        4                                                                                                                        200                60         1
20        2 = 22       (extend to HTU for more able)            200                60         1                              -     100                70         9
-     100                70         9                                                        80        2 = 82
Expanded written method (decomposition)                                               80        2 = 82                                                         (exchange once, then twice).
(exchange once, then twice).

CK/MD Strategy calculation policy
91 - 79 =
Compact written method(decomposition)        Compact written method(decomposition) TH H T U
80         10+
90      1                   Th H T U                                     Th H T U
1   13 14   1                                1 13   14   1
-       70      9
10       2 = 12              2 4 5 6                                      2 4 5 6
-1 5 6 7                                     -1 5 6 7
Extend to HTU for more able.           8 8 9                                        8 8 9

Compact written method.
(B.A continue with expanded decomposition)   (B.A continue with expanded decomposition)
8           1                                                                Compact written method (decomposition) DECIMALS
9          1
6   12   1
-        7          9
1           2                                                                    2 7. 3        1
-      1 4. 9        8
Extend to HTU for more able                                                              1 2. 3        3
Exchange once, then twice.

CK/MD Strategy calculation policy
Multiplication
FS / Year 1                                                       Year 2                                            Year 3
Nursery and Reception:                                 Arrays and repeated addition                           x = signs and missing numbers
Continue using a range of equations as in Year 2 but with
Count repeated groups of the same amount of objects.            4 x 2 or 4 + 4                            appropriate numbers.
   
2x4
Continue to understand multiplication as repeated
2+2+2+2
addition and continue to use arrays (as in Year 2).
Discuss how many in each group and how many
groups.
Number lines
6x3
YEAR 1:
Pictures and symbols
0       1     2      3    4    5   6      7   8
There are 3 sweets in one bag.                                                                                 0            6         12         18
How many sweets are there in 5 bags?                   x = signs and missing numbers
7x2=                =2x7
7 x  = 14          14 =  x 7
 x 2 = 14          14 = 2 x 
 x  = 14          14 =  x 

(Recording on a number line modelled by the            Doubling multiples of 5 up to 50                       Doubling multiples of 5 up to 50
teacher when solving problems)                         15 x 2 = 30                                            35 x 2 = 70

Use of bead strings to model groups of.                     Double                                            Continue to use the same methods as Y2.

15

20       +       10= 30

Partition
12 x 5 = 60                                            Partition
13 x 4 = 52
12 x 5 = (10 x 5) + (2 x 5)
= ( 50 ) + ( 10 )                                13 x 4 = (10 x 4) + (3 x 4)
=          60                                          = ( 40 ) + ( 12 )
=          52

Use known facts and place value to carry out simple
multiplications

CK/MD Strategy calculation policy
e.g. 32 x 3 = 96 using the Grid method
OR using the Grid Method (AA set only)
x        3
x      2
30      90
10    20
5   10                                        2       6
30                                              96

CK/MD Strategy calculation policy
Multiplication
Year 4                                               Year 5                                                 Year 6
x = signs and missing numbers                      x = signs and missing numbers                          x = signs and missing numbers
Continue using a range of equations as in Year 2   Continue using a range of equations as in Year 2 but   Continue using a range of equations as in Year 2 but with
but with appropriate numbers                       with appropriate numbers                               appropriate numbers

Partition TUxU                                     Partition (BA Set only)                                Mental method: Partitioning
23 x 4 = 92                                        47 x 6 = 92                                            See Y5

23 x 4 = (20 x 4) + (3 x 4)                        47 x 6 = (40 x 6) + (7 x 6)
= ( 80 ) + ( 12 )                                   = ( 240 ) + ( 42 )
=          92                                      =        282

OR                                                 OR

Pencil and paper procedures:                           Pencil and paper procedures:
Pencil and paper procedures:
Grid method: TUxTU                                     Grid method THUxTU
Grid method: TUxU
38 x 72 is approximately 70 x 40 = 2800                372 x 24 is approximately 400 x 20 = 8000
23 x 7 is approximately 20 x 10 = 200

x         7                                     x           70 2                                      x          20            4
30        2100 60                                    300       6000         1200
20     140
3       21                                       8        560 16                                      70      1400          280
2        40            8
161                                               2660 + 76 = 2736
Expanded written method
Expanded written method HTUxU                                    7440 + 1488 = 8928
TUxU
Compact written method
Short multiplication HTUxU; ThHTU x U
23                                                  287
x 7                                                  x 6                                                    287
3x7             21                                  7x6              42                                                 x 6
20 x 7          140                                 80 x 6           480                                                  1722
161                                200 x 6          1200                                                   54
1722

