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A Skeleton Progression
for
Teaching of the Standard Algorithm
with
Some Reference and Support Materials.
East Riding of Yorkshire
Numeracy Team
November 2002
A Skeleton Progression
Contents
 Introduction
 Addition Grid for Yrs 3 to 6
 Extracts from the Framework for easy reference
 Subtraction Grid for Yrs 3 to 6
 Extracts from the Framework for easy reference
 Subtraction: An alternative approach using negative numbers
 Multiplication Grid for Yrs 3 to 6
 Extracts from the Framework for easy reference
 Napier’s Boxes (An approach to multiplication)
 Division Grid for Yrs 3 to 6
 Extracts from the Framework for easy reference




Year
Year
Year
Year
3
4
5
6
Grid
Grid
Grid
Grid
for
for
for
for
all
all
all
all
four
four
four
four
operations
operations
operations
operations
 “Always Ask” A poster for classroom use.
Introduction
This booklet provides a skeleton progression for the teaching of the standard algorithm that is recommended in the
“Framework for Teaching Mathematics from Reception to Year 6”. These written methods are to be used when
mental calculations become too difficult and jottings may be inefficient or prone to mistakes.
Definitions:
Mental methods: The ability to calculate “in your head”, quickly recalling a growing number of known number facts and
using these and an understanding of the number system to deduce others.
Jottings: Children’s own recordings that support their mental methods and which, although informal, help memory,
keep track of the steps in a calculation and are mathematically sound.
Formal written methods: A structured and efficient written recording that supports the pupils’ mathematical thinking
and can be understood and recognised by others.
The progression described appertains to teaching pupils how to calculate with large or difficult numbers. When pupils
are using mathematics to solve problems they should be allowed to choose the most appropriate method for
calculation. They should be encouraged to consider whether they can solve the calculation mentally, either with or
without jottings. If this is inappropriate they should then be able to move to a formal written method.
APPROACHES TO WRITTEN CALCULATIONS:
Addition
Year 3
Year 4
Rapid recall Number bonds to 20.
Within 100, addition of any number to
a multiple of 10.
UNDERSTANDING OF THE NUMBER
SYSTEM. Place value to at least 100.
Ability to partition within 100. Use of
the open number line.
Framework-Sec 5-Pg 43


A proposed progression with expectations for each year.
( The “average” child )
Develop partitioning of numbers
and use empty number lines with
increasingly difficult numbers.
Work calculations horizontally
and vertically side by side
working with most significant
digit first.
Rapid recall Add strings of upto 4
numbers. Within 1000 addition of
any number to a multiple of 10 or
100
UNDERSTANDING OF THE
NUMBER SYSTEM. Place value to
at least 1000. Decimals in money
(£1.36).Partition within 1000. Use
of open number line.
Framework-Sec 6-Pg 48
NOT NECESSARY to use
compensation as a written method.

Begin expanded method, adding
most significant digit first. See
A.

Progress to handling least
significant first. See C.
[This will prepare for carrying
below the line ~ compact method.]
Year 5
Year 6
Rapid recall Add strings of upto 5
numbers.
Rapid recall Add strings of numbers
UNDERSTANDING OF THE
NUMBER SYSTEM. Place value to
at least
10 000 and decimals in money and
measures. Use of open number line
with decimals.
Framework-Sec 6-Pg 49
NOT NECESSARY to use
compensation as a written method.
UNDERSTANDING OF THE NUMBER
SYSTEM. Place value to any number of
digits and 2 dp. Use of open number
line with upto 2 dp.

Use Carrying method. See
C. For those not confident
from Y 4 continue with A
but teach C when
appropriate.
[If appropriate use expanded
method A but handling least
significant digit first for decimals.]
Framework Sec 6-Pg 49
NOT NECESSARY to use compensation
as a written method.

