1
Foundation Stage
Begin to represent numbers using
fingers, marks on paper or
pictures.
Begin to relate addition to
combining 2 groups of objects.
Eg. Practical activities, counting
songs and number stories.
In practical activities and
discussion begin to use the
vocabulary involved in adding
Find the total number of items in
two groups by counting them all.
Adults model use of number tracks
and number lines to show how you
arrive at another point when something
is added.
Clifton Primary School Recording and Written Calculations Policy
ADDITION
Year 1
Year 2
Record simple mental addition in a number sentence
Record mental addition in a number sentence using
using the + and = signs, particularly all number bonds
the + and = signs.
to 10 then 20 Record opposite way round e.g. 6+4 =
10, 10 = 6+4
Be able to complete number sentences where a
Recognise the use of symbols such as Ο ∇ to
missing number is shown by a symbol eg.
stand for unknown numbers and complete number
5+2= ∆
∆ =5+2
sentences.
5+∆=7
7=∆+2
9 + ∆ = 13 ∆+ 4 = 13
∆ + 2 =7
7 = 2 + ∆ etc.
40 + = 100
+200 = 400 etc
Extend to 3 numbers eg
5 + ∆ + 4 = 13
Use prepared number lines then progress on to
Record addition by:
drawing own empty number lines to count in
- showing jumps on prepared number lines
tens/multiples of 10s, eg 23+20
- drawing own number line
+10
+10
6 + 5 = 11
6
7
8
9
10
11
Using the empty number line to add 10 to a single
digit number. Eg.8 + 10 = 18
+10
8
18
Begin to use empty number lines
Use a number line to add a pair of single digit
numbers to bridge through 10 eg 8 + 5 =13
+2
+3
8
10
13
Bridge through a multiple of 10 to add, explaining
method eg 18 + 5 = 23
+2
+3
23
33
43
To bridge through a multiple of 10
eg 36 + 8 = 44
+4
+4
16
40
44
Partition 2 digit numbers eg 35+23 (not crossing
the tens or hundreds barrier) using different
methods of recording
A) Number line: eg 35+23 =
+20
+3
35
55
58
B) Not using number line eg
35 +23
OR
30 + 20 = 50
35+20=55
5+3=8
55+3=58
50 + 8 = 58
Year 3
Continue to develop recording of equations using
+and =with larger numbers.
Recognise the use of symbols such as Ο ∇ to stand
for unknown numbers and complete number
sentences.
19 + ∆ = 33 ∆+ 14 = 33
Use 3 numbers eg
10 + ∆ + 50 = 100 ∆ + ◊ + O =100
347 +
= 447
Autumn and Spring term:
A) Partitioning using empty number lines with
increasingly difficult numbers (crossing tens and 100
barrier).
86+57
+50
+4 +3
86
136 140 143
B) Partitioning not using number line:
356+427 =
OR
300+400=700
356+400=756
50+20=70
756+20=776
6+7=13
776+7=883
700+70+13=783.
Summer Term:
Present calculations vertically using partitioning
skills. Least significant digit first (expanded
method).
67
+ 24
11 (7+4)
80 (60+20)
91
18
20
23
Represent number line calculations in a number
sentence.
Add 9 or 11 by adding 10 and adjusting by 1. Begin to
add 19 or 21 adding 20 and adjusting by 1.
Demonstrate number line, record jottings eg
27 + 9
27
27+10=37
37-1=36
Use developing mathematical
ideas and methods to attempt to
solve practical problems.
Solve simple problems explaining methods and
reasoning. Good activities for plenary/paired work.
+10
36
37
Solve problems explaining methods and reasoning orally
and where appropriate in writing.
Add a near multiple of 10 to a two digit number and
show on a number line, record jottings
eg 45 +19
+20
45
45+20=65
65-1=64
64 65
Solve problems explaining methods and reasoning orally and
where appropriate in writing.
Aim: By end of Y3 all children to add two 2-digit numbers,
some children should be able to add 2 and 3-digit numbers
showing method used.
2
Clifton Primary School Recording and Written Calculations Policy
Year 4
Use symbols and missing numbers:Continue to develop as in Y1, 2 and 3 but with appropriate
numbers.
