Multiplication
Multiplication with Arrays
Use of arrays (via
objects/dots). Use in
context with physical
resources.
Multiplication as Repeated
Addition on a Number Line
Small numbers (up to 20)
only.
Grid Method
TU x U 22 x 2
X 20
2
2
3 x 6 = 18
Expanded Column
Multiplication
(without carrying)
40
23
X 2
6 (2x3)
40 ( 2 x 20 )
4
= 44
3 x2=
Expanded Column
Multiplication
(with carrying)
34
X 5
20 ( 5x4 )
150 ( 5x30 )
170
Column Multiplication
(without carrying)
Column Multiplication
(with carrying)
23
x 2
46
O
O
HTU x U 222 x 2
X 200 20 2
O
O
2 400
O
O
40
4
Model multiplying 2 groups
of 3 units and 2 groups of 2
tens.
Model multiplying 5 groups
of 4 units and 5 groups of 3
tens.
Model multiplying 2 groups
of 3 units and 2 groups of 2
tens.
6 x 3 = 18
O
O
O
O
O
Multiply by ten/hundred to
create a whole number.
2
Use column method.
Model multiplying 3 groups
of 8 units and 3 groups of 5
tens.
Progress to HTU x U and
HTU x TU.
= 444
O
58
X 3
174
2
46
Progress to HTU x U.
Return to this stage when
teaching TUxTU (Year 5) :
Progress to HTU x U.
Progress to HTU x U.
N.B. You can only model
this with dienes if the
numbers are very small.
TU x TU 22 x 22
x
20
2
20
400
40
2
40
4
=400
40
40
4
484
HTU x TU 222 x 22
x 200
20 2
20 4000 400 40
2
400 40
4000
400
400
40
40
4
4884
4
X
Column Multiplication with
decimals
324
23
972( 3x324)
1
6480(20x324)
7452
11
Divide by ten/hundred to
return to a decimal
number.
Division
Understanding Division as
Sharing AND Grouping
15 ÷ 3 = 5
Can mean 15 shared between 3
(3 lots of 5).
But it can also mean 15
grouped into 3s (5 lots of 3).
For written calculations, it is the
idea of division as grouping
which is used.
Division with Objects
I have 12 sweets and I share
them between my 4 friends.
How many do they get each?
Sharing
Start with sharing out into four
groups and putting one at a
time in each group.
Division as Repeated
Subtraction on a Number Line
Short Division Bus Stop method
÷ by a 1 digit number
(without remainders)
Short Division Bus Stop
÷ by a 1 digit number
(with remainders)
Short Division Bus Stop
÷ by a 2 digit number
Small numbers (up to 20) only.
Counting back (repeated
subtraction)
Example 1
TU ÷ U:
TU ÷ U:
HTU ÷ TU:
96 ÷ 4 = 24
97 ÷ 4 = 24 r1
496 ÷ 11 = 45 r1
2 4 r 1
4 9 17
0 4 5 r 1
11 4 49 56
24
4 9 16
12 ÷ 4 = 3
•
•
•
•
•
•
•
•
•
Model by explaining that you
are grouping nine tens into
groups of four – which is 2
groups with one ten left over.
Model carrying this into the
units and turning it into ten
units. Then group sixteen units
into groups of four – which is 4
groups.
•
•
•
Grouping
Progress to drawing arrays of 4.
How many groups of 4 are there
in 12?
• • • •
• • • •
• • • •
Or it can be shown using beads:
Short Division Bus Stop
(interpreting remainders as
fractions)
Model by explaining that you are
grouping nine tens into groups of
four – which is 2 groups with one
ten left over. Model carrying this
into the units and turning it into ten
units. Then group seventeen units
into groups of four – which is 4
groups with one left over. This is
the remainder.
Progress to HTU ÷ U:
Counting forwards (counting
groups inside a number)
Progress to HTU ÷ U:
Example 2
136 ÷ 4 = 34
622 ÷ 5 = 124 r2
0 3 4
4 1 13 16
1 2 4 r2
5 6 12 22
Model by explaining that you are
grouping six hundreds into groups of
five – which is 1 group with one
hundred left over. Model carrying
this into the tens and turning it into
ten tens. Then group twelve tens
into groups of five – which is 2
groups with two tens left over.
Model carrying this into the units
and turning it into twenty units.
Then group twenty two units into
groups of five – which is 4 groups
with two left over. This is the
remainder.
Include examples with zeroes:
700 ÷ 5 = 140
1 4 0
5 7 20 0
Model by explaining that you
are grouping four hundreds into
groups of eleven. You can’t do
this so model carrying the four
hundreds into the tens column
and turning them into forty
tens. Then group the forty tens
into groups of eleven – which is
4 groups with five tens left
over. Model carrying this into
the units and turning it into 50
units. Then group fifty-six units
into groups of eleven – which is
5 groups with one left over.
This is the remainder.
Progress to ThHTU ÷ U.
496 ÷ 11 = 45 1/11
0 4 5 r 1
11 4 49 56