Standard written methods of calculation
INTRODUCTION
This calculation policy has been written in line with the programmes of
study taken from the revised National Curriculum for Mathematics (2014).
It provides guidance on appropriate calculation methods and progression
to be used in Church Lane.
It reflects a whole school agreement on what we feel is best for the
children at our school and will ensure consistency and progression
throughout the school.
The content is set out in yearly blocks under the following headings:
addition, subtraction, multiplication and division.
Statements taken directly from the programmes of study are listed in bold
at the beginning of each section.
A separate mental maths section is attached and is currently taken from
Hamilton Trust.
Also attached is a section on additional guidance on methods/models and
images/ideas/extra resources particular to our school and experience of
our children’s problems when learning mathematical concepts.
Children will use mental methods as their first port of call when
appropriate, but for calculations that they cannot do in their heads, they will
need to use an efficient written method accurately and with confidence.
AIMS OF THE POLICY
• To ensure consistency and progression in our approach to calculation
• To ensure that children develop an efficient, reliable, formal written
method of calculation for all operations
• To ensure that children can use these methods accurately with
confidence and understanding
• HOW TO USE THIS POLICY
• Use the policy as the basis of your planning but ensure you use previous
or following years’ guidance to allow for personalised learning
• Always use Assessment for Learning to identify suitable next steps in
calculation for groups of children
• If, at any time, children are making significant errors, return to the
previous stage in calculation
• Cross reference with the mental maths guidance and other attachments
on key facts, key vocabulary and mental methods
• Always use suitable resources, models and images to support children’s
understanding of calculation and place value, as appropriate
• Encourage children to make sensible choices about the methods they
use when solving problems in particular the bar method.
• Our approach is detailed in this policy, which is to be shared with all
staff, governors and parent helpers so that we will have a consistent
approach to calculation.
• The information within this document is shared with parents by way of
a ‘Helping your child with Maths’ leaflet and regular parent
information evenings.
Written Calculations
General Points to Remember
The use of informal written methods, or ‘informal jottings’ is useful throughout
KS1 and KS2, for instance, to support children when they move on to larger
numbers.
Number lines are a useful way for children to visualise the calculations they are
attempting. The steps being added or subtracted should be made larger, ie.
multiples of 10, 100. The grid method for multiplication is good for allowing
children to see how they are tackling the calculation.
The development of mental methods must continue even when children are
progressing towards a standard written method.
Calculations should still be attempted mentally if possible, even if the
calculation is to be recorded, so it is a good idea to begin with digits that can be
tackled mentally.
It is useful to try and approximate an answer to a calculation, before attempting
it, as a guide to whether the answer is reasonable or sensible. Also use
approximation to find the highest multiple starting point for a division calculation.
Showing expanded methods alongside more compact forms can help
children to make connections between different methods they are being asked
to use.
Revert to previously taught expanded methods if children are having
difficulties grasping more standard forms, for instance when they first begin
carrying in addition problems.
Revert to expanded methods when moving on to calculations with larger
numbers, to ensure that children can calculate using methods they were
previously secure with.
In the case of children with SEN, or specific difficulties, it may be necessary to
continue using expanded or informal methods of recording, as it may prove
difficult to unlearn previously taught methods. For instance, some children may
need to
continue adding the most significant digit first.
It is useful to note that an alternative method may be necessary for a group or
individual, if they are experiencing specific difficulties with the methods being taught to
that class or group.
Pre-requisite skills for Written Calculations • Understanding of place value in three-digit numbers
• Knowledge of addition facts to 20, and of
corresponding subtraction facts
. Ability to add three single digits menatally
• Ability to partition three-digit numbers into
HTU
• Experience of using a number line for addition and subtraction
problems
• Ability to add mentally any pair of two-digit numbers, using a
strategy of their choice
.Ability to explain their mental strategies orally and record them
using informal jottings.
. Knowledge of 2,3,4,5 and 10 multiples
.Understanding of 0 as a place holder
Understand result of multiplying by 0 and 1
.Ability to multiply two and three digit numbers by 10 and 100
Derive mentally other multiplication facts from known ones
Ability to double and halve two digit numbers mentally
• Experience of using informal pencil and paper methods, or
‘jottings’
• Having a developing vocabulary to describe and explain
calculations, mental and recorded
Not exhaustive list but a guide for teachers to judge when a child
is ready to move to formal methods of calculation. Steps Towards Adding and Subtracting Mentally Any Pair of Two-digit Numbers Step 1
U +/- 1
U +/- U
10 +/- U
tU +/- U
Not crossing the tens boundary
Not crossing the tens boundary
3+1
4-1
2+4
6-4
10 + 4
10 - 4