Continue to develop use of empty number lines,
partitioning and other informal recording methods
developed in Y1,2 and 3 to support and explain
calculations where appropriate.
A) Using Number Lines:
Eg 58+24
+20
+2
+2
58
78
80
B) Not using number lines.
58 +24
OR
50 + 20 = 70
58+20 = 78
8+4=12
78+4 = 82
70+12 = 82
ADDITION
Year 5
Use symbols and missing numbers:Continue to develop as in Y1, 2, 3 and 4 but with
appropriate numbers.
Year 6
Use symbols and missing numbers:Continue to develop as in earlier years but with
appropriate numbers (including decimals).
Develop use of empty number lines, partitioning and other
informal recording methods developed in Y1,2,3 and 4 to
support and explain calculations where appropriate
(including decimals).
Develop use of empty number lines, partitioning and other
informal recording methods developed in earlier years to
support and explain calculations where appropriate
(including decimals).
Use compact carrying method.
587
3587
+ 475
+ 675
4262
1062
As Yr 5 but extend to any number of digits and
decimal places.
82
Continue with standard written method. Least
significant digit first. Start with expanded, move on to
‘carrying’ below the line (compact recording). See
Guidance Paper Calculation.
358
358
+ 73
+ 73
11 (8+3)
4 3 1
120 (50+70)
11
300 (300+0)
431
Emphasise vocabulary when adding (e.g., 5 tens add 7
tens)
Solve problems explaining methods and reasoning orally
and in writing.
AIM: By the end of Year 4 Most children should be
able to use ‘compact’ method when appropriate to add
two 3- digit numbers or several numbers.
Note: ‘compact’ method is not appropriate for adding two
2-digit numbers – this is a mental KLO.
11
111
For children that have not yet mastered compact method,
use expanded.
Addition of decimals (teach expanded method first to
ensure understanding.) Ensure that children know the
importance of ‘lining up’ the decimal points particularly
when adding mixed amounts eg 16.4 m. + 7.68 m.
16.4
+ 7.68
2 4 . 0 8 m.
1 1
Solve problems explaining methods and reasoning orally
and in writing.
AIM: By the end of Year 5 most children are able to
use compact method, when appropriate, (numbers up
to 10,000 and decimals).
For children that have not yet mastered compact method,
use expanded. Do not re-teach expanded if children are
competent at carrying.
Solve problems explaining methods and reasoning orally
and in writing.
AIM: By the end of Year 6 Children should be able to
use carrying method, accurately and reliably – when
appropriate.
3
Clifton Primary School Recording and Written Calculations Policy
SUBTRACTION
Foundation Stage
Encourage children to record what
they have done e.g. by mark
making.
Begin to relate subtraction to
‘taking away’
In practical activities and discussion
begin to use the vocabulary
involved in subtracting
Adults model use of number
tracks and number lines to show
how you arrive at another point
when something is taken away.
Year 1
Year 2
Record mental subtraction in a number sentence using the – and =
signs
eg 18 – 4 = 14
Extend to
9 + 6 = 20etc.
Record mental subtraction in a number sentence using
the – and = signs, using appropriate numbers.
Be able to complete number sentences where a missing number
is shown by a symbol eg.
6-2=∆
∆ = 6 - 2etc.
Use a marked, partly marked or empty number line to count
back (take away) or to count on (find the difference).
•
17 – 5 (counting back) - marked line
Recognise the use of symbols such as or∇ to stand for unknown numbers
and complete number sentences.
13 - ∆ = 9
∆ - 4 = 9 Extend to: 13 + 5 = ∆ - 10
Use marked, partly marked or empty number lines to count back (take
away) or to count on (find the difference) – see Y1 but use appropriate
numbers.
Understand when it is sensible to count back and when to count on.