As Yr 5 extending method to any
number of digits and decimal
places.
[Children not confident with carrying use
expanded method.Teach C again when
and if appropriate.]
AIM
All children add two 2-digit
numbers; some add two 3-digit
numbers.
AIM
Most children use compact method
when appropriate, ie two 3-digit
numbers or several numbers. (NOT
two 2-digit numbers)
AIM
Most children able to use carrying
by end of year; numbers upto 10
000 and decimals]
AIM
Children use carrying method when
appropriate.
Decimals, including money
Two or more 3-digit sums of money
eg £4.21 + £3.87
Adding two or more 3-digit numbers
with 1 or 2 decimal places.
Adding 2 or more numbers with upto 4
digits and / or 1 or 2 dp.
TIME :- Teach addition of time by counting on, use open number lines.
APPROACHES TO WRITTEN CALCULATIONS:
year.
Subtraction
Year 3
Rapid recall Number bonds to 20.
Within 1000, subtract any multiple
of 100.
UNDERSTANDING OF THE
NUMBER SYSTEM. Place value to at
least 100. Ability to partition within
100. Use of the open number line.
Framework-Sec5-Pg 45
NOT NECESSARY to use
compensation as a written
method.


Develop counting on / back
with empty number lines and
shortened vertical method
side by side, using 2 & 3
digit numbers. See A Pg 45.
Expanded decomposition only
as in C. [ Recording as 50&7,
not 50+7 ]
AIM
All children able to use empty
number lines and most secure with
Sec C, using 2-digit numbers.
Decimals, including money
A proposed progression with expectations for each
( The “average” child )
Year 4
Rapid recall Number bonds to 20. All
complementary numbers within 100.
UNDERSTAMDING OF THE
NUMBER SYSTEM. Understand
relationship between + & -.
Understand commutative and
associative laws.
UNDERSTANDING OF THE
NUMBER SYSTEM. Place value to at
least
10 000 and decimals in money and
measures. Use of open number line.
Year 6
Rapid recall Use known number facts
and place value for rapid mental
calculation.
UNDERSTANDING OF THE
NUMBER SYSTEM. Understand
difference between positive and
negative integers and 2 negative
integers.
Framework-Sec6-Pg 50
Framework-Sec6-Pg 51
Framework-Sec6-Pg 51
NOT NECESSARY to use
compensation as a written method
NOT NECESSARY to use
compensation as a written method
NOT NECESSARY to use
compensation as a written method

Teach expanded
decomposition ( using “and” or
& as in Y3) leading to
compact method. See C.

Also continue to use counting
up with informal jottings
when appropriate, eg
subtracting from 1000’s or
100’s.
Year 5
Rapid recall Decimal complements
within 1 and 10.


AIM
Most children use compact
decomposition when appropriate.
3-digit minus 3-digit / 3-digit minus
2-digit.
Two or more 3-digit sums of money
eg £4.20 - £3.87

Continue to develop compact
decomposition with different
numbers of digits and with
decimals (See C, Pg 51)
Children not confident from
Y4 continue to use preferred
reliable method. Teach C
again when appropriate.
Continue counting up with
jottings, when appropriate.

