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Calculation Policy
Trinity St Stephen First School
(NC2014)
November 2013
Aims
• To support greater consistency in the teaching of written
calculation across the school
• To strengthen continuity and progression in children’s
understanding of the development of written calculation
• To form a ‘spine’ or ‘core’ set of methods which every child will
experience and can be built upon.
Once children acquire mastery of these, other calculation
methods can be introduced
• To build on models and images introduced to promote
conceptual understanding
• To provide reference and guidance on the teaching of
calculation skills for teaching staff and teaching assistants
The Place of Writing in Maths
Lessons
• Recording of calculations takes place throughout KS1 and
KS2
• Development of formal written calculation methods follows
development of mental methods
• Early stages of formal written calculations begin in the
summer term of Year 3
• By end of Year 6, children should have a reliable written
method for tackling all four operations
– not necessarily a ‘standard’ written method
For some this may still be supported by a number line
Developing a Maths Concept
Abstract
‘Just do it’
Visualise
‘With eyes closed’
Visual
‘With eyes open’
Language
Concrete
Using objects
Good Practice in Calculation
•
Establish mental methods, based on good understanding of place value in
numbers and tables facts.
•
Show children how to set out written calculations vertically, initially using
expanded layouts (starting without adjustments of 'carrying', and introducing
this adjustment slowly and systematically).
•
Make sure that the children always look out for special cases that can still
be done entirely mentally.
•
Gradually refine the written record into a more compact standard method.
•
Extend to larger numbers and to decimals.
•
Ensure that mental approximations are carried out before written methods
are used.
•
Ensure that the understanding of remainders and what to do with them in
context is taught alongside division throughout.
•
Once written methods are introduced, keep mental skills sharp by
continuing to develop and apply them to appropriate examples.
Encourage children always to use mental methods as a first resort.
Addition - Reception
3
+
= 5
2
5 = 3 + 2
•
•
Record the outcome when
two groups of objects are
combined into one group
•
Estimate how many objects
can they see
•
Say the number that is one
more than a given number
Record the outcome of physically moving
along the number track
1
2
3
4
5
6
7
8
9
10
“Standing on three and moving forwards two spaces”
Addition – Year 1
5 and 1 more is ?
6
•
Combining sets to
make a total
5 and 2 more is ?
6,7
•
Add 3 single digits
pictorially to make a total
5 and 3 more is ?
6, 7, 8
•
Counting along a number
track, then number line in
1s and 10s
•
Patterns using known facts
e.g. 4+3 = 7, so we know
24-3 = 27 & 44+3 = 47 etc
•
Number bonds within 20
•
Number bonds to 5, 6, 7,
8, 9
6
1
2
3
4
8
7
5
6
Count on one, two, three
7
8
9
10
Addition – Year 2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
•
Counting on in 10s then 1s on a
number square and number line
48 + 35 =
+10
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
48
+1
58
68
78 79 80 81 82 83
•
Addition of three numbers
E.g. 7 + 6 + 3 =
•
Number bonds to 10 and 20
•
Number bonds to 11, 12, 13, 14,
15, 16, 17, 18 and 19
Addition – Year 3
•
Use a number line
Start from the largest number, partition the second and add the most
significant digit first
+4
+3
86 + 57 =
+50
86
•
136
Partition both numbers and
add the tens, then the units,
finally recombining
86 + 57 = (80 + 50) + (6 + 7)
=
130
=
143
+
13
•
140
143
Expanded vertical layout,
adding the tens first
86
+ 57
130
13
143
(80 + 50)
(6 + 7)
Addition – Year 4
•
Use a number line, partitioning and adding the thousands first
+30
+4
1387 + 1334 =
+300
+1000
1387
•
2387
Expanded vertical layout,
adding the hundreds first
1387
+1334
•
Leading to expanded
vertical layout adding
the units first
1387
+ 1334
600
110
11
11
110
600
2000
2721
2721
2000
2717 2721
2687
•
Leading to formal
written method
1387
+ 1334
272 1
1 1
Subtraction - Reception
10 grapes, eat
one, how many
left? 9.
And another? 8.
Another, 7 . . .
10 grapes,
eat two. How
many left?
•
Establishing
take away
9,8
8 left
•
Show their calculation on a
numbered track
“Sophie has 5 sweets. She eats 2 of
them. How many sweets are left?”