Eg 43 – 5 (count back) 43 - 38 (count on)
Use empty number lines to
• Bridge through a multiple of 10
eg 22 – 5 = 17(counting back)
Recognise the use of symbols such as or∇ to stand for
unknown numbers and complete number sentences
36 – 17 =∆
∆ - 15 = 19 20 - ∆ - ◊= 5 etc
Autumn and Spring term:
Develop counting on or counting back with an empty
number line (see Y1 and 2)
eg 82-67
+3
+10
+2
•
8 9 10 11 12 13 14 15 16 17
What is the difference between 17 and 12? (counting on)
– marked line
-3
10
•
11 12
13 14
15
16 17
What is the difference between 12 and 17? (counting on)
– empty line
12
17
Children need to begin to understand when it is sensible to
count back eg 18 – 5 and when it is sensible to count on eg
18 – 13.
Use developing mathematical
ideas and methods to attempt
to solve practical problems.
Year 3
Record simple subtraction in a number sentence using the
– and = signs eg.
There were 8 cakes on a plate. Mary ate 3 of them. How
many were left?
8–3=5
Explain methods and reasoning orally.
-2
17
20
• Bridge through a multiple of 10
eg 23 – 18 = 5(counting on)
+2
22
+3
18
20
23
Partition 2 digit numbers eg 55-23 (not crossing the tens or hundreds
barrier) using different methods of recording
A) Number line: eg 55-23 =
-3
-10
-10
32
35
45
55
B)
Not using number lines:
Partitioning both numbers partitioning the second number only
48 – 23
71-25
40 – 20 =20
OR
71-20=51
8–3=5
51-5=46
20 + 5 = 25
67
70
80
82
Extend to three digit numbers.
Summer term:
Begin to record calculations in preparation for an efficient
standard method.
Expanded decomposition.
Use ‘and’ not ‘+’.
(No exchange first).
57 – 43
50 and 7
- 40 and 3
10 and 4 = 14
Include HTU - TU
157 – 43
100 and 50 and 7
-0 and 40 and 3
100 and 10 and 4 = 114
Then exchange (tens/units). Eg 81 –57
81
= 80 and 1 = 70 and 11
50 and 7
50 and 7
- 57
20 and 4 =24
Subtract 9 or 11. Begin to subtract 19 or 21. Show number line,
demonstrate jottings.
45-9.
-10
35
36
45
45 – 9 =
45 – 10 =35
35 +1= 36
Subtract a near multiple of 10 from a two digit
number. As Yr 2 with appropriate numbers.
Explain methods and reasoning orally and by using any of recording
methods shown above eg 45 – 9
‘I subtracted 10 from 45 – 35 -that was too much so then added 1 and
got 36.’
Explain methods and reasoning orally and by using any
of recording methods shown above or in Y1 or 2.
Aim: by the end of Y3 all children should be able to
use a number line to subtract 2 and 3-digit numbers.
Some should be able to use expanded decomposition
as shown.
4
Clifton Primary School Recording and Written Calculations Policy
SUBTRACTION
Year 4
Year 5
Year 6
Continue to use counting up method, with informal notes or
Continue to use counting up using an empty number line,
Continue to use counting up method, with empty number lines,
jottings, when appropriate eg
informal notes or jottings when appropriate (see Y4 and 5
informal notes or jottings, when appropriate eg
examples) and with appropriate numbers eg
•
When subtracting from multiples of 100 or 1000
•
When subtracting from multiples of 100 or 1000
•
Finding a small difference by counting up
•
Finding a small difference by counting up
•
0.5 – 0.31
eg 5003 – 4996 =7. (can be modelled using an empty number line eg 8006 – 2993 = 5013. (can be modelled using an empty number
+0.09
+0.1
or jottings)
line or jottings)
+4
+3
+7
4996
5000
5003
•
To support or explain mental calculations eg. 322 – 86
+14
+200
+22
•
86
100
300
322
Explaining the subtraction of the nearest multiple of 10 and
adjusting (see Y2/3 examples)
Do not use Compensation Method.Teach expanded
decomposition leading to compact decomposition. (see Guidance
Paper Calculation)
Note: when partitioning numbers use and as in Y3 example eg
700 and 50 and 4
Begin with exchange from tens to units only, then hundreds to
tens, then both. Demonstrate with HTU equipment.
6 14
754 = 700 and 50 and 4
80 and 6
- 86 -
754
86
688
= 700 and 40 and 14
80 and 6
= 600 and 140 and 14
80 and 6
600 and 60 and 8 = 668
When children are secure in the expanded method, move on to
compact method and teach alongside at first.
