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Calculation Strategies – St. Bernadette’s R.C School.
Addition
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
Addition
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 +
and adding three numbers
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
Add 9 or 11 by adding 10 and adjusting by 1
+ = 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
Addition
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
Mental Strategy (Complementary addition)
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
up (complementary addition). up(complementary addition). up(complementary addition)
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
then adjust. or 100, 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
or repeated addition Arrays and repeated addition
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: 428 = 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
Answer : 14 remainder 2
CK/MD Strategy calculation policy
