This sample guidance is intended to be used as an appendix to the
school’s mathematics policy.
Guidance to support the teaching of
written calculations
We aim to ensure that by the end of year
6, as many children as possibly can will understand, and use
successfully, compact written methods to carry out and record
calculations they cannot do in their head.
It is important that children approach
any calculation by always asking themselves the following questions:
q
‘Can I do this in my head?’
q
‘Do I know the approximate size of the
answer?’
q
‘If I can’t do it wholly in my head,
what do I need to write down in order to help me calculate the
answer?’
q
‘Will the written method I know be
helpful?’
In Years 5 and 6, children will also need
to consider
q
‘Would it be more useful to use a
calculator to work this out?’
when considering a more complex
calculation that they could not easily perform using pencil and paper
procedures.
Whenever appropriate, children should do
a mental calculation e.g. although the numbers in the following
calculation are large it is nonetheless easy to calculate mentally:
3002 – 2998
In order to support this approach,
calculations are always presented to children horizontally so that they
can make the decision how to tackle them.
To enable children to move towards
compact written methods with full understanding a step-by-step approach
is taken. For each of the four operations children are first introduced
to expanded methods that lead to the compact form of calculation. It is
important that children feel secure and comfortable with each stage
towards compact methods before they move on to the next. Children will
progress through the stages of expanded calculation at different rates.
It is far better that they can operate efficiently at any stage and with
understanding than to move them on too quickly. Not all children will
reach a compact method by the end of year 6.
Expanded methods for addition and
subtraction are introduced in the Summer Term of Year Three. Prior to
this children will be doing informal recording of their mental
calculation. Expanded methods for multiplication and division are
introduced in Year Five.
Criteria which would indicate a child’s
readiness for formal written methods of addition and subtraction
include:
q
Knowledge of addition and subtraction
facts to 20
q
Understanding of place value and ability
to partition numbers into hundreds, tens and ones
q
Understanding of commutative and
associative laws of addition (though not of these terms)
q
Ability to add at least three
single-digit numbers mentally
q
Ability to add and subtract any pair of
two-digit numbers mentally
q
Ability to explain mental strategies
orally and in writing
Criteria which would indicate a child’s
readiness for formal written methods of multiplication and division
include:
q
Recall of multiplication and
corresponding division facts for 2, 3, 4, 5 and 10 times tables
q
Understanding of what happens when a
number is multiplied by 0 or 1
q
Understanding of 0 as a place holder
q
Ability to multiply two- and three-digit
numbers mentally by 10 and 100
q
Understanding of commutative,
distributive and associative laws of multiplication (though not of these
terms)
q
Ability to double and halve two-digit
numbers mentally
q
Ability to use multiplication facts to
derive mentally new multiplication facts
q
Ability to explain mental strategies
orally and in writing
Resources
The teaching of written methods may be
supported by the use of resources such as place value cards or multibase
(e.g. Dienes) apparatus. It is important the any textbooks used reflect
the approach being taught to the children so as to avoid confusion.
Language
It is important that the language used
when modelling calculations for children reflect the size of the numbers
involved. In the following example where an addition calculation is
completed using a compact written method one might say the following:
|
4 |
8 |
9 |
Nine plus eight equal seventeen. Put down seven ones and carry one
ten.
|
| + |
2 |
6 |
8 |
Eighty plus sixty equals one hundred and forty. Add the extra ten
which equals one hundred and fifty. |
|
___________ |
Put down the fifty and carry one hundred. |
|
7 |
5 |
7 |
Four hundred and two hundred equal six hundred. Add the extra one
hundred which equals seven hundred.
|
|
___________ |
Put down the seven hundred. The answer is
seven hundred and fifty seven.
|
|
1 |
1 |
|
|
