### Video Transcript

Multiplying by Two

In this video, we’re going to learn
how to model multiplication by two and also how to recite the two times table.

Ethel here is about to start
watering her plants. Can you see how she’s planted them
in groups of two or pairs? This is useful because this video
is all about groups of two. Let’s turn the hose on. The water is only going as far as
one pair of flowers to begin with. And one group of two is worth
two. Let’s turn the hose up a little
more. Now, she’s watering another group
of two. This is the same as four
flowers. Each time Ethel turns up the water,
she waters another two flowers.

Three lots of two is the same as
six flowers. Four twos are the same as eight
flowers. And five lots of two equals 10
flowers. Did you notice anything about the
numbers that we said? They’re numbers in the two times
table. We’re counting in twos. And this means that every number we
say is even, two, four, six, eight, 10. Do you remember all of the two
times table facts?

Let’s practice them. Why don’t you try to be quick and
say each fact before the answer appears on the screen. One times two equals two. Two times two equals four. Three times two is six. Four twos are worth eight. Five times two equals 10. Now, before we continue, let’s stop
for a moment. Let’s imagine we’ve been asked to
find six times two. Don’t quite remember what it
is. We don’t want to start all the way
back at one times two and count up to six times two.

Now, one fact we do know is the one
that comes just before it, five times two equals 10. How can knowing five times two help
us to work out six times two? Well, if we know that five lots of
two are worth 10, then all we have to do is add two more to find six lots of
two. 10 plus another two equals 12. We didn’t need to start all the way
back at one times two to find the answer. Instead, we used a fact we knew
already and we counted on from there.

Your brain is like a tool kit. It’s full of different tools that
we can use to solve different problems. And what we’ve just done is used
one of the many tools that we can use to multiply by two. Let’s try some of the others.

Let’s imagine that we’ve been asked
to find the answer to seven times two this time and we don’t know what that is. But one thing we do remember is
that seven lots of two is exactly the same as two lots of seven. This means we can use a doubles
fact to help us. Multiplying by two is the same as
doubling. Seven add another seven equals
14. To find seven times two, we could
just double seven. Seven times two equals 14. So, there’s another tool we can use
to help us.

Eight times two equals... What other tools could we use? What about skip counting? We could skip count in twos eight
times, two, four, six, eight, 10, 12, 14, 16. Eight times two equals 16.

Nine times two equals 18. Let’s imagine we don’t know the
answer to 10 times two. We’ll try one last tool to help
us. Although we’re not quite sure what
10 times two is, we do remember that fact from earlier on, five times two equals
10. Is there a way we could use this to
help? So, we know what five times two is,
and we want to find out what 10 times two is.

Do you notice something about the
numbers five and 10? If we double five, we get 10. And in the same way, if we double
our answer to five times two, we should get the answer for 10 times two. As we’ve said already, five times
two is 10. And if we double this answer, we’ll
get 20. It worked! We took the answer to five times
two and doubled it to help us find 10 times two.

And you know this works with other
pairs of times tables too. Three doubled is six, so if we take
the answer to three times two and we double it, this will give us the answer to six
times two. Or if we double the answer to four
times two, we can use it to help find the answer to eight times two. What a lot of doubling facts we got
flying around in this video!

Although we’ve learned lots of
tools here to help us, probably the best thing we could ever do to help us with our
two times table, or any times table, is just to learn the facts. And the two times table is perhaps
one of the easiest times tables to remember because these numbers are all even.

Let’s practice our two times table
facts one more time. And just to really test you, we’re
going to start rubbing them out from one end as we start saying them at the
other. Let’s see if you can remember them
if they’re not on the screen anymore. Ready? One times two equals two. Two times two equals four. Three times two equals six. Four times two equals eight. Five times two equals 10. Six times two equals 12. Seven times two equals 14. Eight times two equals 16. Nine times two equals 18. And 10 times two equals 20.

How did you get on? Hopefully you remembered the ones
that were missing. Let’s answer some questions now
where we have to put into practice all the tools that we’ve learned about to help us
multiply by two.

Try the following method to
calculate multiplications by two. Two times four equals four plus
four, which equals eight. Complete the following: Two times
five equals five plus five, which equals what. And then, use the same method to
complete the following: Two times six equals what.

In this question, we’re shown
several calculations to do with multiplying by two. But we can’t just find the answer
however we like. We’re shown a method or a way of
doing things. And once we’ve understood it, we
need to try it for ourselves to help us find the answers. To begin with then, we’re shown an
example. And this example is all about
finding out two times four.

What does this mean? Well, one way we can think of this
is as two groups of four. Here’s one group of four. Now, we have two groups of
four. We could write this as the addition
four plus four. We could even say double four. And we know that four plus four, or
double four, is equal to eight. So, we’ve used this doubling fact
to help us find that two times four equals eight.

Now that we understand this
doubling method, we can use it again to help us fill in the blanks in these other
calculations. Two times five is the same as two
groups of five or five plus another five. And we know that five plus five, or
double five, equals 10. That’s how we know two times five
equals 10.