As in Y5 with increasingly
complex numbers.
AIM
Most children able to use compact
decomposition with all types of
numbers, including decimals.
AIM
Most children able to use compact
decomposition when appropriate.
Subtracting two 3-digit numbers
with 1 or 2 decimal places.
Subtracting numbers with upto 4
digits and / or 1 or 2 dp.
TIME :- Teach time, eg “45 minutes before 1:30” by counting back; use open number lines.
Subtraction
Remember it is far better to learn through using numbers in context than to
learn methods in an abstract way and then attempt to apply them.
e.g. There are 76 boys and 93 girls in Year 3. How many more girls than boys
are there?
Stage 3 (Year 3)
may use blank number lines
+4
+10
+3
_________________________________________
76
80
90
93
+ 4 takes us to the next multiple of
10
+ 10 takes us to 90
+ 3 takes us to 93
So there are 17 more girls than boys.
Note Encourage checking by 76 + 17
The number line can be used throughout Year 3 (Stage 1) with number
sentences written side by side.
The garden centre had 104 rose bushes. During the spring it sold 67. How
many are left?
+3
+30
+4
______________________________________________
67 70
100 104
+ 3 makes 70
+30 makes 100
+ 4 makes 104
Check?
Answer: - 37 rose bushes left.
How?
Record also as 104 – 67 = 37
Also teach partitioning and re-combining but no exchanges.
e.g. 59 - 23 = 50 - 20 & 9 - 3
30
&
6
= 36
Stage 2 (Year 4) Negative Number method
A
36 – 14
N.B. no exchanging.
36 = 30 & 6
partitioning and re-combining
- 14 = 10 & 4
as in teaching of addition
20 + 2 = 22
B
52 – 17
52 = 50 & 2
-17 10 & 7
40 – 5 = 35
NB Teach as “the most I can take from 2 is 2. So I still need to take
away 5, hence –5.
Or teach using positive, negative number line.
___________________________________________
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
2 - 7 = -5
C
754 – 329
754 = 700 & 50 & 4
-329 = 300 & 20 & 9
400 + 30 – 5 = 425
D
620 – 173
620 = 600 & 20 & 0
-173 = 100 & 70 & 3
500 -50 -3 = 447
Stage 3 (Year 5)
Stay within 3 digit numbers, use “0” in the 10’s column and for those who are
ready no partitioning by Summer Term.
A
B
704 = 700 & 0 & 4
322 = 300 & 20 & 2
400 - 20 & 2 = 382
702
-165
600 – 60 – 3 = 537
REMEMBER
CHECK
USING
INVERSE
165
+537
702
Year 6 (Stage 4)
Extend to 4/5 digit numbers.
May be appropriate to recap and use partitioning/re-combining initially.
A
14632 = 10000 & 4000 & 600 & 30 & 2
9847 =
& 9000 & 800 & 40 & 7
10000 -5000 -200 -10 -5
To support children
they may need to make
jottings
5000 – 200 = 4800 – 10
4790 - 5
Ans 4785
Remember to encourage checking by using the inverse.
B
TTh Th H T U
1 4 6 3 2
9 8 4 7
1 - 5–2–1-5
10000 – 5000 – 200 – 10 – 5
4800
Ans 4785
This can only be done when pupil is
thinking “number value”
not digit.
Year 6 (Stage 4)
Decimals, partition/re-combine initially.
A
63.4 =
9.7 =
60 & 3 & 0.4
9 & 0.7
60 -6 -0.3
Jottings needed
B
75.23
18.79
54 – 0.3 Ans 53.7
=
70 & 5 & 0.2 & 0.03
=
10 & 8 & 0.7 & 0.09
60 - 3 - 0.5 - 0.06
57 – 0.5 = 56.5 – 0.06
Ans 56.44
C
Only contract and have no jottings when confident and thinking “number
value”.
T U
2 7 . 5 3
- 9 . 4 6
2 – 2 .+1 - 3
20 – 2. +1 – 3
Ans 18.07
9.46
18.07
27.53
CHECK
USING
INVERS
E
NB Even when dealing with large numbers many children will be more
confident if they write the real value of the numbers.
e.g. 21007
-2986
20000 – 1000 – 900 – 80 1
Ans 18021
CHEC
K
Through all 4 stages
children should be encouraged
to check using inverse operation
or a number line.
CHEC
K
2986
+18021
21007
+4 +10
18000
+7
_______________________________________________________
2986
3000
21000
21007
Ans 18021
APPROACHES TO WRITTEN CALCULATIONS:
year.
Multiplication
A proposed progression with expectations for each
( The “average” child )
Year 3
Rapid recall 2, 3, 4, 5, 10 x tables
and corresponding multiplication and
division facts.
Year 4
Rapid recall 2, 3, 4, 5, 10, 6, 8 x
tables and corresponding
multiplication and division facts.
Year 5
Rapid recall All x tables and
corresponding multiplication and
division facts.
Year 6
Rapid recall All x tables and
corresponding multiplication and
division facts.
UNDERSTANDING OF THE
NUMBER SYSTEM. Understand
grouping, sharing and arrays.
Understand that multiplication can
be done in any order. Recognise
relationship between division and
multiplication.
Framework-Sec 5-Pg 57
UNDERSTANDING OF THE
NUMBER SYSTEM. Understand
commutative, associative and
distributive laws in relation to
multiplication.
UNDERSTANDING OF THE
NUMBER SYSTEM. Understand the
effect of, and relationship between
the four operations.
UNDERSTANDING OF THE
NUMBER SYSTEM. Understand the
use of brackets
Framework-Sec 6-Pg 66
Framework-Sec 6-Pg 67
Framework-Sec 6-Pg 67


No formal method but
children should understand
multiplicat’n as repeated
addition and as describing an
array.
Continue with informal
methods. eg 17 x 5

Teach grid method. See A.
Use 2 /3 digit numbers.

