Creative Maths brings you, Maths made really clear,
for parents, with Dr Nic.
Long Multiplication both ways - using the area model and the standard algorithm.
Hi, I'm Dr Nic from Creative Maths. This video is for parents who are having difficulties
with the way their children are being taught to do long multiplication.
And it is also good for people who struggle with long multiplication.
Back when I was at school, long multiplication looked like this:
And now for many learners it looks like this.
This method is called the area model or box method.
In this video I will talk about why this method is used and how it works.
When I was at school we needed to know how
to do long multiplication. We needed to be fast and we needed to be accurate.
We were taught a method or algorithm. It is sometimes called the standard algorithm.
There was not always a big emphasis on understanding how the method works.
Learning how to multiply helps develop number sense.
It also reinforces an understanding of place value.
Understanding place value is essential.
See in the description below for links to videos about place value.
The basis for the Area model of multiplication
is that multiplication is used to find the number of elements in a rectangular array.
Here is a rectangular array or arrangement of twenty circles.
There are four rows and each row has five circles in it.
We can count to see that there are twenty circles.
We also know that four lots of five make 20. 4 times 5 = 20.
Similarly to find an area we multiply the lengths of the two sides.
This rectangle is six squares by five squares for a total of six times 5 equals 30 squares.
The following is a progression towards understanding the area model.
Say we wanted to multiply 13 by 24. We can represent this in terms of squares
There are 13 rows of squares and each row has 24 squares in it.
We can divide up the 13 rows into ten rows plus 3 rows.
We can divide the 24 columns into twenty columns plus four columns.
You can see that we end up with four groups of squares.
Finding the area of each of these groups involves basic multiplication.
This first group is 10 by 20, which is 10 times 20 which equals 200 squares
This next one is 3 by 20 , which is sixty squares.
Then 10 by 4 which is 40.
And finally 4 by 3 which is 12.
To find the total number of squares we add 200 + 40 + 60 + 12 = 312.
Drawing the squares helps with conceptual understanding. If we need reassurance that
it works we can even count the squares. However, once the concept is clear, we do
not need to keep drawing all the little squares. We can use a grid with numbers.
This is the grid for 24 by 13. We use one row for each place value and one
column for each place value. tens and ones and tens and ones.
Let us compare the area model with the standard algorithm.
Using the standard algorithm we say: three fours are twelve, put down the two carry the one,
three twos are six plus one makes seven.
Then bring down a zero, one four is four, one two is two.
Add them up to get 312.
Comparing with the area model:
See how the 72 corresponds to the 60 plus 12
and the 240 corresponds to the 200 plus 40.
A grid, or set of boxes can be used for multiplying any two numbers.
For example 796 times 58
That is a bit of a nasty one!
Were we to use the traditional long multiplication
method it will look a bit like this:
There are many places we can get a bit confused
due to carrying, adding and place value.
Or we can use the area model or box method.
50 times 700 = 35,000
50 times 90 = 4500
50 times 6 = 300
8 times 700 = 5600
8 times 90 = 720
8 times 6 = 48
Then we add these up and get 46168
Some people complain that the area model takes
up more room. It's true. But it also reduces the opportunities for mistakes.
You do need to be able to multiply numbers with lots of zero placeholders.
This reinforces place value understanding
and is a useful skill for estimation.
Check in the description below for links to a video about multiplying powers of ten.
I have taught adults who found maths difficult when they were at school.
Many of these adult learners have found the area method really helps them to understand
what is happening when they multiply,
and to be confident about getting the correct answer
I hope this video will help you to reinforce
your child's learning in multiplication, and maybe help you as well.
If you have any questions, please ask in the comments below.
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