MULTIPLICATION
Multiplication and Division should be taught alongside the learning of formal times
tables
PHASE ONE: PRACTICAL METHODS - DOUBLING
Strategies and methods:
Recording:
Teacher to model verbally: “Double three is six”
 Practical work using a variety of objects
and 2 of 3 is 6
 Lay out a small amount of numbers
Teacher to model recording both in columns and
 Count them
horizontally
 Double using a mirror or more counters
 Put them together and count the total
 Extend by moving into doubling mentally
3
2
6
x
MULTIPLICATION
PHASE TWO: PRACTICAL METHODS – COUNTING IN TWOS, FIVES AND TENS
Strategies and methods:
Recording:
Emphasise the links to repeated addition,
Teacher models the calculations as follows:
groupings and the commutative nature of
multiplication (i.e. 3 x 2 = 2 x 3)
Create several pairs and count them:
Create groups of five and count them:
Create groups of ten and count them:
1
1
3
3 x
2
6
5
x
2
0
0
x
3
0
MULTIPLICATION
PHASE THREE: REPEATED ADDITION USING AN ARRAY / EQUIPMENT
Strategies and methods:
Recording:
Children to start recording their calculation in
 Move on to developing the children’s
columns
understanding of arrays
 Solve one-step problems involving
multiplication, by calculating the answer using
concrete objects, pictorial representations
and arrays with the support of the teacher.
 Make connections between arrays, number
patterns, and counting in twos, fives and tens.
2
5
4
0
x
MULTIPLICATION
PHASE FOUR: REPEATED ADDITION ON A NUMBER LINE
Strategies and methods:
Recording:
1
2
Extension: Start from numbers other than zero. Sums
recorded in the same way
3
1
2
6
2
4
6
4
5
7
4
2
6
2
x
x
x
x
MULTIPLICATION
PHASE FIVE: GRID METHOD – UP TO HUNDREDS, TENS AND ONES BY ONES
Strategies and methods:
Recording:
EXAMPLE 1
 The children use their knowledge of
23 x 4 = ?
partitioning to understand the larger
number
 This is then partitioned into its constituent
tens and ones
 The multiplier is placed to the bottom left of
the grid, and first the ones, then the tens
are calculated by multiplying by the
multiplier. The answer to each part of the
calculation is written into the
corresponding box on the grid
 The ‘part’ answers are added together to
give the final total
80
x
4
20 3
80 12
80 + 12 = 92
23 x 4 = 92
12
92
+
23
x
4
92
EXAMPLE 2
123 x 7 = ?
x 100 20 3
7 700 140 21
700 + 140 + 21 = 861
123 x 7 = 861
700
+ 123
140
x
+
7
21
861
861
MULTIPLICATION
PHASE SIX: GRID METHOD – HUNDREDS, TENS AND ONES BY TENS AND ONES
Strategies and methods:
Recording:
EXAMPLE 1
 The children use their knowledge of
34 x 25 = ?
partitioning to understand the larger
number
 This is then partitioned into its constituent
hundreds, tens and ones
 The multiplier is also partitioned into its
constituent parts.
 The multiplier is placed to the bottom left of
the grid, with the tens in a row above the
ones
 First the ones, then the tens are calculated
by multiplying by the ones multiplier. The
answer to each part of the sum is written
into the corresponding box on the grid
 Next the ones, then the tens are calculated
by multiplying by the tens multiplier. The
answer to each part of the calculation is
written into the corresponding box on the
750 + 100 = 850
grid
34 x 25 = 850
 The ‘part’ answers are added together to
EXAMPLE 2
give the final total
351 x 43 = ?
 Check with estimation
x 30 4
20 600 80
5 150 20
x 300
50
1
40 12000 2000 40
3 900 150 3
21000 + 2150 + 43 = 861
123 x 7 = 861
MULTIPLICATION
PHASE SEVEN: FORMAL METHOD – UP TO HUNDREDS, TENS AND ONES BY ONES (SHORT
MULTIPLICATION)
Strategies and methods:
Recording:
EXAMPLE 1
 The children again use their knowledge of
24 x 3 = ?
partitioning here, but do not write the
number into its constituent parts, but leave
it as a whole number, with each digit sitting
in the correct column
 The children start with the ones, and record
the answer to this part of the calculation
with the one in the ones column, and the
ten value carried into the tens column
 The children then multiply the tens by the
multiplier. Any carried tens are added to
this, and the answer is record in the tens
column.
2
4
3
7
x
2
1
EXAMPLE 2
351 x 4 = ?
3 5 1
4
1 4 0 4
2
x
MULTIPLICATION
PHASE EIGHT: FORMAL METHOD (LONG MULTIPLICATION)
Strategies and methods:
Recording:
 This expands on the short multiplication
method of Phase Six
 The children use their knowledge of place
value to make sure that digits of
corresponding value are in the correct
column
 When multiplying by the tens multiplier, a 0
is automatically placed in the ones column
for that row. The children use their
knowledge of tables to work out the
answers, then restate them with the correct
values: “Seven multiplied by three is twenty
one, so seven multiplied by thirty is two
hundred and ten”. In the example given, the
2
2
tens multiplier is calculated first
 When multiplying by the ones multiplier,
there is no place holder needed.
 Children must remember to record any
carried numbers, and include them in the
3
final total for the calculation
2 8
3
8 6 1
1 1 4
9 7 5
2
7
x
4
0
8
8
MULTIPLICATION
PHASE NINE: SHORT AND LONG MULTIPLICATION USING DECIMALS
Strategies and methods:
Recording:
 This expands on the short multiplication
method of Phase Eight
 Children need to be reminded that the ones
need to line up in the ones column
 The decimal points need to line up as part
of the column method
 Use the short multiplication method to
multiply numbers up to two decimal places
by a single-digit number
2
3
6
.1 5
x
.4 5
1



Use the long multiplication method to
multiply numbers up to two decimal places
by a two-digit number
The decimal points need to line up as part
of the column method
As with long multiplication in Phase Eight,
start with the larger multiplier – use place
holder zeros to support column methods
3 .1 6
x
2 4
6 3 .2 0
1
1 2 .6 4
2
7 5 .8 4