Yr 4 to 5 age appropriate.
William Reynolds Primary School
Calculation Policy
Stages E & F
Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4
Addition
Subtraction
Multiplication
Stage E
Stage E
Stage E
HTU + TU, then HTU + HTU. Cross
10s, 100s boundary.
Add least significant figures first.
Check for mental approach first
before written method.
HTU – TU, then HTU – HTU
Extend to simple decimals with or
without exchange from pence to
pounds.
Ensure that all calculation is checked
before started for any other possible
‘tricky’ bits.
Ensure that the setting out is
accurate.
Know table facts up to 12 x 12.
Partitioning / distributive law
Pupils to explain the effect of
multiplying by 10 and 100
Addition to be done mentally.
Continue to partition TU x U
754 – 86 = 668
23 x 8
Record steps in brackets then move to
working without.
Double lines for answer.
+
625
48
13 (5+8)
60 (20 + 40)
600 (600 + 0)
673
Take away
-6
Record using grid notation.
Support the grid by using
multiplication sentence.
X
←
-80
________________________
668
674
754
20
8
Use Multiplication grid itp to support
teaching the grid method.
Find the difference
Plot landmarks on number line first.
+14
+600
http://www.taw.org.uk/lic/itp/mult_grid.html
+54
Stage E
Know by heart multiplication facts up
to 12 x 12.
Relate fractions to division. ¼ means ÷
4
Know ÷ 4 is the same as halve and
halve again.
Approximate answer first using
multiplication facts
Recognise that division is noncommutative.
Know that a number cannot be divided
by 0.
Divide any integer up to 1000 by 10
3
23 x 8 = 184
205
+ 176
11
70
300
381
Division
“900 ÷ 10 = 90 because the digits move
one place to the right”
Reinforce finding of remainders on the
number line (adding on or subtracting)
21 ÷ 5
“What do I know? I know that 61 is
not a multiple of 5, so there will be a
remainder.”
____________________________
86
100
700
754
10 x 5
2x5
___________________________
0
50
60
61
22
Yr 4 to 5 age appropriate.
+
356
97
13
140
300
453
Add mentally from top or bottom.
Simple decimals £ and pence notation
(fix the decimal point)
To use the money target boards to
extend decimal notation
http://nsonline.org.uk/node/47820
£
0.45
0.55
+ 0.32
0.12
1.20
1.32
(fix the decimal point)
Decision making to include the
use of the calculator
William Reynolds Primary School
Calculation Policy
Stages E & F
Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4
Complimentary addition
-
Short multiplication for TU x U
754
86
14 (100)
600 (700)
54 (754)
668
Most significant digit first.
23
x 7
140 (20 x 7)
21 (3 x 7)
161
Simple decimals:
Fix the decimal point.
Move to least significant digit.
£
8.95
- 4.38
.62 (5.00)
3.00 (8.00)
.95 (8.95)
4.57
Decomposition
Record remainders in fraction or
decimal notation when appropriate
61 ÷ 5 = 12 r 1 12 r 1/5 12 r 0.2
Continue to use partitioning/rearranging method.
69 ÷ 3 =
23
x 7
21 ( 3 x 7)
140 (20 x 7)
161
60 ÷ 3 = 20
9÷3 =3
69 ÷ 3 = 33
Move to extending using bigger
numbers on grid.
96 ÷ 6
754
700 and 50 and 4
- 86 80 and 6
Use chunking method for TU by U
division
60 36
↓
↓
10 6
Exchange
96 ÷ 6 = 16
140
80
60
(because 6 ÷ 3 = 2 )
“What do I know? 6 x 10 = 60”
“ It’s tricky to take 6 from 4 and 80 from 50
because it becomes a negative answer”
754
600
- 86 600
12 lots of 5 and a remainder of 1
which can be seen on the number line.
61 ÷ 5 = 12 r 1
4
6
6 =668
23
Yr 4 to 5 age appropriate.
