Video Transcript
Multiplying by Eight
In this video, we’re going to learn
how to model multiplication by eight. And we’re also going to practice
reciting eight times tables facts.
Let’s start with an octopus. We need to start with an octopus in
a video like this because, as you may know already, an octopus has eight
tentacles. Well, it was either octopuses or
spiders. We didn’t want a whole video full
of spiders now, did we? So far, we can see one group of
eight tentacles or eight. Now, there are two groups of eight,
two times eight. And two times eight is? Well, it’s the same as eight plus
another eight; it’s 16. Now, there are three octopuses. And three times eight means we need
to count in eights three times. Eight, 16, 24. Three times eight equals 24.
Now I wonder, “Do you remember your
eight times table facts?” Let’s start at the beginning. And as we go through each fact, see
if you can say it before it appears on the screen. One times eight is? Eight. Two lots of eight are? 16. Three times eight equals? Three eights are 24. Four times eight equals? Let’s press pause on the video for
a moment because so far the facts that we’ve listed are the three facts we started
the video with. Now, we’re getting on to some new
facts that we haven’t practiced already. But although the best thing to do
with a times table is just to memorize it and to know the facts, when we’re learning
facts like these, particularly with a times table like the eight times table, there
are all sorts of tools we can use to help us.
So, let’s imagine that we don’t
know what four times eight is. One tool we could use to help us is
a number line. If we want to know what four eights
are, we could make four jumps of eight along a number line. Eight, 16, 24. And then if we make another jump of
eight, we get to 32. So, we can do this by adding eight
each time. Or if you’re quick enough, we could
think of this as skip counting in eight. Eight, 16, 24, 32. Ready to start up the video
again? Four times eight equals 32.
Now, five groups of eight are? Let’s pause the video again because
there’s a really good tool we could use for this fact. And it’s all to do with
doubling. What do you like at doubling? Because if you can double a number,
you can use it to find out any eight times table fact. Now, we know that four doubled
equals eight. And so, if we know what five times
four is, we can double it to find five times eight. Now, we know that five times four
is 20. And so, if we double this, we’re
going to have 40 altogether. I think we might be ready to
restart the video, don’t you? Five groups of eight are the double
of five groups of four. Five times eight is 40. Six times eight equals 48.
Now, what is seven multiplied by
eight? Let’s look for another tool we can
use. Now imagine that we’ve been asked
to find seven eights. And we don’t know what they are at
all, but what we do know is what six eights are. In other words, we know the fact
that comes before the fact we want to know. Can you think of a way to use this
to help? Well, if we know what six eights
are and all we want to do is find out seven eights, we could just add one more
eight. And 48 add eight equals 56. By the way, do you know how to add
eight quickly? Eight is two less than 10, and
adding 10 is really quick to do. So, if we want to add eight, we can
add 10 and then take away two. 48 plus 10 is 58. And then take away two, 56.
And that’s why if we took 100
square and we mark all the numbers in the eight times table on there, we’d see a
pattern, down one square and back two; down one square and back two. Moving down one square on 100
square is the same as adding 10. And then moving back two is the
same as taking away two. It’s just a quick way to add
eight. And it’s one of the many patterns
that we can find with the eight times table. Do you think it’s time to restart
the video? Seven multiplied by eight is
56. Eight times eight is? 64. Interesting fact for you, eight
times eight is the number of squares there are on a chessboard, 64.
Eight times nine equals? Hang on a moment. We’ve just got to press pause
here. Eight times nine; we’re supposed to
be working through the eight times table, not the nine times table. But wait a moment. What do we know about
multiplication facts? It doesn’t matter which way around
we multiply two numbers together. They’ll always give the same
answer. So, eight times nine is exactly the
same as nine times eight. We could use whichever fact we find
easier to help us. Now, let’s imagine we already know
what eight times nine is; it’s 72. And if we know that eight times
nine is 72, we also know what nine times eight is. Eight times nine or nine times
eight is 72.
And 10 groups of eight are? This is usually quite an easy fact
to remember. 10 groups of eight are 80. That was a nice fact to finish
on. But wait a moment. Who said we have to finish at 10
times eight? The eight times table goes on and
on and on. Should we try two more facts? 11 times eight equals? Well, if we know that 10 lots of
eight are 80, we just need to add one more lot of eight, don’t we? And that’s quite easy to do to the
number 80. 80 plus another eight equals
88. 11 times eight equals 88.
By the way, how good are you at
counting in twos? Zero, two, four, six, eight. Now, what about counting backwards
in twos? Eight, six, four, two, zero. Well, let’s take a moment to look
at the digits that each of our numbers in the eight times table end with. Eight, six, four, two, zero; eight,
six, four. There’s a pattern here; they seem
to end in the digits eight, six, four, two, zero and then start all over again. So if 11 eights are 88, do you
think maybe the next number in the eight times table might end in a six? Let’s find out.
12 lots of eight are? Now, so far in this video, we’ve
gone through lots of ideas to help us remember the eight times tables. But you know, there’s one more that
could help us here. And this is also to do with
doubling. We heard about doubling earlier on,
didn’t we? We know that 12 is double six. So, if we know the fact for six
times eight, we could double it to help us find the fact for 12 times eight. We know that six times eight is
48. And if we double 48, we get 96. 12 lots of eight are 96.
Now, although we’ve gone through
all the multiplication facts that we really need to cover in this video, we’ve done
so quite slowly, haven’t we? We’ve used a lot of tools to help
us, lots of ideas and patterns that we can use in case we’re ever stuck. But as we’ve said already, probably
the best thing to do is actually to learn these facts so that we can recall them
straightaway. So, let’s recite our eight times
table facts starting with one times eight. But this is no good. This is just a reading
exercise. The answers are on the screen
already.
