Supporting your child in
Maths
Multiplication and Division
Supporting your child in Maths
Multiplication and Division
The aims of this morning:
To share the methods we use to teach
multiplication and division calculations at
school;
To explore the practical methods that children
use to support their learning in Maths;
To provide activities that you can use to
support your children at home in a way that
encourages enthusiasm for the subject.
Supporting your child in Maths
Multiplication and Division
What the children said...
It was fun being
with your parents
doing maths. Now
my mum and dad
know how to do it.
I enjoyed having
maths with my mum
because I got to be
like the teacher and
show her how to use a
number line.
I enjoyed being with my mum and dad and
showing them my talent.
Supporting your child in Maths
Multiplication and Division
Place Value
As with addition and subtraction, understanding of place
value is key to the understanding of multiplication and
division.
Being able to break a number down into smaller parts
means that we can break a calculation into smaller steps.
Children are taught how to partition numbers from KS1 and
throughout the school.
Supporting your child in Maths
Multiplication and Division
Times Tables
Mental recall of times table facts begins to be more
formally taught in KS2.
In KS1 the emphasis is placed on counting in steps, a skill
which is required for carrying out calculations with all four
mathematical operations.
10x
4x
8x
Supporting your child in Maths
Multiplication and Division
Multiplication
Children are first introduced to the idea of multiplication in
school through setting up groups in role-play.
This is done using a number of different models and
images:
Putting 5 flowers in
each vase.
This practical method would also be used to introduce the
concept of doubling as finding ‘2 lot’s of’.
Supporting your child in Maths
Multiplication and Division
Multiplication
Once the use of role-play has begun to develop the
understanding of the very idea of what multiplying is,
children will begin to use arrays to represent multiplication
problems.
At first this would be done using a variety of practical
equipment.
Peg Boards
Counters
Supporting your child in Maths
Multiplication and Division
Multiplication
Once the use of role-play has begun to develop the
understanding of the very idea of what multiplying is,
children will begin to use arrays to represent multiplication
problems.
At first this would be done using a variety of practical
equipment.
3 x 5 = 15
3
5
Supporting your child in Maths
Multiplication and Division
Multiplication
Once the use of role-play has begun to develop the
understanding of the very idea of what multiplying is,
children will begin to use arrays to represent multiplication
problems.
3 x 5 = 15
3
5
As their understanding deepens further children will be
expected to create jottings of these arrays using dots, on
their whiteboards or in their books, to help them calculate
such questions independently.
Supporting your child in Maths
Multiplication and Division
Multiplication
Alongside using arrays to represent their calculations
visually children will continue to link multiplication to
finding ‘lots of’ by counting on.
Children may be supported in this by using number lines to
count-on in steps.
These may be numbered tracks:
3 x 5= 15
+5
+5
+5
___________________________________
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Or blank lines that the children would be expected to number themselves:
3 x 5= 15
+5
+5
+5
___________________________________
0
5
10
15
Supporting your child in Maths
Multiplication and Division
Multiplication
As children move through KS2 the use of arrays and their
knowledge of place value will be used to introduce the grid
method. This method can be used to multiply numbers of
any size by breaking the calculation down into smaller
steps.
4 x 24 = 96
x
By using arrays
inside the grids
initially children are
encouraged to link
the grid method to
previous use of
arrays.
20
4
4
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
....
= 80 dots + 16 dots
= 96 dots
Supporting your child in Maths
Multiplication and Division
Multiplication
As children move through KS2 the use of arrays and their
knowledge of place value will be used to introduce the grid
method. This method can be used to multiply numbers of
any size by breaking the calculation down into smaller
steps.