Extend to decimals as appropriate. Eg money knowing that the
decimal points should line up under each other.
Explain methods orally or using any informal recording methods.
AIM: By the end of Year 4 most children should be able to
use compact decomposition when appropriate ie 3-digit – 3digit or 3-digit – 2-digit. But continue to use counting up
method, with jottings, where appropriate.
Note ‘compact’ method is not appropriate for subtracting two 2digit numbers – this is a mental KLO
+5000
+6
2993
3000
8000 8006
• Using known number facts and place value to subtract eg 4.1
– 1.8 = 2.3
+0.2
+2.0
+0.1
2.0
4.0 4.1
To support or explain mental calculations
To support or explain the subtraction of the nearest multiple
of 10 or 100 then adjust.
Do not use Compensation Method. Continue to develop
compact decomposition with different numbers of digits and
decimals.
Children should understand the importance of lining up units
digits under units digits, tens under tens etc.
0.31
0.4
•
•
0.5
Subtracting the nearest multiple of 10,100, 1000
Subtracting from any multiple of 1000, 10,000 etc ie
where using decomposition would be very
complicated.
1.8
•
•
4
Do not use Compensation Method.Continue to develop compact
decomposition with different numbers of digits and decimals.
Children should understand the importance of lining up units
digits under units digits, tens under tens
3
5 '7 6 4 .' 0
- 821. 6
4942. 4
Children who have not mastered compact decomposition in Y4
continue to use preferred, reliable method, but teach again when
appropriate.
Extend to include calculations up to two decimal places.
e.g
4
3
5 '7 6 4 .' 0 5
- 821. 6 2
4942. 4 3
Explain methods orally or using any informal or formal recording
methods.
AIM: By the end of Year 5 most children should be able to
use compact decomposition with all types of numbers,
including decimal, where appropriate. But should continue to
use counting up method, with jottings, where appropriate.
Children should also be able to add and subtract whole
numbers and decimals with up to two places.
Explain methods orally or using any informal or formal recording
methods.
AIM: By the end of Year 6 children should be able to use
compact decomposition method accurately when appropriate.
But should be able use counting up method, with jottings,
where appropriate.
5
Clifton Primary School Recording and Written Calculations Policy
MULTIPLICATION
Foundation
Stage
Count orally
in 1s, 2s, 5s,
10s.
Count
repeated
groups of the
same size.
Year 1
Year 2
Oral counting on and back in small steps
Eg. 2’s, 5’s and 10’s
(Understand multiplication as repeated
addition eg There are 5 pencils in one
packet. How many pencils in 4 packets?
lllll lllll lllll lllll = 5+5+5+5 or
4 lots of 5 or 4 x 5
This can also be shown as repeated jumps
on a number line.
+5
+5
+5
+5
0
5
10
15
20
Year 3
Record simple mental multiplications in a number sentence
using the x and = signs.
Record mental multiplications in a number sentence using the x
and = signs.
Recognise the use of symbols such as Δ or Ο to stand for
unknown numbers eg.6 x Δ = 12
Δ x 2 = 12
6x2=Δ
Δ x Ο = 12
20 = Δ x 5
20 = 4 x Δ
Understand multiplication as repeated addition eg There are 5
pencils in one packet. How many pencils in 4 packets?
lllll lllll lllll lllll = 5+5+5+5 or
4 lots of 5 or 4 x 5
This can also be shown as repeated jumps on a number line.
+5
+5
+5
+5
Recognise the use of symbols such as Δ or Ο to stand for
unknown numbers eg. 6 x Δ = 18
Δ x 3 = 18
6 x 10 = Δ
Δ x Ο = 24
20 = Δ x 5
20 = 4 x Δ
Understand multiplication as:
•
repeated addition
•
describing an array
(see Y2 examples of these, but use appropriate numbers for Y3
children)
0
5
10
15
20
Understand multiplication as describing an array.
●●●●●
● ● ● ● ● 5 x 4 = 20
●●●●●
●●●●●
4 x 5 = 20
Know 2x ,5x and10x tables
Be able to count in steps of 2, 5, 10.
Begin to interpret situations as multiplications calculations and
explain reasoning. Eg.How many wheels are there on 3 cars?