William Reynolds Primary School
Calculation Policy
Stages E & F
Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4
Decomposition
£
8.95 =
-4.38
£
8 . 90
4 . 30
Underline the non-divisor.
6x6
5
8
____________________________
0
36
96
“ 5 takeaway 8 is tricky because it becomes a
negative answer”
For children who are secure on the
number line, begin to move to vertical
takeaway chunking method – relating
to subtracting chunks along a number
line:
Exchange
8.95 =
-4.38
8 . 80
4 . 30
4 . 50
10 x 6
15
8
7 = £4.57
96 ÷ 6 =
Insist the answer is written in the original
algorithm if given a space or in a number
sentence if given an = sign
96
- 60
36
- 36
0
(10 x 6)
( 6 x 6)
Placing the answers back into the
original number sentence.
96 ÷ 6 = 16
24
Yr 4 to 5 age appropriate.
William Reynolds Primary School
Calculation Policy
Stages E & F
Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4
Interactive Teaching Programs that could support a range of teaching methods,
suitable for calculating at Stage E.
Addition
Subtraction
Multiplication
Division
Bead sticks
Add subtract 1,
10, 100, 1000
Complements
Counting on
Counting stick
Data handling
Counting stick
further options
Counting
Counting on
Doubling & halving
guidance)
Difference
Number spinners
Doubling & halving
guidance)
Function Blocks
Number line
Twenty cards
Place value
Tell time
Moving digits
Decimal target
board
Function Blocks
Make numbers
Make numbers
guidance
Place value
Midpoint guidance
Money problems
Patterns of
Make numbers
Make numbers
guidance
Number spinners
Guess my number
Guess my number
guidance (PDF)
Midpoint half way
between
Counting stick
further options
Doubling and
halving
Doubling and
halving
Number facts
Tell time
Twenty cards
Calculate percentages
Twenty cards
Grouping
Converting measures
Grouping
Multiplication
array
Converting units of
measure
Multiplication
array
Number line
Counting stick
Number line
Converting units of
measure
Function Blocks
Counting stick further
options
Function
Blocks
Counting stick
Doubling and halving
Multiplication
board
Counting stick
Data handling
Number line
Number facts
Add subtract 1,
10, 100, 1000
Twenty cards
Counting
Function Blocks
Moving digits
Midpoint half way
between
Multiplication
board
Multiplication
facts
Doubling & halving
guidance)
Facts and place value
Multiplication
facts
Number dials
Guess my number
Guess my number
guidance (PDF)
Number dials
Make numbers
Make numbers guidance
Multiplication
grid
Place value dots
Money problems
Multiplication
tables
Sum Product
Difference
Sum Product
Difference
Guidance (PDF)
Multiplication & division
facts 2-6
Order numbers on
a number line
Patterns of
calculations
Moving digits
Moving digits
Calculate
percentages
Converting
measures
Counting stick
further options
Doubling and
halving
Doubling & halving
guidance)
Facts and place
value
Multiplication grid
Multiplication
tables
Multiplication & division
facts mixed
25
Make numbers
Make numbers
guidance
Multiplication &
division facts 2-6
Remainders
Multiplication &
division facts mixed
Yr 4 to 5 age appropriate.
William Reynolds Primary School
Calculation Policy
Stages E & F
Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4
calculations
Target practice
Multiplication & division
trios
Place value charts
& partitioning tool
Place value chart &
partitioning tool
guidance (PDF)
Multiplication & division
with partitioning
Multiplication grid
Multiplication grid
guidance (PDF)
Place value dots
Sum Product
Difference
Sum Product
Difference
Guidance (PDF)
Multiplication &
division trios
Multiplication &
division with
partitioning
Place value dots
Prime factors
Target practice
Place value charts &
partitioning tool
Place value chart &
partitioning tool
guidance (PDF)
Target practice
Timed number
bonds
Place value dots
Prime factors
Which number
where
Target practice
Which number where
26
Yr 4 to 5 age appropriate.
