Multiplying by Nine
In this lesson, we’re going to
learn how to model multiplication by nine. And we’re also going to practice
reciting nine times tables facts.
This marks the spot where an
amazing new skyscraper is going to be built. Each floor of the skyscraper is
going to have nine windows. How many windows can you see at the
moment? Well, construction hasn’t started
yet. No floors have been built, and so
there are no windows. We could write a multiplication
fact to show this. Zero times nine equals zero. In fact, zero times anything equals
zero. Right, let’s start work. See how many of these nine times
tables facts you remember. One group of nine is, of course,
nine. In fact, any number that we
multiply by one stays the same. We could use doubling facts to help
us with the next one. Two times nine equals 18.
You know, we need to remember that
each of these facts is really two facts in one. For example, we may need a little
bit of help with our nine times table and not know what three times nine is. But maybe we do know our three
times table because three nines is exactly the same as nine threes. And nine times three is 27. Four times nine is 36. Five groups of nine is equal to
45. Let’s pause for a moment and think
about what we’re doing here. Each time we’re finding the next
number in the nine times table, we’re adding another nine.
Now we know that nine is one less
than 10, and adding 10 on a number square like this is as simple as just going down
to the next row. So adding nine is the same as going
down a row and back one. This means that the numbers in the
nine times table, what we call the multiples of nine, have a pattern to them. And just by adding 10 then taking
away one, we can always find out the next multiple of nine. Let’s try this idea of adding 10
and taking away one to find the answer to six times nine.
We know that five times nine is 45,
adding 10 would give us 55, and one less than this is 54. Six times nine is 54. Our skyscraper is really taking
shape now. What other methods could we use to
help us multiply by nine? Well, as we’ve seen already, nine
is really close to 10. And we can remember 10 times tables
facts really quickly. Seven times 10 is 70. So how could we use this to find
seven times nine? Well, we can think of seven times
10 as being 10 lots of seven. And what we want to find is nine
lots of seven. So we just need to take away seven
from 70. Seven times nine is 63. And you know, we could use this
method for any of our nine times tables facts.
Four times nine is the same as four
times 10 take away four; six times nine is the same as six times 10 take away
six. We’re building up quite a
collection of methods here, aren’t we? It’s almost like we’ve been given a
toolbox. If we don’t know a nine times
tables fact, we could dip into our toolbox and use one of the methods we’ve talked
about to help us. Now we’ve already talked about
doubling when we multiplied nine by two. But we can also use doubling to
find out other facts. At the moment, our skyscraper is
eight floors high. And eight is double four. So if we know what four times nine
is, we can double it to find out what, eight times nine is. Well, four times nine is 36. Double 30 is 60. Double six is 12. And if we add 60 and 12 together,
we get 72. Eight times nine is 72.
Now what would you do if you
couldn’t remember what nine times nine was worth? Well, in a way, it’s a good idea to
think about the next floor up in our skyscraper, because if we know what 10 times
nine is — and we do, it’s worth 90 — then nine times nine is just nine less than
this. And 90 take away nine is 81. Let’s continue with these facts up
to 12 times nine. 11 times nine is 99. And finally, 12 nines. Well, how are we going to work out
this? We could partition the number 12
into 10 and two. And so we can think of 12 times
nine as just being the sum of 10 times nine and two times nine. And 90 plus 18 equals 108. 12 nines are 108.
Now there’s a pattern with these
multiples of nine. I wonder have you spotted it? Let’s skip count in nines from
zero. And as we say each number, try to
listen for the pattern. You should be able to hear it. Zero, nine, 18, 27, 36, 45, 54. I wonder can you hear that
pattern? The ones digit of our numbers is
decreasing by one each time. We start with zero, and then the
ones go from nine to eight to seven to six to five to four and so on. And if we look at the tens digits,
we can see that these are increasing by one each time. The first time we come across a 10
is in the number 18, and then we have two 10s in 27, three 10s in 36, four 10s in
45, and five 10s in 54.
And if we think about it for a
moment, we know why the tens digits are going up and the ones digits are going
down. As we’ve discussed already, every
time we find another nine, it’s the same as adding 10, then subtracting one. Tens digit increases; ones digit
decreases. Let’s try this skip counting method
now to find some nine times tables facts.
This sequence chart will help us
multiply by nine using skip counting by nines up to 10 times. Use skip counting to find nine
times two, and then use skip counting to find nine times nine.
In this question, we’re given a
picture of a sequence chart. If we look at it carefully, we can
see it’s pretty much the same as 100 square. Each row contains 10 numbers, but
instead of having 10 rows that go all the way up to 100, we have nine rows and we
stop at 90. And the reason why we stop at 90 is
that this sequence chart is to help us learn our nine times tables facts. The way it’s been labeled helps us
skip count by nines up to 10 times. The number nine, of course, is one
less than 10.