Also:
Scaling eg Make a tower 3 times taller then this.
Draw a line 4 times longer than this.
Know their 2x, 3x, 4x 5x 6xand 10x tables and begin to know their
6x *.Be able to count in steps of 2,3,4,5,6,10
Interpret situations as multiplication calculations and explain
reasoning. Eg.A baker puts 6 buns in each of 4 rows. How many
buns does she make?
Begin to develop informal ways of calculating and recording
eg 17 x 5
by partitioning and recombining.
For example: 10 x 5 = 50
7 x 5 = 35
50 + 35 = 85
In order to provide the children with some of the pre-requisite skills
for Year 4 written approaches, the objective ‘Use knowledge of
number facts and place value to multiply or divide mentally’ is
important. Eg
•
Multiply a single digit by 1,10 or 100.
•
Double any multiple of 5 up to 50/ halve any multiple of 10 to
100.
•
Multiply a 2-digit number by 2, 3, 4 or 5 without crossing the
tens boundary (eg 23 x 3).
AIM: All children know 2x, 5x and 10x tables. Most know 3x
and 4x tables. All children understand the three aspects of
multiplication.
6
Clifton Primary School Recording and Written Calculations Policy
Year 4
Know by heart multiplication facts for 2,3,4,5,6,7,8,9 and10 x tables (including
multiplication by 0 and 1)
Complete quickly 60 x 2 =? ? x 4 = 160 8 x ?= ? = 120 etc
Understand that division is the inverse of multiplication and use this to check
results.
Develop informal written methods eg partitioning. Teach children to
approximate first in order to get a sensible idea of what the answer must be.
Begin with ‘teens’ numbers eg 13 x 8, then progress rapidly on to multiples of
ten eg 23 x 8.
20 x 8= 160
3 x 8= 24
160 +24= 184
AND Grid Method
x 20
3
8
160
24
=184
Short Multiplication - Progress as appropriate to vertical expanded recording,
multiplying by the least significant digit first.
23
leading to compact
23
x 7
when appropriate
x 7
21 (7x3)
161
2
140 (7x20)
161
When moving from expanded to compact, teach side by side.
MULTIPLICATION
Year 5
Know by heart all multiplication facts up to
10 x 10, including multiplication by 0 and 1.
Complete written questions eg.160 x 2 =? ? x 2 = 290
0.9 x ? = 6.3
Δx ? = 1600 etc
Understand that division is the inverse of multiplication and use this to check
results.
Continue to use informal methods including Grid method of recording to
support and explain mental methods where the numbers are appropriate Eg 47 x
5
Short Multiplication – Compact Standard Method of recording to children for
whom it is appropriate (HTU x U).
346
x
9
3114
45
For those who cannot use this method reliably continue to use partitioning,
‘grid’ or expanded methods as necessary (see Y4). Continue to teach children to
approximate answers first.
Long multiplication – begin with the ‘grid’ method. Eg. 72 x 38 (ans. approx.
70 x 40 = 2800)
x
70
2
2100
60
2160
30
560
16
576
8
2736
Only progress to vertical recording for children for whom it is appropriate. Use
expanded method first, least significant digit first.
72
leading to
72
x 38
only when
x38
16 (8x2)
appropriate
576 (8x72)
560 (8x70)
2160 (30x72)
60 (30x2)
2736
2100 (30x70)
2736
Year 6
Know by heart all multiplication facts up to
10 x 10, including multiplication by 0 and 1.
Complete written questions eg. 0.7 x 20 =? ? x 20 = 8000
4 x ? = 3.6 Δx ? = 2.4 etc
Understand that division is the inverse of multiplication and use this to check
results
Continue to use informal methods including grid method of recording to
support and explain their mental methods where the numbers are appropriate Eg
8.6 x 7.
Short multiplication – teach compact method to children who have not grasped
it in Y5.
Children should be able to multiply ThHTU x U (Doesnt mention ‘Th’ in
framework)
Continue to teach children to approximate answers first.
Long multiplication – teach expanded method first. Only move on to compact
for children for whom it is appropriate, extending to HTU x TU. Children can
continue to use ‘grid’ method if it is more reliable and better understood.
