St John’s Catholic Primary School
Written Calculation at a Glance
October2015
Written Calculation At A Glance
Year Addition
Subtraction
EYFS
1
Count on in ones
Practical subtraction (first ‘count all’ then ‘count on’)
On to a number and beyond / Count from a number
St John’s Written Calculations Policy
For extra detail please see full policy.
Written Calculation At A Glance
Count all – 3 + 5 is counted 1, 2 3 and then, 4, 5, 6,7 8 (out loud)
Count all – 3 + 5 is counted 3 and then, 4, 5, 6,7 8
Simple jottings with pictures
3 + 4 = 7
I found 5 pebbles on a beach but I lost 3! How many did I have left.
Simple subtraction using picture jottings
Dots or tally marks
6
St John’s Written Calculations Policy
- 2
= 4
For extra detail please see full policy.
Written Calculation At A Glance
2
Counting in ones along a number line/track
Counting back / on in ones along a number line/track
8 – 4 = 8
The empty number counting back
4+5=9
74 – 27 = 47 worked by counting back:
or
The empty number line
Using an empty numberline to find the difference (counting up)
74 – 27 =
Or
St John’s Written Calculations Policy
For extra detail please see full policy.
Written Calculation At A Glance
Partitioning by horizontal expansion method
Partitioning by horizontal expansion method
3
Use of Manipulatives to bridge to compact method.
Making the link between the practical and columnar subtraction
To ensure the statutory final written method is grounded in understanding,
this stage connects the practical equipment to the formal written method
using a similar and transferrable layout.
To ensure the statutory final written method is grounded in understanding, this stage
connects the practical equipment to the formal written method using a similar and
transferrable layout.
The use of money also suits this method.
St John’s Written Calculations Policy
For extra detail please see full policy.
Now
sect
Written Calculation At A Glance
Compact column method
Compact Method
Column addition remains efficient when used with larger whole numbers
and decimals. Once learned, the method is quick and reliable.
Ensure that children can explain the compact method, referring to the real value of the
digits. They need to understand that they are repartitioning the 60 + 3 as 50 + 13.Later,
extend to multiple steps of exchanging and decimals.
In this method, recording is reduced further. Carry digits are recorded above
the line (in a space the children have left) using the words ‘carry ten’ or
‘carry one hundred’, not ‘carry one’.
258
+
-2 4 6
87
1 1
5 1
5 6 3
----- leaving a space for carrying
--------
3 1 7
This should be to 3 digit minus 3 digit integers.
345
Column addition remains efficient when used with larger whole numbers
and decimals. Once learned, the method is quick and reliable.
Year
Addition
Subtraction
4
Compact column method
Compact Method
Column addition remains efficient when used with larger whole numbers
and decimals. Once learned, the method is quick and reliable.
Ensure that children can explain the compact method, referring to the real value of the
digits. They need to understand that they are repartitioning the 60 + 3 as 50 + 13.
In this method, recording is reduced further. Carry digits are recorded above
the line (in a space the children have left) using the words ‘carry ten’ or
‘carry one hundred’, not ‘carry one’.
258
+
87
St John’s Written Calculations Policy
5 1
5 6 3
-2 4 6
3 1 7
For extra detail please see full policy.
Written Calculation At A Glance
1 1
----- leaving a space for carrying
This should be to 4 digit minus 4 digit integers.
-------345
Column addition remains efficient when used with larger whole numbers
and decimals. Once learned, the method is quick and reliable.
This should be to 4 digit plus 4 digit integers.
5
Compact column method
Compact Method
In this method, recording is reduced further. Carry digits are recorded below
the line, using the words ‘carry ten’ or ‘carry one hundred’, not ‘carry one’.
Ensure that children can explain the compact method, referring to the real value of the
digits. They need to understand that they are repartitioning the 60 + 3 as 50 + 13.Later,
extend to multiple steps of exchanging and decimals.
258
3 6. 6
8 7
or 4 5 .8
5 1
5 6 3
345
8 2. 4
-2 4 6
1 1
This should be more that 4 digit plus more than 4 digit integers. Should also
include adding including decimals.
6
As above extended to larger numbers and more decimal places.
St John’s Written Calculations Policy
3 1 7
This should be more that 4 digit minus more than 4 digit integers. Should also include
subtracting including decimals.
As above extended to larger numbers and more decimal places.
For extra detail please see full policy.
Written Calculation At A Glance
Year Multiplication
Division
EYFS
Sharing / Grouping
1
St John’s Written Calculations Policy
For extra detail please see full policy.
Written Calculation At A Glance
2
Number Beads, Number lines and Hundred Squares
6 x 5 = 30 or 5 + 5 + 5 + 5 + 5 + 5 = 30
6 strawberries shared between 2 children. How many berries do they get each? 62 =
Multiplication as repeated addition
St John’s Written Calculations Policy
For extra detail please see full policy.
Written Calculation At A Glance
Arrays
St John’s Written Calculations Policy
For extra detail please see full policy.
Written Calculation At A Glance
3
Single digit times single digit 3x4 =12
Written in terms of chunking:
Double digit times single digits:
1)Record using arrays. (equipment can be used to support understanding).
Remainders can be
Single digit and small numbers written as an array:
2) Develop Arrays to grid method:
St John’s Written Calculations Policy
For extra detail please see full policy.
Written Calculation At A Glance
Remainders can be given in terms of leftover.
Year
Multiplication
Division
4
Compact Short Method
Compact Short Method
Develop formal written short method for 2 and 3 digit integers by one
digit integers.
This should be introduced with manipulatives to end with formal method on the right.
221
342
X 7
-------2394
The recording is reduced further, with the carried digits recorded line the
line, above the numbers.
It should be checked using arrays.
St John’s Written Calculations Policy
For extra detail please see full policy.
Written Calculation At A Glance
Remainder if given should e as remainders (can use term leftover).
Year
Multiplication
Division
5
Compact Short Method
Compact Short Method
Develop formal written short method for 4 digit integers by one digit
integers.
Again start to solve calculations with remainders.
221
342
X 7
-------2394
The recording is reduced further, with the carried digits recorded line the
line, above the numbers.
Children can look at putting remainders into decimals using this method
Compact Method of Long Multiplication
1) Back to arrays
St John’s Written Calculations Policy
For extra detail please see full policy.
Written Calculation At A Glance
Children can look at putting remainders into fractions using this method
2) Develop to formal written method:
If carrying from the tens column, the number does above (sitting) on the line.
When adding the two answers,
12
X
124
36
1
----------------744 (124 x 6)
3720 (124 x 30)
------1----------44 6 4
Year
Multiplication
St John’s Written Calculations Policy
Division
For extra detail please see full policy.
Written Calculation At A Glance
6
Compact Short Method
Compact Short Method
221
342
X 7
-------2394
The recording is reduced further, with the carried digits recorded line the
line, above the numbers.
As above extended to larger numbers and more decimal places.
Compact Method of Long Division
This should be through the use of efficient chunking (not repeated subtraction
of 10 lots of a number but using mental skills to support).
Compact Method of Long Multiplication
Getting pupils to write out their multiplication menu will help:
If carrying from the tens column, the number does above (sitting) on the line.
When adding the two answers,
12
X
Develop from empty array to formal method
124
36
1
----------------744 (124 x 6)
3720 (124 x 30)
------1----------44 6 4
St John’s Written Calculations Policy
For extra detail please see full policy.
Written Calculation At A Glance
St John’s Written Calculations Policy
For extra detail please see full policy.