Progress to B, vertical,
expanded recording, most
significant digit first.


Where appropriate teach
compact standard method,
B(ii)

Continue expanded or grid
method for those not
confident.
Progress to handling units
first leading to ………..

Long multiplication ~ begin
with grid method, See A.
Compact standard method,
See B.

Compact method when
appropriate, See B (iii)
17

10 x 5 = 50
7 x 5
=35
Decimals including money
Teach compact method for
those not confident in Y 5.

Long multiplication ~ teach
compact method when
appropriate.

Continue with grid method
where this is more reliable.
Use Napier’s Boxes as
possible alternative to long
multiplication.
( See example sheet )
TABLES:- Regular revision of all
tables
AIM
Children can use compact short
method with any number of digits.

85
TABLES 2, 3, 4, 5, 10

TABLES 2, 3, 4, 5, 10, 6, 8
TABLES 2, 3, 4, 5, 10, 6, 8, 9, 7
AIM
Most confident with vertical,
expanded method (B). Some able to
use compact standard method.
AIM
Most children able to use compact
method for short mult. of 4-digit
numbers. Grid method for long mult.
Compact method for simple decimals
( 1 dec. place ) eg 5.8 x 3 =
Compact method for short mult’n.
Chosen method for long.
NAPIER’S BOXES
Examples
1.
8 x 2 = 16
4.
46 x 25 = 1,150
6
4
8
6.
1
1
2
6
2
3
1
6
2.
Answer:
16
1,
1
98 x 2 = 196
x
8
9
1
1
6
8
3.
47 x 9 = 423
2
4
7
3
4
3
6
2
3
9,
0
8
6
0
8
23.7 x 3.2 = 75.84
7
8
9
Write down 2, carry 1 which added to 3
4
x
2
9
6
2
1
8
2
3
x
6
1
9
4
3
2
2
5
2
4
6
7.
x
1
4
4
2
4
2
1
6
9
1
2
2
1
784 x 37 = 29,008
8
6
4
3
0
7
x
1
1
0
5
5.
2
5
0
2
3
2
2
8
1
x
x
13.2 x 24 = 316.8
1
1
7
4
7
1
5
2
6
8
3
4
4
APPROACHES TO WRITTEN CALCULATIONS:
A proposed progression with expectations for each
year.
Division
( The “average” child )
Year 3
Rapid recall 2, 3, 4, 5, 10 x tables
and corresponding multiplication and
division facts.
UNDERSTANDING OF THE
NUMBER SYSTEM. Understand
grouping, sharing, arrays. Recognise
relationship between Multiplication
and division.
Year 4
Rapid recall 2, 3, 4, 5, 10, 6, 8 x
tables and corresponding
multiplication and division facts.
UNDERSTANDING OF THE
NUMBER SYSTEM. Understand
relationship between division and
subtraction.
Understand rounding.
Year 5
Rapid recall All x tables and
corresponding multiplication and
division facts.
UNDERSTANDING OF THE
NUMBER SYSTEM. Understand the
quotient as a fraction or decimal.
Year 6
Rapid recall All x tables and
corresponding multiplication and
division facts.
UNDERSTANDING OF THE
NUMBER SYSTEM. Understand the
quotient as a fraction or decimal.
Understand rounding, in context.
Framework- Sec 5 – Pg 49/51
See these pages for skills to develop.
No formal written methods.
Framework- Sec 6 – Pg 68
Framework- Sec 6 – Pg 69
Framework- Sec 6 – Pg 69

Derive division facts for 2, 3,
4, 5, 10 x tables.