Interpret situations as multiplication calculations g. There are 6 eggs in a box.
How many in 45 boxes? (single step and multistep problems.)
Extend to simple decimals, with one decimal place, multiplied by a single digit.
Approximate first.
4. 9
Use expanded method first.
x 3
2 .7 (3x0.9)
12 .0 (3x4)
14.7
Interpret situations as multiplication calculations Eg.I think of a number, then
divide it by 15. The answer is 20. What was my number?
Interpret situations as multiplication calculations Eg.There are 35 rows of
chairs. There are 28 chairs in each row. How many chairs are there altogether?
AIM: By end of Y4 most children are confident with the vertical, expanded
way of recording multiplication and are able to explain reasoning. Some
are able to use the compact standard method (carrying below the
line).They know 2,3,4,5,6,7,8,9,and 10 x tables .
AIM: By the end of Year 5 most children are able to use compact method
for short multiplication of HTU x U and for simple decimals. Most are able
to use ‘grid’ method for long multiplication. They know all table facts up to
10 x10 (multiplication and division)
AIM: By the end of Year 6 all children can use compact short
multiplication method with any number of digits and decimals. They use
their preferred method for long multiplication. They know all tables up to
10 x 10 (multiplication and division)
Extend to decimals, with up to 2-decimal places, multiplied by a single digit
7
Clifton Primary School Recording and Written Calculations Policy
Foundation
Stage
Share objects
into equal
groups and
count how
many in each
group.
Year 1
Solve problems practically, for example,
involving 2, 5, or 10 or sharing into
equal groups. *
‘We need to put 12 cakes into boxes of 3
or 4. How many boxes will we have?’
Understand the operation of division as
Sharing equally Eg 6 sweets are shared
equally between 2 people. How many
sweets does each one get?
DIVISION
Year 2
Record simple mental divisions in a number sentence using the ÷ and = signs.
Eg. ‘Share 18 between 2’ could be recorded as 18 ÷ 2
Recognise the use of symbols such as
or
to stand for an unknown number. Eg 12 ÷ 2 =
= 12 ÷ 2
Understand the operation of division as Sharing equally Eg 6 sweets are shared
equally between 2 people. How many sweets does each one get?
And
Understand the operation of division as Grouping Eg There are 15 apples in a
box. How many bags of 5 apples can be filled?
ie. How many groups of 5 can you make from 15?
Grouping should also be modelled on a number line by the teacher and later by
pupils. Use prepared number lines and also draw own lines as appropriate eg.
8 children are put into teams of 2. How many teams are there? ie How many
groups of 2 are there in 8? 8÷ 2 = 4
Year 3
Record simple mental divisions in a number sentence using the ÷ and
= signs. Eg. ‘Divide 25 by 5’
Recognise the use of symbols such as
or
to stand for an
unknown number. Eg 16 ÷ 4 =
= 24 ÷ 4
Understand the operation of division as
Sharing equally
Grouping
(see Y2 examples, but use appropriate numbers)
Also that division is the inverse of multiplication.
Ensure that grouping continues to be modelled by adults and children
on prepared and blank number lines. Eg
How many 5s make 35?
0
5
10
15
20
25
30
35
Answer: Seven 5s make 35
0
2
4
6
8
8 cakes are put into boxes of 4. How many boxes are there? ie How many
groups of 4 are there in 8? 8 ÷ 2 = 4
0
4
8
Explain methods and reasoning orally.
This includes being able to interpret division number sentences eg 20 ÷ 4
could mean ‘If £20 is shared between 4 people how much would each get?’
Understand the relationship between multiplication and division and therefore
be able to derive division facts for 2x, 5x and 10x tables.
Eg 5 x 10 =50 so 50 ÷ 10 = 5 etc.
Explain methods and reasoning orally and in writing.
‘If 24 tulips are shared equally between 4 plant pots, how many will
be in each pot?’
Understand the relationship between multiplication and division and
therefore be able to derive division facts for 2, 3, 4, 5, 6 and 10x
tables.
Eg 8 x 4 =32 so 32 ÷ 4 = 8 etc.
Understand the concept of a remainder. Eg.
How many lengths of 10 cms can you cut from 51 cm of tape? How
many will be left?