CK/MD Strategy calculation policy
Compact written method TUxU               Compact written method HTUxU                               Long multiplication TUxTU
165 x 24 is approximately 200 x 20 = 4000
23                                       287
x 7                                      x 6                                                    165
161                                      1722                                                 x 24
2                                        54                                         165 x 20 3300
165 x 4   660
AA Set only – Grid method TUxTU           Extend to simple decimals with one decimal place.                    3960
38 x 72 is approximately 40 x 70 = 2800
12.5                                      Extend to decimals with up to two decimal places.
x           70 2                                         x 2
30        2100 60                       2.0 x 0.5         1.0                                                  12.5
8        560 16                       2.0 x 2.0         4.0                                                 x 2.5
2.0 x 10.0       20.0                                      2.5 x 0.5    1.25
2660 + 76 = 2736                               25.0                                      2.5 x 2.0    5.00
2.5 x 10.0 25.00
Moving to formal methods of multiplication for decimals.               31.25
Carrying numbers underneath.

Moving to formal methods of multiplication for decimals.
Carrying numbers underneath.

CK/MD Strategy calculation policy
Division
FS / Year 1                                                   Year 2                                                      Year 3
Nursery and Reception:                                                                                       ÷ = signs and missing numbers
Continue using a range of equations as in Year 2 but with
Share objects into equal groups and count how     Understand division as sharing and grouping                appropriate numbers.
many in each group.
Sharing – 6 sweets are shared between 2 people. How many
8 objects shared by two.                          do they have each?

Understand division as sharing and grouping
18 ÷ 3 can be modelled as:
                                                Sharing (18 shared between 3) (see Year 2 diagram)
           
0        3       6           9       12        15        18

6  2 can be modelled as:
YEAR 1:                                                                                                      Or
Share objects into equal groups and count how
Grouping – There are 6 sweets. How many people can have
many in each group.                                                                                          Grouping (How many 3’s make 18?)
2 each? (How many 2’s make 6?)
8 objects shared by two.

0       3       6           9        12        15        18

0           2          4       6
Remainders
16 ÷ 3 = 5 r1
Sharing - 16 shared between 3, how many left over?
Grouping – How many 3’s make 16, how many left over?
÷ = signs and missing numbers                              e.g.
6÷2=                =6÷2
R1
Pictures / marks
6÷=3                3=6 ÷
÷2=3                3=÷2                                      0       3           6       9        12    15 16
12 children get into teams of 4 to play a game.   ÷=3                3=÷
How many teams are there?

CK/MD Strategy calculation policy
Division
Year 4                                                                   Year 5                                                        Year 6
÷ = signs and missing numbers                                                      ÷ = signs and missing numbers                               ÷ = signs and missing numbers
Continue using a range of equations as in Year 2 but with                          Continue using a range of equations as in Year 2 but with   Continue using a range of equations as in Year 2 but with
appropriate numbers.                                                               appropriate numbers.                                        appropriate numbers.

Sharing and grouping                                                               Sharing and grouping                                        Sharing and grouping
Continue to understand division as both sharing and                                Continue to understand division as both sharing and         Continue to understand division as both sharing and
grouping (repeated subtraction).                                                   grouping (repeated subtraction).                            grouping (repeated subtraction).

Remainders                                                                         Remainders                                                  Remainders
Progress from counting up on a number line: 428 = 5 r2                            Quotients expressed as fractions or decimal fractions       Quotients expressed as fractions or decimal fractions
R2                                   61 ÷ 4 = 15 ¼ or 15.25                                      676 ÷ 8 = 84.5

0
8        16            24       32           40   42         0     1              21                              61     0        4              36                        676
4 groups                 80 groups
To counting back in groups of 10:                     41 ÷ 4 = 10 r1                          5 groups                   10 groups
-4         -32
-640
0                1                                             41                    -1       -20
-40
10 x 4

-1
-40
To: 48  3 = 16
0        3                  18                                            48

5 groups                      30 groups

-3           -15
-30
Pencil and paper procedures                                 Pencil and paper procedures
Chunking                                                    Short division
Pencil and paper procedures                                                        256 ÷ 7 lies between 210  7 = 30 and 280  7 = 40
Chunking                                                                                 36 r 4
7 1 r 4 or 71 4/13
48 ÷ 3 lies between 30  3 = 10 and 60  3 = 20                                      7 256                                                     13 9 2 17
16                                                                            -     70     (10 x 7)
3 48                                                                                  186
-   30 (10 x 3)                                                                   -    140     (20 x 7)                                            1 4 3 r 1 or 143 1/6
18                                                                                  46
-   15      (5 x 3)                                                                -    42      (6 x 7)                                       6    8 25 19
3                                                                                   4
-     3      (1 x 3)                  Answer = 16                                               (36)           Answer: 36 remainder 4

CK/MD Strategy calculation policy
585

Short division
72 ÷ 5 lies between 50  5 = 10 and 100  5 = 20         Introduce in summer term – see Year 6
14 r 2
5 72
-    50 (10 x 5)
22
-    20      (4 x 5)
2

CK/MD Strategy calculation policy

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