NEW LEAKE PRIMARY SCHOOL
PARTNEY CHURCH OF ENGLAND PRIMARY SCHOOL
STICKNEY CHURCH OF ENGLAND PRIMARY SCHOOL
ST MARGARET’S CHURCH OF ENGLAND PRIMARY SCHOOL
COLLABORATIVE PARTNERSHIP
Calculation Policy: Multiplication and Division
Missing Number
Problems
Multiplication
Spring 2014
Division
Stage
Multiplication
Stage 1 and 2
Counting practically
in repeated groups/
patterns.
Examples
Two
Division
Sharing objects in a
group, through
practical contexts.
Six
Four
Examples
For example, sharing 6 biscuits between 3 children (show them
that 6 ÷ 3 = 2.
3x2=6
Grouping
4 x 3 = 12
Stage 3
And introduce the
inverse
Arrays
Stage 5
Repeated Addition
5 times 3 is 5 + 5 + 5 =
15 or 3 lots of 5 or 5 x
3
or
Partitioning
3 x = 12
÷ 3=5
x = 24
Using arrays and
linking
multiplication and
division
3 x = 12
÷ 3=5
x = 24
Repeated
15 ÷ 5 = 3
subtraction using a
-5
-5
-5
number line or bead
bar. Still use
0
5
10
15
apparatus as
required.
Show them, using apparatus, why we are subtracting.
So we know
6÷2=3
+5
+5
5
10 x 5 = 50 and 3 x 5 = 15
50 + 15 = 65
12 ÷ 3 = 4
4 x 3 = 12
5 x 3 = 5 + 5 + 5 = 15
13 x 5 =
Stage 6
Children will
develop their
understanding of
division and use
jottings to support
calculation
If we know that 3 x 2 = 6, we can begin to explore that
if we share those 6 among 3 people we will each have
2. Demonstrate practically.
3 x 4 = 12
Stage 4
3x =6
÷ 2=6
x = 12
+5
10
15
13 x = 65
÷ 6 = 4r3
x = 24
Calculations
involving
remainders through
repeated
subtraction.
or
12 ÷ 4 = 3
27 ÷ 6 = 4 r 3
-6
3
-6
9
-6
15
-6
21
27
NEW LEAKE PRIMARY SCHOOL
PARTNEY CHURCH OF ENGLAND PRIMARY SCHOOL
STICKNEY CHURCH OF ENGLAND PRIMARY SCHOOL
ST MARGARET’S CHURCH OF ENGLAND PRIMARY SCHOOL
Calculation Policy: Multiplication and Division
COLLABORATIVE PARTNERSHIP
Missing Number
Problems
Multiplication
Spring 2014
Division
Stage
Multiplication
Stage 7
Informal examples
Formal Method
38
x
7
266
Multiplication of
TU x U
5
Division
Using the methods
children are learning Long Division by
about
subtraction of
3 x 7 = 266
÷ 6 = 4r3
x = 420
multiples
TU ÷ U
Examples
3
4 r 3 or 4 6
6 27
- 2 4 (4 x 6)
3
1
6 x 345 = 2070
Stage 8
Multiplication of
HTU x U
Then THTU x U
x
300
6
1800
40
5
240 30
345
x 6
2070
23
2 3 r 1 or 23 6
6 139
- 6 0 (10 x 6)
79
(10 x 6)
60
- 1 9 (3 x 6)
18
Using the methods
children are learning
Long Division by
about
3 5x =
2070
÷ 6 = 23r1
subtraction of
multiples
HTU ÷ U
52 x 27
Stage 9
Using the methods
children are learning
about
Multiplication of
TU x TU then
HTU x TU
2 x 52 = 1512
432 ÷ =
28r12
42 x 5.3
Short Division
5
Stage 10
Multiplying
decimals
HTU ÷ TU
40 200
2 10
0.3
12
0.6
212
10.6
222.6
42
x 5.3
1 2 .6
1
2 1 0 .0
2 2 2 .6
Spring 2014
Calculation Policy: Multiplication and Division
Multiplication
Division
Stage
Multiplication
Stage 8
Examples
Division
Grid Method
It is better to place the
38 x 7 = 266
number with the most digits in
the left-hand column of the
grid so that it is easier to add
the answers of each part of
the multiplication together.
7 x 38 =
56 ÷ 4 = 14
Introduce short division with no
remainders for small divisors.
Ensure children understand
their place value.
Do this for TU ÷ U questions
with no remainder.
Link to their knowledge of
times tables.
Then move onto to HTU x U
using the same method (e.g.)
346 x 5
Develop this into TU ÷ U with
remainders, still keeping divisor
relatively small. Check
responses with the inverse.
42 x 5.3
Then move on to U.t x U.t
(e.g.) 4.6 x 5.9
51 6
We know this because we know that
4 x 10 = 40 and 4 x 4 = 16, 40 + 16 = 56
1 3 r1
Then move onto HTU x TU
using the same method (e.g.)
427 x 36
Stage 10
4
79 ÷ 6 =
Multiplying two, two digit
numbers
This follows the same steps as
the first grid method but for 2
digit numbers.
Using grid method to multiply
decimals. Start with TU x U.t
1 4
Use apparatus to demonstrate.
56 x 27 = 1512
Stage 9
Examples
40
2
5
0.3
200
10
12
0.6
212
10.6
222.6
6
719
Check with 6 x 13 = 78
78 + 1 = 79
Short division is used for
HTU ÷ U questions with
remainders (which may be
turned into decimals by level 5
children)
Extension—use short division
for HTU ÷ TU (where the divisor
is less than 20 to begin with),
writing down multiples first.
NEW LEAKE PRIMARY SCHOOL
PARTNEY CHURCH OF ENGLAND PRIMARY SCHOOL
STICKNEY CHURCH OF ENGLAND PRIMARY SCHOOL
ST MARGARET’S CHURCH OF ENGLAND PRIMARY SCHOOL
COLLABORATIVE PARTNERSHIP
3 2
17 5 4 34
17
34
51
68
85
102