12 +4
16 - 4
Step 2 T +/- U
TU +/- 10
T +/- T
TU +/- U
U +U
tU +/- U
TU +/- T
TU +/- U
50 + 4
50 - 4
Not crossing the hundreds boundary
52 + 10
62 - 10
Not crossing the hundreds boundary
50 + 30
80 - 30
52 + 4
56 - 4
Not crossing the tens boundary
Crossing the tens boundary
Crossing the tens boundary
6+8
15 + 8
15 - 8
Not crossing the hundreds boundary
52 + 30
82 - 30
Crossing the tens boundary
55 + 8
63 - 8
Step 3 TU +/- TU
TU +/- T
T +/- T
Not crossing the tens boundary or the hundreds boundary 52 + 14
52 + 34
66 - 14
86 - 34
Crossing the hundreds boundary
92 + 10
102 - 10
Crossing the hundreds boundary
80 + 50
130 - 80
Step 4 T +/- TU
TU +/- TU
Crossing the hundreds boundary or the tens boundary
80 + 52
Crossing the tens boundary but not the hundreds boundary 55 + 18
55 + 38
TU +/- TU Crossing the hundreds boundary but not the tens boundary
TU +/- TU Crossing the tens boundary and also the hundreds boundary
80 - 52
73 - 18
93 - 38
52 + 84 136 - 84
55 + 78 133 - 78
Notes
1. U is a number of units or ones, such as 3 or 7
t is 10 (or one ten)
T is a single-digit multiple of 10, such as 30 or 70
2. Children should achieve competence in the calculations (that is doing them mentally
without using
fingers or apparatus) by the end of Year 4 and should regularly rehearse skills learned
in earlier years. Grading of Difficulty in Whole Number
Additions and Subtractions Addition 1. No carrying
2. Extra digit in answer
3. Carrying U (units/ones) to T (tens)
4. Carrying T to H
5. Carrying U to T and T to H
6. More than 2 numbers to be added
7. Different numbers of digits
23
+ 42
315
+ 624
94
+ 73
561
+ 718
47
+ 25
237
+ 516
371
+ 485
293
+ 541
376
+ 485
295
+ 547
47
36
+ 58
424
916
+ 532
324
75
+ 4 8 Subtraction 1. No adjustment
2. Adjustment T to U
864
- 621
51
36
432
- 217
437
- 182
658
- 277
-
3. Adjustment H to T
4. Adjustment H to T and T to U
5. Noughts
47
- 23
432
- 187
700
- 236
604
- 327
-
470
142
Grading of Difficulty in Whole Number
Multiplications and Divisions Multiplication 1. No carrying
2. Extra digit
x
32
3
x
32
x 4
3. Carrying but keeping in same decade
x
83
7
51
x
4
34
4
x
4. Carrying and going into next decade
5. Noughts
6. Multiply by multiples of 10
7. ‘Long’ multiplication
44
2
68
x 8
202
x
4
430
x
6
87
x 10
x
416
60
47
x 23
832
x
74
Division Single-digit division
1. No remainder, no carrying
3)69
2. Remainder, no carrying
3)68
3. No remainder, carrying
3)45
4. Remainder, carrying
3)47
5. Placing of the quotient
7)287
6. Noughts
4)816
2)264
8)5608
Two-digit division
7. No remainder
32 ) 6 4
31 ) 9 3
8. Similar but remainder
13 ) 2 9
31 ) 9 7
9. Quotient not so apparent
22 ) 5 6
41 ) 9 2
10. Placing the quotient
21 ) 1 2 6
11. No remainder
21 ) 4 4 1
12. Remainder
33 )7 1 8
13. Noughts
17 ) 6 8 3 4
32 ) 2 2 4
32 ) 7 3 6
Additional Guidance For Successful
Mathematical Progression In Church Lane
1. Remember to follow the key skills for your year group and have enlarged,
coloured and pinned up for the children to see.
2. When referring to units use vocabulary “ones” too.
3. When working with any numbers on the board always ask other facts about
them eg 36 tell me something about 36 – even, tens is half the units, square
number, 4 less than 40 etc This is a great starter activity at any age group.
4.Use number squares which go over 100.
5. When teaching halving ensure they are competent with halving all multiples
of 10 to 100.
6.When teaching halving of odd numbers teach children to go to number before
or after to help them eg 99 go to 100 and take half off.
7.When teaching partitioning once they have mastered say 64 to 60 and 4
encourage partitioning to other multiples of 10 eg 64 = 50 + 14. This is
essential preparation for understanding of decomposition.
8.When introducing column addition put the “carry” above the answer box.
64
+38
1
102
This helps pupils to remember to add “carry” in.
9. Constantly draw out patterns of last digits eg 19+5 will end in 4 so will 39 +
5 etc.
Link number bonds to 10 constantly throughout school eg 194 + ? = 200 it
must be 6.
10. Number bonds to 100 draw out total of tens is 90 and units is 10.
11. When ready always teach the three related to facts to any stated fact in
the four rules eg 6x3 = 18 3x6 = 18 18/6 =3 and 18/ 3 =6.
Mental Maths Booklets
These must be differentiated and marked immediately for weak areas to be
addressed effectively.
Maths Whizz
All class teacher’s Y1 upwards are responsible for using this resource correctly
and effectively to inform planning of weaker areas and for promoting use at
home where possible.
More able reception to have access during Summer term.
Multiplication/Division Tables
1. When teaching early multiples (3 and 4) such as 3 x 8 = 24 always teach 8 x 3
at same time, 4x 9 = 36 so 9 x 4 = 36. Always encourage doing larger
numbers first across all four operations. This helps enormously when we have
to move onto 6,7,8s as they already confident then with first few in patterns.
2. Count forwards and backward. Consider teaching half first rather than all in one
go.
3. All rules of divisibility are a key skill and should be constantly taught when
appropriate.
4. Use language of multiples and multiplication tables not times tables. Use
“groups of “ rather than “lots of.”
5. All classes to have a file containing each pupils record of “steps”
programme and multiplication achievement card. This should also contain
number bond/facts card.
Problem Solving
The bar model is to be used to support children in problem solving by
transformation of real life problems into a mathematical form and can bridge
the gap between concrete mathematical experiences and abstract
representations.
ITPS for support in lessons
Maths Packs, Maths whizz, Hit the Button, Interactive number squares and
multiplications tables.
Teacher’s own.
Due for review July 2016
Amendment July 2015 – Progression in four rules is further supported by Head
Start Material.