Transcript 7 - Heatherside Junior School

Methods of
Multiplication
Heatherside
Junior School
xxxxxxxxxxxxxxx
x lots of
times
groups of
x repeated addition
array
x
Multiplication
x
x
product of
x multiple of
multiply
double
x
xxxxxxxxxxxxxxxx
x
x
x
x
x
x
x
x
Step 1 – Multiplication as arrays
Recognising that 3x2 gives
the same answer as 2x3
3x2=6
2x3=6
2+2+2=6
3+3=6
Understanding that
multiplication is repeated
addition
Step 2 – Knowing tables facts is key
‘Learn Its’ – a progressive approach
x
2
3
4
5
6
7
8
2
4
3
6
9
4
8
12
16
5
10
15
20
25
6
12
18
24
30
36
7
14
21
28
35
42
49
8
16
24
32
40
48
56
64
9
18
27
36
45
54
63
72
9
3 facts
5 minutes
3 weeks
Stage 1: counting in
10s, 5s, and 2s
Stage 2 (by the end of
Year 2): x10, x5, x2
81
Stage 3 (by the end of
Year 3): x3, x4, x9
Stage 4 (by the end of
Year 4): x6, x7, x8
‘Learn Its’ vocabulary
FACTS
3X3=9
4 X 3 = 12
5 X 3 = 15
SWITCHERS
FACT FAMILIES
3 X 4 = 12
3 X 5 = 15
9÷3=3
12 ÷ 3 = 4
15 ÷ 3 = 5
Step 3 - Partitioning
This method helps show the
value of each digit in a number.
Children develop a greater
understanding of the
reasonableness of an answer
and they are able to apply
known facts.
23 x 8 =
20
3
Step 4 - The Grid Method
X
20
3
8
160
24
23 x 8 =
160 + 24 = 184
• The number is partitioned and placed on the grid.
• The total is added to calculate the final answer.
Step 5
The Expanded Column Method
The question is…
38 x 7 =
The number is
partitioned…
38 x 7
30
8 x 7
30 + 8
x
7
56 (7 x 8)
+ 210
(7 x 30)
266
Step 6 ….This is then reduced to
Short Multiplication
38 x 7 =
38 x 7 = 266
The short method
38
x
7
266
5
We aim for children to begin to
be able to use short
multiplication for TU x U
by the end of Year 4.
Using the Grid Method for TU x TU
Remember to
partition the
numbers using
known facts first.
63 x 42 =
X
40
2
60
2400
120
3
120
6
2400 + 120 = 2520
120 + 6 = 126
2520 + 126 = 2646
Moving from the Grid to Column Method
for TU x TU
The question is
56 x 27 =
56
x 27
42
350
120
+ 1000
1512
1
(7x6)
(7x50)
(20x6)
(20x50)
The Grid Method for larger numbers
89 x 123
First partition each
number
89
[80
x
9]
123
[100 20 3]
This is then shown
on a grid like this…
X
100
20
3
80
9
Multiplying using the grid method
X
80
9
100
8000
900
20
1600
180
240
27
3
Firstly,
multiply
each column
and row and
record the
answer in
the correct
box
Completing the calculation
X
Now total up
all the yellow
numbers.
80
9
100
8000
900
= 8900
20
1600
180
= 1780
3
240
27
=
Add all the totals to get the final answer
267
= 10,947
Step 7 - Long Multiplication
256
x 28
48
400
1600
120
1000
+4000
7168
(8x6)
(8x50)
(8x200)
(20x6)
(20x50)
(20x200)
If children are very secure
at Level 5 they may go on to use
the compact method, where 0
is used to denote the multiple
of 10.
56
x 27
392
4
+ 1120
1
1512
1