Video Transcript
Dividing by Four
In this video, we’re going to learn
how to use different strategies to divide by four. Some of these are going to include
using models and also using times tables facts that we already know to help. Let’s start by thinking about what
it means to divide by four. And we’ll start with a question,
“What’s 12 divided by four?” Now when we divide by any number at
all, we’re doing one of two things. We’re either finding a number of
groups or the number of things in each group. Let’s show what we mean by this
because it will really help us when we’re working out the answer to divisions.
Here is our starting number 12
represented by 12 chickens. And Let’s imagine that they decide
to split into groups of four. This would be the same as 12
divided by four. And the answer to this division
would be the first thing we mentioned. It will be the number of groups
they’ll make. Four, eight, 12. The chickens have made three equal
groups. So we can say 12 divided by four
equals three. And the number three in this
division, if we think about it this way, is the number of groups. But there’s another way we can
think about division.
Let’s imagine that this time our 12
chickens decide to divide themselves up into four equal groups. This time, the answer to the
division is going to be the number of chickens that there are in each group. There’ll be three chickens in each
group. So the answer to the division is
still going to be three. But it’s going to mean something
different. And we can use these two ideas to
help us as we divide by four in this video. We can either think of dividing by
four, as finding out how many fours there are in the number, or by seeing what we
get when we split the number into four equal parts. Different ways of thinking about
it, same answer.
Now with this question, we’ve used
pictures to help us. But there are other strategies we
could use. Let’s imagine that we want to find
the answer to 24 divided by four. As we’ve said already, we can think
of dividing by four as finding out how many fours there are in a number. And so we could ask this question a
different way. How many fours are there in 24? And to find the answer, we could
start with this number, 24, and keep counting back taking away fours until we have
nothing left. We call this repeated subtraction,
and we can show this on a number line.
So we could start by sketching a
line. And because we’re going to be
counting backwards, we’ll label 24 which is our starting number on the right. We’ll draw a little arrow to show
that our number line continues. But then we’re going to be heading
all the way back to zero. So we’ll label zero right at the
end on the left. Now we can subtract fours to see
how many there are in 24. 24 take away four equals 20. 20 take away four leaves us with
16. 16 take away four equals 12. Only a few more jumps of four
before we get back to zero, aren’t there? 12 take away four equals eight. By the way, can you see that all
these numbers are multiples of four? The’re all the numbers in the four
times table. Eight take away four leaves us with
four. And if we subtract this last lot of
four, we’re going to get back to zero.
Did you count how many jumps we
made? We subtracted four one, two, three,
four, five, six times. So we can say that there are six
fours in 24. 24 divided by four equals six. Now when we worked out the answer
that time, we did a lot of subtractions. 24 take away four, then 20 take
away four, and so on. But if we know how to skip count in
fours, particularly skip count in fours backwards, we can just work out the answer
by making quick jumps of four, rather than thinking of them as separate
subtractions. It’s the same thing, but it’s a
little bit quicker. And it works if we know our
multiples of four really well. So we start with 24 and then just
say 20, 16, 12, eight, four, zero.
You know there’s an even quicker
way to find out how many fours there are in the number. And there’s another strategy we can
use. It’s probably the quickest way we
could divide by four if we know how to. And we know that addition and
subtraction are opposites in maths. They’re inverse operations. And in the same way, multiplication
and division are inverse operations too. They’re the opposite of each
other. And so, to help us find the answer
to division questions, we can use times tables facts we already know. Because in this video we’re
thinking about dividing by four, we need to think about four times tables facts.
Now let’s stick with this question,
24 divided by four. If we want to use times tables
facts we already know to help us, we need to ask ourselves a little question. It’s very similar to the one the
red chicken is asking at the top of this screen. How many fours are there in 24? But this time, the question
mentions multiplication. What do I multiply by four to give
me the answer 24? Something times four is 24. And if we know that fact, we can
solve the division. Now perhaps you know your times
tables facts off my heart. Or maybe you need to start at one
times four and keep counting on. Either way, we can still get to the
answer.
