Multiplying by Six
In this video, we’re going to learn
how to model multiplying by six. And we’re also going to recite six
times table facts.
Now, I wonder, “Have you ever
played a board game like this?” One where there’s a board a little
bit like a number track with numbers along it, you have a counter that you need to
move along the track, and then a dice that you roll to show how many spaces you need
to move. If we roll our dice once, what’s
the furthest number we’re going to get to? Well, if this is the sort of dice
that we would normally use in games like this, then it’s got six faces, and the
highest number on the dice is six. So, if we pick up the dice and then
roll it once, the largest number we could roll is a six and one lot of six is
six. We could write this number fact as
one times six or one multiplied by six equals six.
But what if we didn’t have one dice
to start with? What if we had two? And let’s imagine, we still have
this incredible skill of rolling the most possible. The most we could roll this time is
two lots of six. So, we need to move on our counter
another one, two, three, four, five, six. Two lots of six takes us to 12. And so, we can say two times six
equals 12. But you know, if we carried on
increasing the number of dice, instead of counting on six every time, just like
we’ve done, perhaps it might make sense to skip count in sixes and start to remember
some of these six times tables facts.
Three times six equals six, 12,
18. Four lots of six are six, 12, 18,
24. Four times six equals 24. And you know the more that we
repeat these multiplication facts, the more they sink in. Six, 12, 18, 24, 30. This is taking us to the end of our
board now. Five multiplied by six equals
30. By the way, did you notice anything
interesting about all the squares that we landed on? They’ve all been orange, haven’t
they? And on this particular board, the
orange squares are the even numbers. This shows us that all the
multiples of six that we’re gonna be thinking about in this video are going to be
So far, we’ve practiced up to five
times six. But let’s carry on going. How many facts do you know? See if you can say each number
before it appears on the screen. One times six equals six. Two times six equals 12. Three times six is 18. Four lots of six equals 24. Five times six equals 30. Six times six equals 36. Seven sixes are 42. So far, we’ve just been reciting
these facts. But what if we don’t know what the
next fact is? Are there any strategies that we
could use to help us find eight sixes?
Well, what if we know the fact that
comes before the one we want to find out? As we’ve said already, seven times
six is 42. And so, if we want to find eight
sixes, we just need to add another six. And 42 plus six equals 48. We’ve counted on from a fact we
already knew to help us find a fact that we didn’t know. So, eight times six is 48.
But what about nine sixes? Another method we could use is
doubling. Now, we know that half of six is
three. Let’s imagine that we don’t know
what nine times six is, but we do know our three times table and we know what nine
times three is. Hopefully, you can see from the
picture if we double nine lots of three, we get the same as nine lots of six. Now, we might already know nine
times three is 27. And so, we could double this
multiplication fact to help us find nine lots of six.
We know that double 20 is 40, and
double seven is 14. So, double 27 is the same as 40
plus 14 is 54. Nine times six is 54. And we found out this fact by using
a fact we already knew and then doubling it. In fact, we can do this with all of
the six times table. If we know our three times table,
we could double up our fact to make a six times table fact.
Let’s move on to 10 times six. Something else we could do if we’re
ever stuck with a multiplication fact is to use what we know about multiplication to
help us. Now, we know that 10 lots of six
are the same as six lots of 10. You can do that with
multiplication. You could switch the numbers
around. If we think of our array as showing
10 columns of six or 10 lots of six and then just turn it slightly, can you see what
we’ve got now? There are six columns of 10 or six
lots of 10. And if we know our 10 times table
and know that six lots of 10 equals 60, we also know that 10 times six equals
62. They’re just two ways of saying the
Now, often, we might stop at 10
times the number. But should we carry on? Let’s think of two more facts. Let’s go up to 12. If 10 lots of six are 60, 11 sixes
are 66 and 12 sixes must be 72. So, all the pink numbers here are
multiples of six; they’re the numbers in the six times table. Six, 12, 18, 24, 30, 36, 42, 48,
54, 60, 66, 72. And not only are these all even
numbers, there’s a pattern to them, too. If we just take a moment to look at
the ones digits in the six times table. The numbers end in six, two, eight,
four, zero. And then the pattern seems to
repeat itself. Six, two, eight, four, zero and
then again, six, two, and so on. It’s an interesting pattern, and it
can help us predict what the next multiple of six is going to be.
For example, if we know that 12
sixes are 72, we could use this idea of six, two, eight, four, zero to predict that
13 sixes are going to end in an eight. Now, we’ve gone through one or two
methods that we could use to help us here. But the best way to remember our
six times tables is just to learn a fact.
So, let’s go through the multiples
one more time. And what we’ll do to make it a
little bit more tricky, we’re going to rub some of them out. Now as we get to the facts that
aren’t on the screen, we need to say them out loud and we’ll see if you’re right at
the end. One time six is six, two times six
is 12, three times six is 18, four times six is, five times six is 30, six times six
is, seven times six is, eight times six is 48, nine times six is, 10 times six is,
11 times six is 66, and 12 times six is 72.
Did you get all the missing
numbers? Four sixes are 24, six sixes are
36, seven sixes are 42, nine sixes are 54, and 10 sixes are 60. Well done! And as we’ve said already, the best
thing we could ever do to learn our six times table is simply to practice it again
and again. So, let’s do that. We’re gonna try answering some
questions where we have to recall these six times tables facts.
We can skip count by sixes on a
number chart to help us multiply by six. Use skip counting to find six
multiplied by two. And then use skip counting to find
six multiplied by 10.