Be secure at subtracting
multiples of 10 from any given
number
eg 126 – 20/30/50 etc.

Teach A, “using multiples of the
divisor” ( chunking ) for
repeated subtraction.


[NB when chunking in 4’s may prefer to
record “10 lots of 4” rather than 10 x
4]

Continue to develop standard
method B.
Progress to subtracting 20/30/x
divisor when appropriate.
6 )197
- 180 ( 30 lots of 6 )
etc.
Progress to B.

Do not write answer above bracket and
again use term “lots of”.
Progress to standard compact
method B (ii)
6 )195
180
15
12
3
AIM
Understand grouping and sharing; that
division is inverse of multiplication.
Record simple mental divisions in number
sentences.
Decimals, including money
AIM
Most children using chunking (B) able to
divide 2 or 3-digit numbers by single
digit numbers.


Continue compact short division
as in Yr5. See A.
Progress to long division. See B
28 )763
560 ( 20 lots of 28 )
203
140 ( 5 lots of 28 )
63
56 (2 lots of 28 )
7
Ans: 27 R 7 or 27 ¼ or 27.25
Ans: 32 R
3 or 32 ½
AIM
Most children use compact method for
short division. For those not secure
continue B (i)
Division of money.
Relate remainders to fractions and
decimals.
AIM
Children able to use appropriate short
method for any number, including
decimals: Some able to do long division.
Extend methods to decimals with upto 2
dp.
APPROACHES TO WRITTEN CALCULATIONS:
Addition
Rapid recall Number bonds to 20.
Within 100, addition of any number to
a multiple of 10.
UNDERSTANDING OF THE NUMBER
SYSTEM. Place value to at least 100.
Ability to partition within 100. Use of
the open number line.
Framework-Sec 5-Pg 43


Develop partitioning of numbers
and use empty number lines with
increasingly difficult numbers.
Work calculations horizontally
and vertically side by side
working with most significant
digit first.
Year 3.
Subtraction
Multiplication
Division
Rapid recall Number bonds to 20.
Within 1000, subtract any multiple
of 100.
UNDERSTANDING OF THE
NUMBER SYSTEM. Place value to
at least 100. Ability to partition
within 100. Use of the open number
line.
Rapid recall 2, 3, 4, 5, 10 x tables
and corresponding multiplication and
division facts.
UNDERSTANDING OF THE
NUMBER SYSTEM. Understand
grouping, sharing and arrays.
Understand that multiplication can
be done in any order. Recognise
relationship between division and
multiplication.
Framework-Sec 5-Pg 57
Rapid recall 2, 3, 4, 5, 10 x tables
and corresponding multiplication and
division facts.
UNDERSTANDING OF THE
NUMBER SYSTEM. Understand
grouping, sharing, arrays. Recognise
relationship between Multiplication
and division.
Framework-Sec5-Pg 45
NOT NECESSARY to use
compensation as a written
method.

Develop counting on / back
with empty number lines and
shortened vertical method
side by side, using 2 & 3
digit numbers. See A Pg 45.


No formal method but
children should understand
multiplicat’n as repeated
addition and as describing an
array.
Continue with informal
methods. eg 17 x 5
17

Expanded decomposition only
as in C. [ Recording as
50&7, not 50+7 ]
10 x 5 = 50
Framework- Sec 5 – Pg 49/51
See these pages for skills to
develop.
No formal written methods.

Derive division facts for 2,
3, 4, 5, 10 x tables.