4 x 24 = 96
x
4
20
80
4
16
= 80+ 16
= 96
The children then
use the method
themselves, writing
in the numerical
solutions to each
part of the
calculation
Supporting your child in Maths
Multiplication and Division
Multiplication
The grid method can then be developed to multiply bigger
numbers:
U x HTU
TU x TU
3 x 124
72 x 38
x
3
x
30
8
100
300
70
2100
560
20
60
2
60
16
4
12
= 300 + 60 + 12
= 372
= 2100 + 560 + 60 + 16
= 2736
Supporting your child in Maths
Multiplication and Division
Multiplication
The final stage is to link the grid method to an expanded
vertical method:
7 x 38
x
7
30
210
8
56
= 210+ 56
= 266
38
7 x
-------210
(30 x 7)
56
(8 x 7)
------266
Supporting your child in Maths
Multiplication and Division
Multiplication
As they near the end of KS2 some children may be shown
the full vertical method:
136
x 24
2 712 0
41224
312 6 4
Supporting your child in Maths
Multiplication and Division
Division
As with all the other operations we have looked at, children
will first meet division in practical ways.
There are two ways that children are encouraged to
think about division.
Sharing
If 6 apples are shared
between 2 people, how many
would they have each?
3
Grouping
There are 6 apples.
How many people
could have 2 each?
3
Supporting your child in Maths
Multiplication and Division
Division
As with all the other operations we have looked at, children
will first meet division in practical ways.
There are two ways that children are encouraged to
think about division.
The idea of
grouping as talking
away ‘lots of’ is then
used to introduce
the use of repeated
subtraction....
Grouping
There are 6 apples.
How many people
could have 2 each?
3
Supporting your child in Maths
Multiplication and Division
Division
The idea as grouping as repeated subtraction is first taught
through numerous practical methods, using counters and
other practical equipment to represent calculations.
12 ÷ 3 = 4
After this children
would be shown
how to use the
vertical number line
to carry out division
problems more
independently:
12
11
10
9
8
7
6
5
4
3
2
1
0
3
3
3
3
Supporting your child in Maths
Multiplication and Division
Division
This method can be built upon once the children are
confident in using blank lines which they number
themselves
And here we
13
12 ÷ 3 = 4
12
13 ÷ 3 = 4 r 1
see why we
3
3
now count
10
back on our
9
3
3
number
7
lines...
6
..remainders!
3
3
3
3
0
4
3
1
0
Supporting your child in Maths
Multiplication and Division
Division
The vertical number line method can be used to divide with
larger numbers, and with greater efficiency:
52 ÷ 4 = 10 + 3
= 13
126 ÷ 4 = 10 + 10 + 10 + 1 r2
= 31 r 2
126
52
10 x 4
86
10 x 4
10 x 4
46
10 x 4
12
6
3x4
0
1x4
2
0
Supporting your child in Maths
Multiplication and Division
Division
From this point children would be expected to use the
vertical number line method if they are finding a calculation
difficult. However they may be shown the chunking
method as an introduction to short division:
72÷3 = 10+10+4
= 24
3 72
- 30 (10x3)
42
- 30 (10x3)
12
- 12 (4x3)
0
387÷12 = 30 + 2 r3
= 32 r3
12 387
-360 (30x12)
27
- 24 (2x12)
3
Supporting your child in Maths
Multiplication and Division
Division
As they near the end of KS2 some children may be shown
the full bus stop method:
644÷7
0 9 2
7 6 64 14
Supporting your child in Maths
Multiplication and Division
.......
.......
Talking about Maths
As some of you will remember from the
addition and subtraction morning, there are
many ways you can build maths into the time
you spend with your children at home.
There are further ideas in the leaflets on your
chairs for you to take away from this morning.
.......
.......
Supporting your child in Maths
Multiplication and Division
In the classrooms....
You may spend time in your child’s classroom until approximately
10.10, at this point the children will be getting ready for assembly.
If you have more than one child please feel free to move from one
room to the other in your own time.
Lessons are being taught as normal and the teachers attention will
be with the other children in the classroom. We would appreciate it
if you did not take away from this valuable input by asking
questions of the teacher yourself. You may ask questions of Miss
Everton or Miss Godbold who will both be available in the entrance
after the session has finished.
Space will be tight and we apologise that we can not
accommodate seating in the classrooms for you.