The first part of this question
tells us that we’re going to be multiplying by six. And to help us do this, we’re told
that we can skip count by sixes on a number chart. Now, we could skip count by sixes
on a number track or a number line, or maybe even just by thinking of the numbers in
our heads. But when we use a number chart like
this, we can not only seal the numbers that we’re skipping, but also we can spot
patterns. If we look at this number chart, we
can see that all of the multiples of six have been written in blue.
Let’s practice skip counting in
sixes to begin with. Six, 12, 18, 24, 30, 36, 42, 48,
54, 60. And each of these numbers is found
by adding six to the last number. But instead of saying every single
number in the grid, we’ve skip counted by sixes. Now that we’ve circled these
multiples of six, can you see what we meant by a pattern? We can see them in diagonal lines
across the grid, can’t we? We can see that they’re all even
Now, the first thing we’re asked to
do is to use skip counting to find the answer to six multiplied by two. Then, you might look at this
multiplication and say, “Well, this is talking about a number of twos, six lot of
twos, not a number of sixes.” But one thing we know about
multiplications is that we can switch the numbers in a multiplication and it’ll
still give the same answer.
So, we could think of this as six
times two or two lots of six. We could think of six times two as
meaning six repeated twice. So, let’s count in sixes twice to
find the answer. Six, 12. We skip counted by sixes twice to
find the answer. Two lots of six are 12.
Next, we’re asked to use skip
counting to find six multiplied by 10. And again, we can think of this as
10 times six or skip counting by sixes 10 times. Well, we know how far we get when
we skip count by sixes twice, so let’s carry on counting from there. 12 and then 18, 24, 30. That’s five sixes. Let’s carry on skip counting
another five sixes. 36, 42, 48, 54, 60. This time, we’ve skip counted by
sixes 10 times. And the last number we said was
So, we use this number chart to
help us skip count by sixes and find the answer to these six times tables facts. Six times two equals 12 and six
times 10 equals 60.
What is six times nine?
Now, this is a very straightforward
question, isn’t it? Perhaps you know the answer
already. Perhaps you can recall the number
fact and say six times nine is this. But if we were to make a video like
this, it would be very interesting to watch. let’s try going through and answer for
those of you who perhaps don’t know this fact off by heart.
If we don’t know what six times
nine is, what do we know that could help us? Well, the first thing that we can
say is that six times nine is exactly the same as nine times six. This is something you can do with
multiplication facts. You can switch the numbers around
and it still makes the same product. So, we can see that this question
is asking us to find nine lots of six. Now, maybe you don’t know nine lots
of six. But there is a nearby fact that you
probably do know, a fact that’s easy to remember when we’re learning our times
tables. And that’s 10 times six.
Now, we can use this to help. Because if we know what 10 times
six is and here are 10 columns of six counters as an example, then to find nine
times six, we just need to lose one of our columns. In other words, we need to subtract
six. Now, 10 times tables facts are
quite easy to remember. 10 times six equals 60. And so, if we take away one lot of
six from 60, this is going to take us back to 54, isn’t it? And so, we can say that nine lots
of six are 54. Or if we switched the numbers
around, six times nine equals 54.
Now, perhaps you knew this fact
already, but this is just one method you could have used if you didn’t. We’ve used a known multiplication
fact to find an unknown fact. We knew 10 times six. So, we subtracted six to find nine
times six. And nine times six or six times
nine equals 54.
Notice how each row is six more
than the previous one. One times six equals six. Two times six equals 12. Three times six equals 18. Find the result of the following:
four times six equals what. And then also find the result of
the following: five times six equals what.
Did you notice in this question
we’ve got some six times table facts to find out? We need to find the answer to four
times six and also five times six. But you know, in the first
sentence, we’re given a clue that can help us. It’s pointed out to us that each
row is six more than the previous one. And can you see what the rows are
that this is talking about? It’s these rows of cubes. And if we look at each cube, we can
see it has the number six on it. We could think of it as a dice that
shows the number six.
So, what does it mean that each row
is six more than the previous one? Well, our first row of cubes just
shows one cube with a six on it. But our second row shows the one
from before and then a new cube. In other words, it shows six
more. And the next row shows the two from
before. But again, one new cube, so six
more. And knowing that each multiple of
six in the six times table is worth six more than the last one can help us. One time six is six, and six more
than six is 12. So, we know two times six is
12. Six more than 12 is 18. So, we know three times six is
And now, we need to find four times
six. And If we look at our cubes, we
could take our three cubes that we already know from the last fact and then add one
more cube. Or, in other words, take three
sixes, which are worth 18, and then add one more six. And we know that 18 plus six equals
24. That’s how we know four times six
Finally then, we need to find out
what five sixes are. As we’ve just said, the four sixes
from our last fact are worth 24. And if we find six more than 24, we
get the answer 30. So, five times six must be worth
We got each answer by finding six
more than the last one. Four times six is 24 and five times
six is 30.
Find the missing numbers. Two times three equals what. Two times six equals what. Three times three equals what. Three times six equals what.
Did you notice anything about the
multiplication facts we need to find out here? Each time we’ve got a number
multiplied by three and then the same number multiplied by double three or six. How can we use a three times table
fact to help us with a six times table fact? Well, as well as making us feel
hungry, this array of donuts that we can see in the picture can help us.
Two times three can be shown by
this group of donuts here, can’t it? Two threes are six. But if we double this amount, in
other words, we include this group of donuts here, we now have a six times table
fact, two rows of six. Now, we know that double six is
12. So, if two times three is six, two
times six must be 12. And we can use the same idea for
the next two facts. We know that three times three is
nine. And if we double this, we find the
answer to three times six. And double nine is 18.
We’ve used doubling to help us find
six times table facts here. Two times three is six. So, two times six equals 12. Three times three is nine. So, three times six is 18.
What have we learned in this
video? We’ve learned how to model
multiplication by six and recite the six times table.