William Reynolds Primary School
Calculation Policy
Stages E & F
Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4
Addition
Subtraction
Stage F
Stage F
HTU + HTU, then ThHTU + ThHTU.
Approximate using the most
significant digit, rounding skills.
Check using the inverse.
Refer to the carried digit as a ten or a
hundred.
Decision making -appropriate
teaching/use of the calculator.
Consolidate decomposition.
(HTU – HTU) (ThHTU – ThHTU)
(THHTU – HTU)
Pupils taught to cross out the numbers
and replace them with the exchanged
number.
Consolidate decimals
Check answers through inverse and
equivalent calculations.
587
+ 475
12
150
900
1062
587
+ 475
1062
11
Multiplication
Stage F
Know all multiplication facts to 12 x 12.
Approximate first, appropriate use of
the calculator
HTU and U, TU x TU to be introduced
with the grid method first.
HTU x U
TU x TU
346 x 9
Continue to consolidate rearranging
with Diennes.
X 300
1 ten to carry over.
80 add 70 equals 150 and the one ten
to carry makes 160. That’s 6 tens and
100 to carry over. 500 add 400 equals
900 and the one hundred to carry
makes 1000”
40
6
9
346 x 9 = 3114
Addition to be done mentally or across
followed by column addition
28 x 27
X
20
27
20
What do I know? 3 x7 = 21.
210 14
↓
↓
30 2
224 ÷ 7 = 32
Column addition
one ten from 50 which leaves 40 and
makes 14 in the units. 40 to subtract 80 is
tricky. I will rearrange one hundred from
700 and make 140. 600 to subtract 200 is
400. 14 subtract 6 equals 8. 140 subtract
80 equals 60 and 600 subtract 200 equals
400.”
Know all multiplication facts to 12 x 12
Use the relationship between
multiplication and division
Extend chunking method to include
HTU by U, with an integer remainder
Dividing up to 10,000 by 10/100
Check with inverse operation. Use of
calculator.
224÷ 7
Teach checking strategy
“4 to subtract 6 is tricky. I will rearrange
Stage F
Partitioning method when numbers are
easy.
754 = 600 140 14
- 286
200 80 6
400
60 8 = 468
“ 7 add 5 equals 12. That’s 2 units and
Division
8
Relate fractions to division and
calculate fractions of amounts.
http://www.teachfind.com/nationalstrategies/unit-3-ict-resources-1
William Reynolds Primary School
Calculation Policy
Stages E & F
Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4
Yr 4 to 5 age appropriate.
Short method column subtraction:
7648
+ 1486
14
120
1000
8000
9134
7648
+ 1486
9134
111
12.45
7.36
+ 24.50
11
1.20
13.00
30.00
44.31
Carry below the line under appropriate
column
Language must be in the context of
place value.
-
754
286
468
Use the number line to find
remainders and express the quotient
as a fraction or decimal.
222 ÷ 5
7
Column addition
28 X 27 = 756
“What do I know? 222 is not a multiple
of 5”
4x5
£2.73 x 3
40 x 5
£
____________________________
0 2
22
222
£2.73 x 3 = 273p x 3
“When I have a number left which is
smaller than the divisor I know it’s a
remainder.”
x 200
44 r 2
70
3
3 600 210
9
273p x 3 = 819p
= £8.19
(Continue to use ITP multiplication)
http://www.taw.org.uk/lic/itp/mult_grid.html
28
or
44 2
5
or
44.4
Use vertical chunking method if
secure on number line.
196 ÷ 6 is approximately 30 because 6
x 30 = 180
196
180 (30 x 6)
16
12 (2 x 6)
4
196 ÷ 6 = 32 r 4 or
-
32 2
3
Yr 4 to 5 age appropriate.
William Reynolds Primary School
Calculation Policy
Stages E & F
Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4
Division of numbers involving decimals
using chunking method.