To count in tens using a chart like
this, we would simply go down a row. Six becomes 16 and then 26. So if that’s how to skip count in
tens using a sequence chart like this, to skip count in nines, we could move down a
square and then back a square. It’s the same as adding 10, taking
away one. And we can see all the multiples of
nine have been labeled on this chart. They make quite a clear diagonal
pattern, don’t they? In the first part of the question
we’re told to use skip counting to find the answer to nine times two, or if we think
of the numbers the other way around two times nine or two lots of nine. Let’s do this then.
Starting at nine, we say nine,
18. Nine times two is 18. Next, we need to use the same skip
counting method. But this time, we need to count a
lot further. We need to count up to nine lots of
nine. So we’ll start at nine again and
say nine, 18, 27, 36, 45, 54, 63, 72, 81. The whole sequence chart only shows
up to 10 times nine, and we’ve said all the numbers apart from one. We’ve skip counted in nines nine
times, and we’ve ended on the number 81. There are lots of patterns with a
nine times table, and we can see some in this sequence chart. We followed the pattern to skip
count by nines to find the answer to two multiplications. Nine times two equals 18, and nine
times nine equals 81.
So far, we’ve learned about lots of
strategies we can use to help us find out nine times tables facts. In our toolbox, we’ve got skip
counting, using doubling to help, adding on, spotting patterns, using the much
easier 10 times tables facts to help. We’re going to have a go at
answering some questions now where we can use these tools. But don’t forget. The best strategy of all is simply
just learning the facts. Hopefully, these questions are
gonna help us remember them.
Fill in the blank: nine times three
Perhaps you know the answer to this
times table and could say it straightaway. But what if you don’t? What strategy could we use to help
us? The question nine times three is
really asking us, what are nine lots of three or three lots of nine. Now, we may not know what nine
threes are, but there is a calculation quite close to this that we probably do
know. If we know what 10 times three is,
we can use this to help us. 10 threes are 30. And so nine threes are just one lot
of three less than this, in other words, 30 take away three. The answer is 27. We found the answer to nine times
three by finding three less than 10 times three. Nine times three equals 27.
Notice how each row is nine more
than the previous one. One times nine equals nine; two
times nine equals 18; three times nine equals 27. Find the result of the following:
Four times nine equals what. And then also find the result of
the following: Five times nine equals what.
We know that learning times tables
facts is all about thinking about groups of a certain number. And this question is all about nine
times tables facts. We can see in the pictures that
each cube is labeled with the number nine. We’re counting in nines. And the first thing that we’re told
is that each row is worth nine more than the previous one. In other words, as we go through
our nine times tables facts to find the next one, we just add another nine. So that’s why we have one times
nine is nine, and then we’ve got a new orange cube to show that nine more’s been
added. Nine add nine is 18. So that’s why we can say two times
nine is 18. If we add another nine, we get
27. And that’s why we can say three
times nine equals 27.
And next, we’re told to find the
result of four times nine. Well, to find four lots of nine, we
just need to add nine onto three lots of nine. So what’s nine more than 27? Well, we know if we had to add 10,
it would be 37. And nine is one less than this. Four times nine is 36.
And in the final part of the
question, we just need to do the same again because we need to find five times
nine. We know what four nines are, so we
just need to add one more nine. Now we know 36 add 10 would be
46. But again, nine is one less than
ten, so instead of 46, the answer is 45. If we know a nine times tables
fact, we can find the next fact by adding nine. And that’s how we found out that
four times nine is 36 and five nines are 45.
We know that two times nine equals
18. Use this to find four times
This question then is asking us to
find the answer to four times nine, and we’re told how to do it. We need to use the fact two times
nine equals 18 to help. Now, how can we use this first fact
to help? What’s the link between two times
nine and four times nine? Perhaps you’ll be able to spot the
link if we model some arrays. Here’s the fact we know already,
and here’s the fact we need to find. It’s double the size, isn’t it? Four is double two. So if we know what two times nine
is, and we do, we can just double it to find the answer to four times nine.
So what is 18 doubled? Eight doubled is 16, and 10 doubled
is 20. And if we put these two parts
together, we get the total 36. We’ve used doubling to help us with
our times tables facts. If we know what two times nine is,
then we can double it to find four times nine. And that’s how we know four times
nine is double 18. The answer is 36.
So what have we learned in this
video? We’ve learned how to model
multiplication by nine and practice reciting nine times tables facts.