Download Multiplication Describing an array using practical apparatus or

Multiplication
Stage
Foundation
and stage
1
What methods do we used for multiplication?
Notes
Early stages of recording will be mainly pictorial, with lots of practical
based activities using a range of apparatus. Children can be given objects or
pictures and asked to sort or to put rings around them, to experience
grouping objects in a variety of ways.
3 groups of 2 or 3 lots of 2
or
Much of early maths work with
multiplication will be oral, arising through
play activities. In practical activities and
discussion children will develop the
vocabulary involved in multiplication.
The concept of multiplication begins with
counting patterns 2,5,10. At first, results
will be recorded through photographs or
pictorially, then using phrases such as
‘lots of’,
2 groups of 3 or 2 lots of 3
Stage 2
or
sets of
Grouping numbers
When using repeated addition, pupils can combine number pairs or bigger
numbers using facts already known: for example
There are 12 cakes on a tray. How many rows are there if there are
three cakes in each row?
3 + 3 + 3 + 3 = 12
4 rows of 3 cakes
How many rows are there, if there are four cakes in each row?
4
+ 4 + 4 = 12
3 rows of 4 cakes
Repeated addition to model multiplication
is used to consolidate the concept of
‘groups of.’ The children will experience
practical activities to consolidate these
concepts e.g.

There are 12 cakes on a tray. How
many cakes are there if there are
three cakes in each row?

How many rows if there are four
cakes in a row?
At stage 2, when deemed appropriate by
the teacher, the multiplication symbol will
be introduced as meaning the same as
repeated addition.
Derive and recall multiplication facts for
the 2, 5 and 10 times tables.
How many groups of six can you make?
2 lots of 6
Describing an array using practical apparatus or
pictures to describe the different ways to create
amounts, can help children to ‘find’ related facts,
for example:
4 x 2= 8
2 x 4 = 8
Children will be strongly encourages to draw lots of. 5 x2= 5 lots of 2.
The relationship between division and multiplication will be introduced as
being the inverse of each other e.g. 3 x 5 = 15 15  5 = 3 or 15  3 = 5.
Stage 3
In year 3, concepts learnt at year two are
consolidated and extended:
4 x 3 =12
3 x 4 = 12
Using an array also assists children to recognise that multiplication can be
done in any order. The relationship between division and multiplication will
be consolidated as being the inverse of each other e.g. 3 x 5 = 15 15  5 = 3
or 15  3 = 5.
The grid method is used to introduce partitioning
using place value:
How many sweets are needed for party bags if 13 children are to have
3 each?
10 3
3 30
Stage 4
9
= 39 sweets
As pupils begin to work with larger numbers, they will have to use personal
jottings to help break down a calculation into smaller steps. These jottings
will help them to keep track of their mental calculations, explore different
connections and develop a range of approaches to multiplying.
A tyrannosaurus Rex was approximately 60 times long as a lizard. A lizard’s
tail is 15 cm long. About how long was the tail of the dinosaur?
15 x 60 = (10 x 60) + (5 X 60)
= 600 + 300
= 900
or
10 x 60 = 600
5 x 60 = 300
600 + 300 = 900
or
30 x 60 = 1800
1800  2 = 900
or
3 x 60 = 180
180 x 5 = 900
96 pears are to be sold in packets of 4. How
many packets will there be?
Use of mental jottings:
96 x 4 = 384
90 x 4 = 360
6 x 4 = 24
The grid method is consolidated:
How many sweets are needed for party bags if 27 children are to have
6 each?
20 7
6 120
42
= 162 sweets
When pupils work with numbers beyond the 10 x
10 table facts, they will have to decide which facts
they need to use and which methods will be the
most efficient.
During stages 3 and 4, pupils will be
taught additional facts and will work on
different ways to derive new facts from
those they already know. Written
recording of related facts will help the
pupils to make the connections they will
need when calculating.
Written recording will focus on:

Gaining a good understanding of the
meaning of the multiplication and
the different ways results can be
symbolised;

Recognising that multiplication and
division are inverse (opposite)
operations to each other;

Learning multiplication facts

Making connections between
numbers, e.g. 36 is a multiple of 3,
6, 9, 4, 12 and 2
Developing and refining written methods
for multiplying 2-digit numbers by a
single digit
Children must recall facts for the 2, 3, 4,
5, 6 and 10 times tables and recognise
multiples of 2, 5 or 100 up to 1000
Children must derive and multiplication
facts up to 10 x 10 times tables, the
corresponding multiples of numbers to 10
up to the tenth multiple.
Stage 5
and 6
Multiplication with larger numbers
Some pupils might want to use informal jottings, using mental strategies.
Others might want to use the grid method.
The class wants to make 275 spiders for a display. How many legs do they
need?
275 x 8 = 2200
200 x 8 = 1600
70 x 8 = 560
5 x 8=
40
Or
x8
200
70
5
1600
40
560
The written recording in these years will
focus on:

Making appropriate choices from a
flexible range of strategies;

Relating known facts to larger
numbers and decimals;

Establishing clear and efficient
ways to record working, moving
towards using standard methods
1600 + 560 + 40 = 2200
Multiplication with two and three digit numbers
Pupils will use the same methods to solve problems involving numbers of this
size i.e. informal jottings, grid methods or expanded layout and standard
method:
How many hours are there in one year?
365 x 24
300
60
5
20 6000 1200 100
4 1200
240
20
6000+1200+100= 7300
1200+240+20= 1460
8760
to
365
X 24
20 (5x4)
240 (60 x 4)
1200 (300 x 4)
7300 (365 x 20)
8760
Multiplication using decimals
Written methods for decimals can be built on procedures used for whole
numbers.
A chicken’s egg is 5.4 cm long. If an ostrich’s egg
was approximately 4 times as long, how long
would it be?
At stage 5, multiplication calculations will
be extended to include multiplying
numbers with one decimal place by a
single digit, and stage 6, numbers with
two decimal places by a single digit, as
well as a decimal number multiplied by a
decimal number.
5.4 x 4 =
5.0 x 4 = 20 cm
0.4 x 4 = 1.6 cm
20 cm + 1.6 cm = 21.6 cm
What is the product of 23.1 and 1.7?
1.0
0.7
20
20
14
3
3
2.1
0.1
0.1
0.07
23.1
+ 16.17
39.27
or
Turn the numbers in to whole numbers, and then divide by 10.
231 x 17
If children multiply decimals out to whole
numbers, they must first estimate their
answer.
200 30
10
7
1
2000 300 10
1400 210 7
2310 + 1617 = 3927
3927 ÷ 100 = 39.27