87.5 ÷ 7 =
87.5 ÷ 7 is approximately 12 (12 x 7 = 84)
87.5
- 70.0
17.5
14.0
3.5
3.5
0.0
(10 x 7)
(2 x 7)
(0.5 x 7)
87.5 ÷ 7 = 12.5
Underlining non divisor.
Answers written as part of a number
sentence
(Overcoming Barriers Level 4 to Level 5
typical questions)
Work out 575 ÷ 25, explaining your
method.
Peter says that, if you want to divide a
number by 12, you can divide it by 4 then
by 3. Is he right? Explain how you know.
Work out 768 ÷ 12 using Peter's method
and using another method. Do you get
the same answer?
How many 35p packets of stickers can I
29
Yr 4 to 5 age appropriate.
William Reynolds Primary School
Calculation Policy
Stages E & F
Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4
buy with £5? Explain how you know.
Coaches have 56 seats for passengers.
How many coaches are needed to take
275 people on a trip?
Complete this calculation: 943 ÷ 41 = 2
Work out whether or not 29 is a factor
of 811.
30
Yr 4 to 5 age appropriate.
William Reynolds Primary School
Calculation Policy
Stages E & F
Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4
Interactive Teaching Programs that could support a range of teaching methods,
suitable for calculating at Stage F.
Addition
Subtraction
Multiplication
Division
Bead sticks
Add subtract 1,
10, 100, 1000
Counting
Counting on
Counting
Data handling
Counting on
Counting stick
Difference
Data handling
Counting stick
further options
Multiplication array
Number line
Counting stick
further options
Converting units
of measure
Counting stick
Function Blocks
Function Blocks
Counting stick
Multiplication board
Counting stick
further options
Multiplication facts
Doubling and halving
Multiplication facts
Make numbers
Make numbers
guidance
Number dials
Doubling & halving
guidance)
Remainders
Twenty cards
Facts and place value
Number dials
Midpoint half way
between
Moving digits
Find the multiple
Moving digits
Multiplication grid
Guess my number
Guess my number
guidance (PDF)
Twenty cards
Make numbers
Make numbers
guidance
Multiplication tables
Number spinners
Function Blocks
Number facts
Decimal target
board
Number facts
Place value
Find the multiple
Place value
Tell time
Guess my number
Guess my number
guidance (PDF)
Tell time
Make numbers
Make numbers
guidance
Twenty cards
Moving digits
Order numbers on a
number line
Patterns of
calculations
Calculate
percentages
Number line
Multiplication board
Doubling & halving
guidance)
Midpoint guidance
Converting units of
measure
Doubling and halving
Number spinners
Midpoint half way
between
Multiplication array
Doubling & halving
guidance)
Number line
Twenty cards
Grouping
Function Blocks
Doubling and
halving
Moving digits
Calculate percentages
Counting stick further
options
Number line
Function Blocks
Grouping
Counting stick
Complements
Function Blocks
Add subtract 1, 10,
100, 1000
Multiplication tables
Fractions
Place value dots
Multiplication &
division trios
Sum Product
Difference
Sum Product
Difference Guidance
(PDF)
Multiplication &
division with
partitioning
Patterns of
calculations
Doubling and
halving
Doubling &
halving guidance)
Facts and place
value
Find the multiple
Multiplication grid
Make numbers
Make numbers
guidance
Multiplication &
division trios
Multiplication &
division with
partitioning
Place value dots
31
Yr 4 to 5 age appropriate.
William Reynolds Primary School
Calculation Policy
Stages E & F
Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4
Target practice
Multiplication grid
Multiplication grid
guidance (PDF)
Place value charts
& partitioning tool
Place value chart
& partitioning tool
guidance (PDF)
Prime factors
Target practice
Place value charts &
partitioning tool
Place value chart &
partitioning tool
guidance (PDF)
Place value dots
Sum Product
Difference
Sum Product
Difference
Guidance (PDF)
Place value dots
Prime factors
Target practice
Target practice
Which number
where
Timed number
bonds
Which number
where
32