One times four is four, two fours
are eight, three fours are 12, four fours are 16, five times four is 20, and then
the fact we’re looking for, six times four is 24. And if we know this fact, then we
know that there must be six lots of four in 24. So we used times tables facts we
already knew to help us. And also this model or array of
counters helped us too. We can actually see those six
groups of four, can’t we? And before we answer some questions
on dividing by four, let’s look at one more strategy we could use.
Now, so far, all the strategies
we’ve used when we’ve been dividing 24 by four had been about finding how many fours
there are in 24. But if you remember at the start of
the video, we said there was another way of thinking about dividing by four, and
that’s to do with splitting a number up into four equal groups and seeing how many
there are in those groups. To help us understand what we need
to do with numbers, let’s stop for a moment and think about shapes. If you were going to divide this
circle into four equal parts, what would you do? Well, I’m guessing you’d cut it
into half and then half again. And we can do exactly the same sort
of thing if we want to divide a number into four equal groups.
We can find the answer to 24
divided by four by dividing it by two and then by two again. We know that half of 24 or 24
divided by two is 12. And then if we take that number and
divide it by two again, we know half of 12 is six. So a quick way to divide by four is
by halving and then halving again. If we split 24 into four equal
groups, there’ll be six in each group. What a lot of strategies we can use
to divide by four. We’ve talked about repeated
subtraction using a number line to help and also how we can do this a bit quicker if
we skip count backwards.
We’ve looked at how we can use
multiplication facts we already know to help, some of the ways to model a division
using a raise, and finally we looked at how dividing by two twice can help us. Let’s get onto some questions
then. And we’re going to put into
practice some of these strategies as we divide by four.
What is 28 divided by four?
This question tests our ability to
divide by four. But what does it mean to divide 28
by four? What’s this question asking us to
do? Well, we can think of this question
in two different ways, and we can use the array that we’re given to show these. One way we could think of this
question is as 28 split into groups of four. How many groups are there? In other words, how many fours are
there in 28? And we can show this on our
array. Can you see any groups of four? Each of the columns in the array
shows four counters, doesn’t it? So if we count the number of
columns we’ve got, this is the number of fours we’ve got. Let’s split our array into groups
of four.
We’ve got one, two, three, four,
five, six, seven groups of four. But you know, there’s another way
we could think about this division. This time, we could think of it as
asking, what’s 28 split into four equal groups? How many will there be in each
group? Let’s sketch the same array, but
we’re going to split it up in a slightly different way and show how we can find
exactly the same answer. So we’ll start with 28 counters
again. This time, we’re going to split
them into four equal groups. Can you see how we can do this? There are four rows aren’t
there.
So if we think of each row in our
array as a group, we can just ask ourselves how many in each row? And of course, we know there are
seven counters in each row. So whether we split 28 counters
into groups of four and count the groups or we split 28 into four equal groups and
count the number of counters in each group, we get exactly the same answer. 28 divided by four equals
seven.
What is 16 divided by four?
One way we can think of a division
like this is as finding the number of fours there are in 16. And there are several ways we could
do this. We could start at zero and count in
fours until we get to 16. Or we could do the other way
around; we could start with 16 and count in fours backwards until we get to zero, in
other ways, until we’ve got no more fours left. Let’s use this second method of
counting backwards. And we could show what we’re doing
on a number line. So we could start by sketching our
number line. And because we’re going to be
counting backwards, we could label 16 on the right. And we’re going to go all the way
back to zero, so we need to label zero too.
Now we just need to count back in
fours. How many jumps of four do you think
it’s going to take us to get from 16 all the way back to zero? 16 take away four equals 12. 12 subtract four equals eight. Eight subtract four equals
four. And this leaves us with one more
lot of four that we can take away to get to zero. We found the number of fours in 16
by counting backwards in fours. And we’ve done this by taking away
every time; it’s called repeated subtraction. But if we know our multiples of
four, we could have done this a little bit quicker by skip counting backwards and
just saying the numbers. So we just say 16 and then 12,
eight, four, zero.