Be secure at subtracting
multiples of 10 from any
given number
eg 126 – 20/30/50 etc.
7 x 5
=35
85
AIM
All children add two 2-digit
numbers; some add two 3-digit
numbers.
AIM
All children able to use empty
number lines and most secure with
Sec C, using 2-digit numbers.
TIME :- Teach addition of time by
counting on, use open number lines.
TIME :- Teach time, eg “45
minutes before 1:30” by counting
back; use open number lines.
TABLES 2, 3, 4, 5, 10
AIM
Understand grouping and sharing;
that division is inverse of
multiplication.
Record simple mental divisions in
number sentences
APPROACHES TO WRITTEN CALCULATIONS:
Addition
Rapid recall Add strings of upto 4
numbers. Within 1000 addition of any
number to a multiple of 10 or 100
UNDERSTANDING OF THE NUMBER
SYSTEM. Place value to at least 1000.
Decimals in money (£1.36).Partition
within 1000. Use of open number line.
Year 4
Subtraction
Division
UNDERSTANDING OF THE NUMBER
SYSTEM. Understand relationship
between + & -. Understand commutative
and associative laws.
Rapid recall 2, 3, 4, 5, 10, 6, 8 x
tables and corresponding multiplication
and division facts.
UNDERSTANDING OF THE NUMBER
SYSTEM. Understand commutative,
associative and distributive laws in
relation to multiplication.
Rapid recall 2, 3, 4, 5, 10, 6, 8 x tables
and corresponding multiplication and
division facts.
UNDERSTANDING OF THE NUMBER
SYSTEM. Understand relationship
between division and subtraction.
Understand rounding.
Framework-Sec 6-Pg 48
Framework-Sec6-Pg 50
Framework-Sec 6-Pg 66
Framework- Sec 6 – Pg 68
NOT NECESSARY to use compensation
as a written method.
NOT NECESSARY to use compensation
as a written method


Begin expanded method, adding most
significant digit first. See A.
Rapid recall Number bonds to 20. All
complementary numbers within 100.
Multiplication

Progress to handling least significant
first. See C.
Teach grid method. See A. Use
2 /3 digit numbers.

Progress to B, vertical,
expanded recording, most
significant digit first.


[This will prepare for carrying below the
line ~ compact method.]
Teach expanded decomposition (
using “and” or & as in Y3)
leading to compact method. See
C.

Also continue to use counting up
with informal jottings when
appropriate, eg subtracting from
1000’s or 100’s.

Progress to handling units first
leading to ………..
Compact standard method, See
B.

Teach A, “using multiples of the
divisor” ( chunking ) for
repeated subtraction.
[NB when chunking in 4’s may prefer to
record “10 lots of 4” rather than 10 x
4]

Progress to B.
Do not write answer above bracket and
again use term “lots of”.

AIM
Most children use compact method
when appropriate, ie two 3-digit
numbers or several numbers. (NOT two
2-digit numbers)
AIM
Most children use compact decomposition
when appropriate.
3-digit minus 3-digit / 3-digit minus 2digit.
Decimals, including money
Two or more 3-digit sums of money
eg £4.21 + £3.87
Two or more 3-digit sums of money
eg £4.20 - £3.87
Decimals, including money
TABLES 2, 3, 4, 5, 10, 6, 8
AIM
Most confident with vertical, expanded
method (B). Some able to use compact
standard method.
AIM
Most children using chunking (B) able to
divide 2 or 3-digit numbers by single
digit numbers.
APPROACHES TO WRITTEN CALCULATIONS:
Year 5
Addition
Rapid recall Add strings of upto 5
numbers.
Subtraction
Rapid recall Decimal complements within 1
and 10.
UNDERSTANDING OF THE NUMBER
SYSTEM. Place value to at least
10 000 and decimals in money and
measures. Use of open number line with
decimals.
Framework-Sec 6-Pg 49
UNDERSTANDING OF THE NUMBER
SYSTEM. Place value to at least
10 000 and decimals in money and
measures. Use of open number line.
NOT NECESSARY to use compensation
as a written method.
NOT NECESSARY to use compensation
as a written method

Where appropriate teach
compact standard method, B(ii)
Continue to develop compact
decomposition with different
numbers of digits and with
decimals (See C, Pg 51)
Children not confident from Y4
continue to use preferred
reliable method. Teach C again
when appropriate.
Continue counting up with
jottings, when appropriate.

Continue expanded or grid
method for those not confident.

Long multiplication ~ begin with
grid method, See A.

