Transcript Multiplication

Recording Multiplication
Calculations
A guide to the progression and written methods for
Multiplication used at:
•Verwood CE VA First School
•Trinity First School
•Hillside First School
•Emmanuel CE VA Middle School
The following is designed to help pupils and parents
understand the written methods for multiplication used in all
of the First Schools and onward through the Middle School
in Verwood at Key Stage 1 and Key Stage 2 (from
reception to year 6).
It is important to realise that the methods shown in this
document might not be what parents were taught while
they were at school, but they are common methods
used today in the teaching of Mathematics.
This presentation starts off with the methods taught in
reception and year 1 and progresses through to the
multiplication methods and some examples of multiplication
problems that your child can expect to come across in
years 5 and 6.
Early multiplication (R)
• Begin to count in 2’s
Counting pairs of objects such as pairs of socks and
shoes
• Using vocabulary lots of, groups of, sets
of.
Early multiplication (1)
• Counting in steps of 2’s, 5’s and 10’s.
Including groups of objects and money.
How many spots are there altogether?
• Doubling numbers up to 10.
2+2=4
7+7=14
Early multiplication (1)
• Use sets of objects.
2 sets of 3
• Begin to use repeated addition including
using a number line.
3+3+3+3=12
• Vocabulary: Double, multiply by, times,
lots of, sets of.
+3
+3
+3
+3
Early multiplication (2)
• Use arrays including using counters.
3
3
• Counting in 3’s and 4’s
• Chanting tables. 2’s, 3’s, 4’s, 5’s and 10’s
• Fact families
or
e.g.
3x5=15, 5x3=15, 15÷3 =5, 15÷5 =3
4x5=20, 5x4=20, 20÷4 =5, 20÷5 =4
Once a pupil has grasped the basics, they
are ready to move on to a more formal
written method for multiplication.
These methods are taught as a progression
and the pupil will need to have an
understanding of place value in order to
progress
1)
2)
3)
4)
Double the hundreds.
Double the tens.
Double the units.
Add the three
answers together.
Following this pupils would progress on to long
Multiplication with 2 digit numbers.
A knowledge of place value is again crucial for this.
e.g 57 x 36
x
3
2
1 7
2 0
1
5
3
4
4
1
5
7
6
2
0
2
Like before start by multiplying the 6 by the 7 and
then the 5 – remembering to carry across any
digits (marked in blue). This gives 342
Before you multiply by the ‘3’ you need to
remember that it is in the ‘tens’ column so you need
to put a ‘0’ (in red) on the end of the next row down
before you start your multiplying.
Then you multiply the 3 by the 7 and then the 5
like before to get 1710
Finally you add the 342 and the 1710 using
column addition to get the answer 2052
Once pupils are able to multiply whole numbers using
these methods they will progress on to multiplying
decimals.
It is possible to multiply decimals using either the grid method or the
formal long multiplication method.
In our experience we have found that some pupils will struggle with
these methods when using decimals so we encourage the use of the
Geolosia method (sometimes called Napiers bones).
Chances are, as a parent, you may not have seen it before.
The good thing about this method is that it is virtually identical no
matter what type of numbers you are multiplying
Using Geolosia to multiply two whole numbers together
e. g
46 x 78
4
Set out the digits as shown with a box in the middle
6
2
x
4
8
3
2
4
2
8
7
Next, put horizontal and vertical lines inside the box
as shown
8
Next, put in diagonal lines as shown – always top
right to bottom left – one small box at a time –
extend slightly at the ends
Now the grid is set up (this is the same for all geolosia questions) you now
need to fill in the boxes by doing times tables as shown – always write the
tens unit in the top left triangle of the box and the unit in the bottom right
6 x 7 = 42
and 4 x 7 = 28
4 x 8 = 32
and 6 x 8 = 48
The final step is to add all the numbers inside the box in their diagonal rows.
4
3
1
6
2
8
2
4
2
8
Always start at the bottom right corner
4
3
5
x
8
8
7
8
There is only ever one number here so it
simply drops in to place as shown
In the next diagonal row you add together the 2, 4
and 2 which gives 8 as shown
In the next column up you add together the 4, 8 and 3 as shown to get 15
You write the 5 as shown and carry the tens unit up to the next coulmn as shown
Next you add the 2 to the 1 that you carried over to get 3 as shown
Finally you read round the digits on the outside to get the answer as
shown. ANSWER = 3588
Using Geolosia to multiply a whole number and a decimal
together
e. g
4.6 x 78
.6
4
3
2
4
8
3
5
2
4
2
8
x
.8
8
7
8
It doesn’t matter if you put the decimal
number at the top or the side of the grid –
you set it up as before and do the question
as before
For this type of question you simply need to
decide where to put the decimal at the end
If the decimal number is at the TOP of the grid as shown then
the decimal point simply ‘drops like a stone’ in to place as shown
This gives us the answer 358.8
e. g
4.6 x 78
7
3
5
8
3
2
8
2
4
4
2
8
x
.8
8
.4
6
If you put the decimal number at the side
instead then the decimal point ‘rolls down
the hill’ in to place instead as shown
This still gives us the answer 358.8
The final type of question is when you multiply two decimal
numbers together
e. g
4.6 x 7.8
.6
4
3
2
4
8
3
5
.8
x
2
4
2
8
.8
7
Similar to all the other questions, the set up
and method is the same, its only at the end
when you need to figure out where to put the
decimal point in the answer is there
something new to do
8
The decimal point at the side moves across
and the one at the top moves down until they
meet. Then you follow the diagonal grid line
from that point to see where you put the
decimal in the answer
This gives us the answer 35.88