So whether we think of what we’ve
done as subtracting fours every time or just skip counting backwards in fours, we’ve
used this number line to help us find how many fours there are in 16. And to get from 16 to zero, we made
four jumps of four. 16 divided by four equals four.
What number is missing from the
table?
The table that we’re given in this
question has two rows. And each of the rows contains a
series of numbers, well, almost all of the rows. Can you see this last part of the
table has a missing number? And when our question asked “What
number is missing from a table?”, it’s this number that we’re looking for. Now, often with a table, we might
have a series of labels for each column or maybe each row to show us what
information they contain. But there aren’t any labels
here. How do we know where all these
numbers are coming from? Well, we need to be really careful
with this table because it would be very easy to make a mistake.
If we try reading the numbers
across the table — 16, 20, 24, 32 — we might think to ourselves that could be a
pattern, especially if we look at the numbers in the bottom row four, five, six, and
then our missing number. If we don’t really think it
through, it would be very easy to write the number seven here. Four, five, six, seven. It looks like a pattern. But if there’s one thing we can
learn from a question like this, it’s to read it really carefully. Something we haven’t mentioned is
that, on the left-hand side of the table, we can see an operation divided by
four. And if we read each column of the
table from top to bottom, this explains how it works. It’s almost like a dividing
machine.
We start with the number on the
top; in the first column, that’s 16. We then divide it by four, and the
answer is the number on the bottom row. We know that 16 divided by four is
four. And that’s why the number four is
on the bottom row. And we can see that the other
numbers in the table are being divided by four too. 20 divided by four equals five. We know this, don’t we, because
five times four is 20, and 24 divided by four equals six. And again, we know a times tables
fact that can help us with this; six times four is 24. And so we know that to find our
missing number, we need to take the top number 32 and divide it by four. We could use our knowledge of times
tables facts to help here.
What do we multiply four by to give
us the answer 32? Well, as we’ve just said, six fours
are 24, so we could start counting from there. Seven fours are 28 and eight fours
are 32. This is the fact that’s going to
help us here. If we know that there are eight
lots of four in 32, if we start with 32 and divide it by four, the answer is going
to be eight. It’s a good job we didn’t write
seven, isn’t it? There isn’t a pattern in the bottom
numbers of this table. We had to find out the answer not
by looking for a pattern, but by dividing the top number by four. 32 divided by four equals
eight. And so the missing number is
eight.
Liam thinks of a number and divides
it by four. He gets the answer nine. What was the number Liam first
thought of?
Let’s start by showing this problem
as a bar model. It might help us understand what we
need to do to find the answer. Firstly, we’re told that Liam
thinks of a number. Let’s use this bar to represent
that. And then we’re told he divides it
by four. We could show this by drawing the
same bar and splitting it into four equal parts. We’re then told that he gets the
answer nine. In other words, each one of his
four parts is worth nine. And we’re asked, “What was the
number Liam first thought of?” We could also write the problem as
a number sentence. Liam thinks of a number. He divides it by four, and he gets
the answer nine.
What number divided by four equals
nine? Can you see from the bar model how
best to find the answer here? Each of the four parts is worth
nine. So to find the first number in our
division, we could work backwards and use multiplication to help. What are nine fours? Well, we know that 10 fours are
worth 40, and so nine fours are worth four less than 40, which is 36. And so we can complete our bar
model and also our number sentence with the number 36. We know that nine times four is 36,
and so 36 divided by four equals nine. The number that Liam first thought
of is 36.
So what have we learned in this
video? We’ve learned different strategies
to help us divide by four. These have included using models,
repeated subtraction or skip counting, using known multiplication facts, and also by
halving twice.