Compact method when
appropriate, See B (iii)
Framework-Sec6-Pg 51
Multiplication
Rapid recall All x tables and
corresponding multiplication and division
facts.
UNDERSTANDING OF THE NUMBER
SYSTEM. Understand the effect of, and
relationship between the four operations.
Division
Rapid recall All x tables and
corresponding multiplication and division
facts.
UNDERSTANDING OF THE NUMBER
SYSTEM. Understand the quotient as a
fraction or decimal.
Framework-Sec 6-Pg 67
Framework- Sec 6 – Pg 69



Use Carrying method. See C.
For those not confident from Y
4 continue with A but teach C
when appropriate.


[If appropriate use expanded method A
but handling least significant digit first
for decimals.]

AIM
Most children able to use carrying by
end of year; numbers upto 10 000 and
decimals]
AIM
Most children able to use compact
decomposition with all types of numbers,
including decimals.
Adding two or more 3-digit numbers with
1 or 2 decimal places.
Subtracting two 3-digit numbers with 1
or 2 decimal places.
Continue to develop standard
method B.
Progress to subtracting 20/30/x
divisor when appropriate.
6 )197
- 180 ( 30 lots of 6 )
etc.

Progress to standard compact
method B (ii)
6 )195
180
15
12
3
3 or 32 ½
AIM
Most children use compact method for
short division. For those not secure
continue B (i)
TABLES 2, 3, 4, 5, 10, 6, 8, 9, 7
AIM
Most children able to use compact
method for short mult. of 4-digit
numbers. Grid method for long mult.
Compact method for simple decimals
1 dec. place ) eg 5.8 x 3 =
Ans: 32 R
(
Division of money.
Relate remainders to fractions and
decimals.
APPROACHES TO WRITTEN CALCULATIONS:
Addition
Year 6
Subtraction
Rapid recall Add strings of numbers
Rapid recall Use known number facts and
place value for rapid mental calculation.
UNDERSTANDING OF THE NUMBER
SYSTEM. Place value to any number of
digits and 2 dp. Use of open number line
with upto 2 dp.
UNDERSTANDING OF THE NUMBER
SYSTEM. Understand difference
between positive and negative integers
and 2 negative integers.
Framework Sec 6-Pg 49
Framework-Sec6-Pg 51
NOT NECESSARY to use compensation
as a written method.
NOT NECESSARY to use compensation
as a written method
Multiplication
Division
Rapid recall All x tables and
corresponding multiplication and division
facts.
UNDERSTANDING OF THE NUMBER
SYSTEM. Understand the use of
brackets
Rapid recall All x tables and
corresponding multiplication and division
facts.
UNDERSTANDING OF THE NUMBER
SYSTEM. Understand the quotient as a
fraction or decimal.
Understand rounding, in context.
Framework-Sec 6-Pg 67
Framework- Sec 6 – Pg 69

Teach compact method for those
not confident in Y 5.

Long multiplication ~ teach
compact method when
appropriate.



As Yr 5 extending method to
any number of digits and decimal
places.

As in Y5 with increasingly
complex numbers.
[Children not confident with carrying use
expanded method.Teach C again when
and if appropriate.]
AIM
Children use carrying method when
appropriate.
AIM
Most children able to use compact
decomposition when appropriate.
Adding 2 or more numbers with upto 4
digits and / or 1 or 2 dp.
Subtracting numbers with upto 4 digits
and / or 1 or 2 dp.

Continue with grid method where
this is more reliable.

Use Napier’s Boxes as possible
alternative to long multiplication.
( See example sheet )
TABLES:- Regular revision of all tables
AIM
Children can use compact short method
with any number of digits.
Compact method for short mult’n.
Chosen method for long.
Continue compact short division
as in Yr5. See A.
Progress to long division. See B
28 )763
560 ( 20 lots of 28 )
203
140 ( 5 lots of 28 )
63
56 (2 lots of 28 )
7
Ans: 27 R 7 or 27 ¼ or 27.25
AIM
Children able to use appropriate short
method for any number, including
decimals: Some able to do long division.
Extend methods to decimals with upto 2
dp.
ALWAYS ASK:
Can I do this in my head?
Do I know the
approximate size of
the answer?
What could I jot down
to help me?
Do I really need to
do a written
calculation?