Oh dear! We seem to have had a little
accident with some ink. Oh dear! And another one. Ready? One times eight is eight, two times
eight is 16, three times eight is 24, four times eight is 32, five times eight is
40, six times eight is 48, seven times eight is 56, eight times eight is 64, nine
times eight is 72, 10 times eight is 80, 11 times eight is 88, and 12 times eight is
96. Eight, 16, 24, 32, 40, 48, 56, 64,
72, 80, 88, 96.
Let’s have a go at answering some
questions now where we have to put into practice everything we’ve learned about
multiplying by eight.
The sequence chart can help us
multiply by eight using skip counting by eights up to 10 times. Use skip counting to find eight
times two. And then use skip counting to find
eight times nine.
In the picture, we can see what’s
described as a sequence chart. It’s a little bit like 100 square,
except it’s not a square and it doesn’t go all the way to 100. But it does show all the numbers
from one to 80. And if we look closely, we can see
that some of the numbers have been written in blue. The numbers eight and then 16, 24,
32. These are all numbers in the eight
times table. And because these numbers have been
written in a different color, they can help us to skip count by eight. Look how they make a pattern on the
chart. To get to the next number, we go
down a row and then back two squares, down a row, back two. And if we think about it, we know
why this is, don’t we?
Skip counting by eight is the same
as adding eight each time. And eight is two less than 10. When we move down a row on a chart
like this, it’s the same as adding 10. And then when we move back two
squares, this is the same as taking away two. Add 10, take away two; add 10, take
away two. That’s why these numbers in the
eight times table show this pattern. And if we continue the sequence, we
can see all the numbers in the eight times table up to 10 times eight, which is
80.
In the first part of the question,
we’re asked to use skip counting to find eight times two. Now, it might sound like this is a
two times table fact, not an eight times table fact, eight lots of two. But we know we can read
multiplication facts like this with the numbers in the opposite order, and it’ll
still give the same answer. So, eight times two is exactly the
same as two times eight. To find the answer, we need to
count in eights twice. Let’s use the sequence chart to
help. Eight, 16. Eight times two equals 16.
In the second part of the question,
we need to count a little further. We’re asked to use skip counting to
find eight times nine. And again, we know that eight times
nine is the same as nine times eight or nine lots of eight. So, let’s use our sequence chart to
count in eights nine times. Eight, 16, 24, 32, 40, 48, 56, 64,
72. We skip counted by eight nine
times. And we reached the number 72. And so, we know that eight times
nine or nine times eight equals 72. In this question, we found the
answer to two multiplication facts by using this sequence chart. We skip counted by eights. Eight times two equals 16, and
eight times nine equals 72.
Noah knows the answer to five times
eight. Five times eight equals 40. Tell him what number to add to five
times eight to get the answer to six times eight. What is six times eight?
This question is all about using
facts that we already know to help us find facts that we don’t. And the boy in the question, Noah,
already knows a fact about the eight times table. He knows that five times eight
equals 40. Now, he can use this fact to help
him find the answer to six times eight. And we know this has got something
to do with adding because in the first part of the question, we are asked to tell
him what number to add to five times eight to find the answer to six times
eight. We could draw an array here to help
us understand what’s going on.
This is what five times eight looks
like. And so, this is what six times
eight looks like. To change five times eight into six
times eight, we need to add one more lot of eight. Noah needs to add eight to his
answer. This is the same for any number in
the eight times table. If we want to find the next number
in the eight times table, we just add another eight.
So, let’s answer the second part of
our question. What is six times eight? Well, as Noah said, five times
eight is 40. And we’ve already found out that we
need to add eight to find six times eight. 40 plus eight equals 48. And so, we can say six times eight
equals 48. In this question, we’ve shown how
to use a fact we already know to find one we don’t. The number that Noah needs to add
to five times eight to find the answer to six times eight is eight. And because five times eight is 40,
six times eight must be worth 48.
This robot multiplies any input by
eight to give an output. If we give the robot an input of
two, it will give an output of 16, which is eight times two. What would the output of the robot
in the following case be? That’s where there’s an input of
four. And then what would the output of
the robot in the following case be? This is when there’s an input of
nine.
So, so far in this question, we’ve
seen that we’ve got a times table robot, which must be a very useful robot to
have. What goes in gets multiplied by
eight and then we get the answer. In the first picture, we can see
that the input is four. This is then going to be multiplied
by eight. We can think of this as four lots
of eight. Let’s count in eights four times to
find the answer. Eight, 16, 24, 32. Four lots of eight are 32. And so, we know that the number the
robot’s going to come out with, its output is going to be 32.
In the second part of the question,
we’re given a new input. What happens if we put the number
nine into our robot? Well, we know it’s going to be
multiplied by eight again. So, what are nine eights? We could use skip counting to help,
just like we did with the first part. But this time, let’s use a doubling
fact. If we know what four nines are,
maybe we could use this to help us find eight nines. Four nines or nine times four
equals 36. And because eight is four doubled,
the answer to nine times eight is going to be nine times four doubled. And 36 doubled is 72. Four times eight equals 32. So, if the input is four, the
output will be 32. And nine times eight equals 72. So, if the input is nine, the
output will be 72.
What have we learned in this
video? We’ve learned how to model
multiplication by eight and practice reciting eight times table facts.