•
1
2
3
4
5
6
7
8
9
10
Beginning to look at difference
Subtraction – Year 1
•
•
Counting back along a
number line when taking
away
•
Counting back in 10’s e.g.
53-20 as 53,43,33
•
Patterns using known facts e.g.
7-3=4, so we know 27-3=24 &
47-3=43 etc
Finding the difference between 3 and 5
Subtraction – Year 2
•
•
•
Looking at appropriate times for counting
back (taking away) and counting on
(difference)
Counting on and back finding differences
on a 100 square
Finding differences;
recording on a number
line
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Subtraction – Year 3
•
Horizontal number line for HTU – TU
625 – 48 =
-500
-50
-20
500 + 50 + 20 + 5 +2
= 577
-5
-2
48
•
100
50
600
620
625
Leading to formal columnar vertical layout
8 12 1
1 1
932
-
457
932
OR
-
457
5 6
475
475
Subtraction – Year 4
• Use a formal written method of columnar subtraction
to subtract Th H T U – TH T H U
8 12 1
1 1
2932
-
1457
1475
2932
OR
-
1457
5 6
1475
Multiplication - Reception
•
Count in 2s
2 4 6 8 10
1
Five pairs of socks. Ten socks
2
3
Count on in 10s (and
back) from a given tens
number
5
6
7
8
9
10
Point to a number track, saying
every other number aloud.
40
•
4
50
30
20
Multiplication – Year 1
•
Count in 2s, 5s &10s
2
4
How many
gloves in 3
pairs?
6
Double 4
is 8
8
10
•
•
Understand doubling
•
Recognise odd and even
numbers up to 10
With help begin to understand
arrays e.g. 3x2=6
Multiplication – Year 2
•
•
Count in 2s, 3s, 5s and 10s from 0, recording on a number line
Recall of 2, 5 and 10 times table
5 + 5 + 5 + 5 = 20
5 x 4 = 20
5 multiplied by 4 is 20
0
•
5
10
15
2 hops of 4
20
4
Introducing arrays
4 x 2 = 8
2 x 4 = 8
4
8
0
2
2
2
4 hops of 2
2
Multiplication – Year 3
•
•
Arrays
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8 x 5 = 40
5 x 8 = 40
•
Count in 2s, 3s, 4s, 5s, 8s,10s,
50s, 100s, recording on a number
line
Know these as tables facts
0
•
Multiplying by 10 and 100
1
2
3
4
5
10
20
30
40
50
100 200 300 400 500 600
4
8
12
16
Use partitioning to double
numbers
Double 18
Double
10 and
double 8
18
10
+
8
20
+
16
=
36
Multiplication – Year 4
•
Grid method for HTU x U – 324x6
x
6
20
4
1800 120
24
300
•
1800
+ 120
24
324
x
6
1944
= 1944
•
Expanded vertical method
324
x
6
24
120
1800
1944
•
Recall multiplication and division facts
for tables up to 12 x 12
Leading to the compact
vertical method
1 1 2
•
Informal jottings supporting mental
multiplication using partitioning
(factors)
17 x 3 = (10 x 3) + (7 x 3)
=
30
=
51
+
21
Division – Reception & Year 1
•
Practical sharing
Half of 8
is 4
Can we share the
cakes fairly between
the four of us ?
Put half of the
animals into
the ark.
•
Beginning to understand halves &
quarters and equivalents
•
Identify own mathematical
problems based on own interests
Division – Year 2
•
Sharing equally
•
Grouping
5 groups of
3
How many groups
of 3 can we make
from these 15 ?
2 groups of
4
Division – Year 3
•
Grouping
How many 3s in
15 ?
15 = 3 + 3 + 3 + 3 + 3
15 ÷ 3 = 5
15 divided by 3 = 5
0
6
3
12
9
15
•
•
Dividing by 10 and 100
Corresponding facts
3 x 4 = 12 implies that 12 ÷ 4 = 3
1
2
3
4
5
10
20
30
40
50
100 200 300 400 500 600
4 x 3 = 12 implies that 12 ÷ 3 = 4
•
Dealing with remainders
practically
Division – Year 4
•
Chunking TU ÷ U
98 ÷ 7
98
−70
÷7
10 x 7 = 70
28
−28
0
•
4 x 7 = 28
14
Leading to short division TU ÷ U
98 ÷ 7
1 4
2
7
•
•
9 8
Introducing TH H T U
(Remainders Year 5 objective)