Video Transcript
Dividing by Three
In this video, we’re going to learn
how to use different strategies to help us divide by three. Some of the strategies we’re going
to use are models and also using times tables facts to help.
Each of these monsters has three
eyes. Now let’s imagine that we turn the
light off, and then we noticed 12 eyes looking back at us. How many monsters is this? We can find the answer by dividing
12 into groups of three. This is one thing that dividing by
three can mean. And so the answer to our division,
this is what we call the quotient, is going to be the number of equal groups that
we’ve made.
So what strategy could be used to
divide 12 by three? Let’s draw a model. We could sketch 12 counters like
this and the way that we’ve drawn them is going to help us split this number into
equal groups of three. We can see one, two, three, four
groups of three. 12 divided by three equals
four. We divided 12 into equal groups of
three. And the quotient or the answer to
our division shows us the number of equal groups that we can make. And in this problem, it’s the
number of monsters that there are. Shall we check that there are
four? It’s time to turn that light switch
back on. We were right. There are four monsters in the
room. 12 divided by three equals
four.
So we used a model to help us solve
that problem. Let’s try a different strategy for
dividing by three. And let’s turn the lights off
again. And let’s imagine we can now see 30
eyes looking back at us. To find out how many monsters there
are, we’re going to need to divide by three again to split these 30 eyes into equal
groups of three. And just like before, the quotient
or the answer to this division is going to be the number of equal groups that we can
make or the number of monsters that there are. And last time we used our model to
find the answer. This time, let’s try a different
method. We could use a number line to
help.
To see how many threes fit into 30,
we could start with 30 and count back three each time. This is very similar to something
called repeated subtraction. This is when we start with 30 and
we keep taking away three and then another three and so on until we’ve got no more
to take away. So let’s see how many threes fit
into 30. We’ll count back three from 30. 30, 29, 28, 27 and then 26, 25, 24
and then 23, 22, 21, 20, 19, 18 then 17, 16, 15. So far, we’ve subtracted five lots
of three. 14, 13, 12, 11, 10, nine and then
eight, seven, six, then five, four, three. And this means we’ve got one more
lot of three we can subtract. Two, one, zero.
So in total, we’ve made one, two,
three, four, five, six, seven, eight, nine, 10 jumps backwards of three, or we’ve
subtracted three 10 times. And we’ve gone from 30 all the way
back to zero. So we can say there must be 10
threes in 30. 30 divided by three equals 10. We used a number line to help us
find the answer, and it looks like there’s going to be 10 monsters. Let’s turn the light back on. What a lot of monsters. And there are 10 of them. 30 divided by three equals 10. Now so far, we’ve looked at
dividing by three where we have to make equal groups of three, and the answer or the
quotient is the number of equal groups we can make.
But you know, we can think of
division another way. Let’s imagine there are six
monsters. And they’ve been asked to divide
themselves into three equal groups. This is the same as six divided by
three. You know, we can also write this
another way: six divided by three. And we’d write the answer up
here. As we learn to divide bigger and
bigger numbers, we’ll use this sort of division more often. But we could write our division
like this. Now the idea of dividing by three
in this problem is slightly different. We’re not splitting the monsters up
into equal groups of three. We’re splitting them up in three
equal groups. It’s almost like there are three
tables in the classroom and your teacher says, “go and split yourselves up so that
there’s an equal number in each group.”
This time, the quotient or the
answer isn’t going to be the number of groups; it’s going to be the number in each
group. So far, we’ve used a model. We’ve counted back on a number line
or used repeated subtraction to help. What else could we do? Well, because division and
multiplication are linked, we could use times tables facts to help. Can you think of a three times
table fact that might be able to help us here? Well, we know that two lots of
three make six; two times three equals six. And we can use this to help. If two times three is six, we know
that six divided by three must equal two.
Let’s share out our monsters into
three equal groups and see whether we’re right. One, two, three; one, two,
three. We divided six monsters into three
equal groups. And we found that there were two
monsters in each group. Six divided by three equals
two. And we used a times tables fact
this time to help us. Let’s have a go at answering some
questions now where we have to divide by three. And perhaps we’ll try drawing a
model, counting back on a number line, and maybe even use our knowledge of times
tables to help.
Find 18 divided by three using the
cubes shown.
In this question, we need to
practice our skills at dividing by three. And we know that we need to use a
model to help us because we’re given a picture of some cubes. And we’re told that we need to find
the answer using the cubes shown. Now when you see the calculation 18
divided by three, what do you think of? We could think of it as 18 split
into groups of three. And we try to find how many
groups. Or we could think of it as 18
shared into three equal groups. And then we’d be trying to find out
how many in each group. In the picture, we’re given 18
cubes. And you know, it doesn’t really
matter which way we think of 18 divided by three. We can find the answer in both
ways. And both ways involve drawing the
lines on our model.