0 10
20
30
40
50 51
Answer: 5 lengths and 1 cm left over
Be able to round remainders up or down depending on context
AIM: By end of Yr 3, children will understand the different
interpretations of division. They should be ble to derive division
facts for 2, 3,4,5 6and 10x tables. Children should be competent
at subtracting multiples of 10 from any number eg 117 – 20/30
etc. in preparation for the ‘chunking’ method.
8
Clifton Primary School Recording and Written Calculations Policy
Year 4
DIVISION
Year 5
Year 6
Complete written questions (using pencil and paper jottings or
mental strategies). Eg 320 ÷? = 80
240 ÷ 6 =?
Complete written questions (using pencil and paper jottings or
mental strategies). Eg 54 ÷ ?= 18
186 ÷ 6 = ?
Complete written questions (using pencil and paper jottings or
mental strategies). Eg9.9 ÷ ?= 1.1 6.3 ÷ 7 = ?
Understand the operation of division as:
Grouping/Sharing / inverse of multiplication (and use this to
check results) See Y2/3 examples.
Understand the different aspects of division and use as
appropriate. (see Y2/3 examples)
Understand the different aspects of division and use as
appropriate. (see Y2/3 examples)
Continue to model grouping on prepared or blank number
lines (and expect children to explain and model it also). Eg.72
÷ 5 = 14 remainder 2
Continue to develop method of recording division from Year
4 progressing to
HTU ÷ U, ‘chunking’ 20x and 30x the divisor, where
appropriate.
256 ÷ 7
7)256
- 140 (7x20)
116
- 70 (7x10)
46
- 42 (7x6)
4
Answer: 36 r.4
Continue to develop method of recording division from Year
5, ‘chunking’ multiples of 10x the divisor (20/30/100x etc) –
see year 5 examples.
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 72
This leads on to ‘chunking’ ie.10 times the divisor is
calculated in one ‘chunk’ because it is quicker and more
efficient (do not push children on to this without
understanding). Eg. 72 ÷ 5
10x5
0
50 55 60 65 70 72
Answer: 14 r. 2
(Demonstrate only. Children record in vertical format).
This should be written in vertical format as in the Framework
(section 6, p.68). The Framework relates division to repeated
subtraction ie.
72 ÷5 5)72
(5x10)
- 50
22
- 20
(5x4) Place divisor on left.
2
Answer: 14 r.2
Children should be taught to approximate first to gain a
sensible idea of what the answer must be.
Children should be taught to approximate first to gain a
sensible idea of what the answer must be
Teach long division (HTU ÷ TU) using ‘chunking’ method
.Children should approximate answers first.
Eg
977 ÷ 36 is approximately 1000 ÷ 40 = 25
36)977
- 360 (10 x 36)
617
- 360 (10 x 36)
257
- 180 (5 x 36)
77
- 72 (2 x 36)
5
Answer: 27 remainder 5
Extend to decimals with up to 2 decimal places as
appropriate.
Explain methods and reasoning orally and in writing,
including whether to round up or down after division
(involving remainders) depending on the context.
Explain methods and reasoning orally and in writing,
including whether to round up or down after division
(involving remainders) depending on the context.
Explain methods and reasoning orally and in writing,
including whether to round up or down after division
(involving remainders) depending on the context.
AIM: By the end of Year 4 most children are able to use
the ‘chunking’ method of division (using 10x the divisor.
Those who cannot are able to ‘chunk’ in smaller steps. All
children are able to explain methods and reasoning and
whether to round up or down after division. Most children
are able to derive division facts for 2,3,4,5,6,7,8,9and10x
tables.
AIM: By the end of Y5 most children are able to use the
‘chunking’ method division (using 20/30x the divisor, if
appropriate) Those who cannot are able to use 10x the
divisor. All children are able to explain methods and
reasoning and whether to round up or down after division.
All children are able to derive division facts for tables up
to 10x10
AIM: By the end of Y6 children should be able to use an
appropriate method for short division for any numbers,
including decimals. Some children are able to do long
division. All children are able to explain methods and
reasoning and whether to round up or down after division.
All children are able to derive division facts for tables up
to 10x10