Finally, we need to find the answer
to two times six. Two times six is the same as two
groups of six or six plus six. And we know that six plus six, or
six doubled, equals 12. So, two times six equals 12.

In this question, we recognized
that multiplying numbers by two is the same as doubling them. And so, we’ve used addition facts
to help us solve multiplication facts. Two times five is the same as five
plus five, which equals 10. Two times six is the same as six
plus six, which equals 12. Our two missing numbers are 10 and
12.

Fill in the blank: Two times three
equals what.

In this question, we’re given a
multiplication fact to complete. Now, when you see this fact, what
do you think? Perhaps you think of the number two
repeated three times. Or perhaps you think of it as two
lots of three. Maybe you know this fact already,
but what could we do if we don’t? We could skip count along the
number line to help us.

Now, we did say that one way we
could think about this multiplication is as two repeated three times or three lots
of two. So, let’s try this method. We’ll start at zero, and we’ll skip
count in twos three times. Zero, two, four, six. Skip counting twos three times, we
reach the number six. And just to show that we found the
correct answer, let’s try the other method. Let’s skip count two lots of three,
zero, three, six. Whether we think of this
calculation as three lots of two or two lots of three, we’ll still get the same
answer. Two times three equals six.

In multiplying by two, each row is
two more than the previous one. One times two equals two. Two times two equals four. Three times two equals six. Complete the following: Four times
two equals what. And then, complete the following:
Five times two equals what.

In maths, there are often patterns
everywhere we look. And in questions like this, we can
use the patterns that we find that help us find the answers. Perhaps one of the best sentences
we could ever say in maths is “I don’t know the answer, but I do know this fact, and
I’m going to use it to help.” And in a way, this is what this
question is all about, using facts that we already know to help us find facts that
we don’t.

Our first sentence tells us about a
pattern. In multiplying by two, each row is
two more than the previous one. In the model, we can see some rows
of cubes. And each cube has a value of
two. We can see the number two written
on them. The first row shows one lot of
two. And of course, we know one times
two equals two. But then, look what happens in our
second row. We’ve taken the answer from before,
and we’ve added one more lot of two, the yellow cube on the end. We now have two lots of two. And two times two equals four.

The pattern continues with our
third row. This is made up of the answer from
before and then two more. We know from the last fact that two
times two equals four. So, if we find two more than this,
we get the answer six. And that’s how we know three times
two equals six. Now, we’ve got some times tables
facts to complete. Perhaps you know the answers
already. But in case you don’t, let’s
continue using this method.

We’ll use facts that we already
know, and we’ll build on them. So, the first fact we need to find
is four times two. And if we look at our row of cubes,
we can see that there are three red cubes. We know where these are from, don’t
we? These are the three cubes that made
up the answer to the last fact. And just like all our other facts,
we’ve got a new cube on the end. These are the two more that we need
to add.

We know from our last fact that
three times two is six. So, to find four times two, we
simply need to add another two. We need to find two more than
six. And six plus another two is eight,
so four times two must equal eight.

In the last part of the question,
we need to find five times two. So, we can do the same thing
again. Take the answer from the last
question, which is eight, and then add another two. Eight add two equals 10. And so, we know five times two
equals 10. Even though we may not have known
all the multiplication facts in this question, we took the facts we did know and we
used them to help. If we know what three times two is,
we simply add two to find four times two. And if we know what four times two
is, we do the same again to find five times two. Four times two equals eight. And five times two is 10. Our two missing numbers are eight
and 10.

What are the two missing numbers in
this table?

Can you see where the two missing
numbers belong? They’re both in the bottom row,
here and here. Now, for us to understand what
these two missing numbers might be, we need to understand how this table works. Can you see a clue that might help
us? This table is all about multiplying
by two. We take a number from the top row,
multiply it by two, and then that gives us the number in the bottom row. It’s a little bit like the idea of
a multiplying machine, where a number goes in, it gets multiplied by two, and then a
different number comes out. This is exactly what’s happening in
our table.

Number one on the top row gives us
number two on the bottom row. One times two equals two. And number two on the top row gives
us four on the bottom row because two times two equals four. So, we can see then that our two
missing numbers are going to be what we get when we multiply three by two and what
happens when we multiply six by two.

Now, we could think about each of
these facts completely separately. We could think about three times
two and then six times two. But these two facts are linked. Can you see what the link is
between three and six? We know that if we double three,
we’d get six. So, do you think if we double the
answer to three times two, we might find the answer to six times two? Let’s see whether multiplications
work like this.

Three times two is worth two, four,
six. So, we know that our first missing
number is six. Can you predict what our second
missing number’s going to be? We can take the answer for three
times two and then double it. And six doubled is 12. Let’s count in twos and see whether
the number 12 fits in the pattern. Two, four, six, eight, 10, 12. It worked!

We multiplied three by two to find
our first missing number. And we knew that we could double
the answer to three times two to find the answer to six times two. This gave us our second missing
number. Three times two is six. And six times two is 12. Our two missing numbers are six and
12.

So, what’ve we learned in this
video? We’ve learned how to model
multiplication by two and practice reciting two times tables facts.