Let’s start with the first
idea. We could think of this as 18 split
into groups of three. And we’re going to count how many
groups we can make. Perhaps this is the way you’d think
of the division. Well by looking at our cubes, can
you see how to split them into groups of three? If we look carefully, we can see
some groups of three already. We can see one, two, three, four,
five, six groups of three. So if we think of our division like
this, we can split 18 into groups of three and see that we can make six groups. But perhaps you thought of the
model another way. Perhaps you thought of it as 18
shared into three equal groups. Let’s show the model again. And we’re going to draw our lines
in a different way this time.
Can you see how you draw the lines
to share 18 into three equal groups? We could do it like this: one
group, two groups, three groups. And they’re all the same size. We can see that they all contain
one, two, three, four, five, six. So if we start with 18 cubes and we
share them into three equal groups, there’ll be six cubes in each group. So it doesn’t really matter how we
think of this division. Whether we want to find the number
of groups or the number in each group, the answer is still the same. We’ve used a model in two different
ways to find the answer to 18 divided by three. And that answer is six.
Count back to find 15 divided by
three.
In this question, we’ve got a
division to solve. We need to divide 15 by three. One way of thinking of this is, how
many threes are there in 15? And one way we could find out how
many threes are in 15 is if we count back, which is what this question tells us to
do. We could do this on a number
line. So we could start by sketching a
number line and labeling zero at one end and 15 at the other. But remember, we’re going to be
working backwards, so we’re going to start at 15 and go back toward zero. Now to find out how many threes
there are in 15, we could count back in threes. So starting on 15, let’s count back
one lot of three. 15, 14, 13, 12.
So we know there’s definitely one
lot of three in 15. Let’s take away another lot of
three, starting with 12, 11, 10, nine, and another jump of three, starting with
nine, eight, seven, six. So we’ve already made three jumps
of three and we’ve landed on the number six. Can you see how many more jumps of
three we need to make? Six, five, four, three. And then if we take away one more
lot of three, it’s going to take us to zero. We’ve made five jumps of three
altogether to get from 15 all the way back to zero. This tells us that there are five
threes in 15. We’ve used counting backwards or
repeated subtraction to help us solve this division. 15 divided by three equals
five.
Find the missing quotient. 24 divided by three equals
what. Hint: How can solving what times
three equals 24 help you?
There’s an interesting word in the
first sentence of this problem, “quotient.” Whatever it is, there’s one missing
because we’re told to find the missing quotient. And underneath this phrase, we can
see a division: 24 divided by three equals what. And the missing number is the
answer to the division. And you know, this is what a
quotient is. It’s the answer when we’ve divided
one number by another. So really, we could say, find the
missing answer to this division. What is 24 divided by three? And we’re given a hint to help
us. We’re asked, how can solving what
times three equals 24 help you? Can you see what number sentence
we’re given? It’s a times table fact.
Now there are lots of ways we could
solve division questions. But probably the quickest way is to
think of a times table fact we already know and use this to help us. Perhaps you already know what
number you multiply by three to get 24. But in case you don’t, let’s go
through our number facts. One times three is three, two
threes are six, three times three is nine, four threes are 12, five times three is
15, six threes are 18, seven threes are 21, and now the important one, eight times
three equals 24. Perhaps you didn’t need to go
through all those facts; perhaps you knew it already.
Eight multiplied by three equals
24. And let’s think about what that
means for a moment. There are eight lots of three in
24. And so if we ask ourselves the
question, what’s 24 divided by three, really what we’re asking ourselves is, how
many threes are in 24? And we know this because the times
tables fact tells us. There are eight threes in 24. We found the answer to this
division question or the quotient by using a multiplication fact to help us. We know that eight times three is
24, and so 24 divided by three must be eight.
Which number is missing? What divided by three equals
seven.
In this question, we’re given a
division calculation, but instead of the quotient or the number we get when we
divide two numbers together being missing, we can see that the first number is
missing. This is the number that we’re
dividing by three. What number if we divide it by
three would give us an answer of seven? Let’s think about what this means
for a moment. We could think of this in two
ways. Firstly, what number if we divide
it into three equal groups will give us seven in each group? Or we could think of it as, which
number if we divide it into groups of three will give us seven groups?
They’re both ways of thinking about
the same division. And if we look at these models
we’ve drawn, can you see what we can do to find the answer? In the first model, we’ve got three
groups of seven. And so we could find the total
amount by thinking of the multiplication fact three times seven. And in the second model, we’ve got
seven groups of three. So we could find the total amount
here by working out seven times three.
Now if there’s one thing we know
about multiplication, it’s that we can switch the numbers around and they’ll still
make the same answer. So three times seven is exactly the
same as seven times three. Do you remember your three times
table? What is seven times three? Seven threes are 21. And so we also know that three
times seven is 21 too. And we can use this fact to help us
complete the division. 21 divided by three equals
seven. Our missing number is 21.
What have we learned in this
video? We’ve learned how to divide by
three using different strategies to help. These have included using models,
number lines, or times tables facts to help.
