Video Transcript
Dividing Numbers Using Bar
Models
In this video, we’re going to learn
how to draw bar models and write equations to represent division problems using
numbers up to 100. When we divide two numbers, we’re
usually trying to do one of two things. Firstly, we can use it to find the
number of groups of a certain size or we can divide an amount into a certain number
of groups and find the amount in each group. Let’s think about an example where
we have to find the number of groups to begin with.
In a bakery, there are 18
cookies. When they’re sold, these cookies
are put in bags of two. How many bags can we make from our
18 cookies? To find the answer, we need to
share 18 into equal groups of two. In other words, 18 divided by two
equals what. Now, there are lots of ways we
could model a division like this. And in this video, we’re going to
be using bar models. Now, bar models are brilliant
things. They’re really useful in helping us
to understand what we need to do to solve a problem because at the moment all we can
see is this pile of cookies and this calculation up here. It can be hard to visualize exactly
what we need to do.
To begin with, we could draw a big
strip like this or a bar to represent the whole amount. So in this example, our whole bar
is worth 18. In fact, as this is our first
example, why don’t we put our cookies inside the bar model? So here are our 18 cookies all in
the line. And remember in our question, we
need to divide 18 into groups of two because that’s how these cookies are sold. So we can start drawing some more
bars underneath to represent this. We can make one group of two, two
groups of two, and so on. Now we can see from this bar model
exactly what we need to do. We need to find the number of twos
that fit into 18. In other words, this division is
about finding the number of groups.
Now that we’ve represented the
problem using our bar model, we can solve it. How could we find out how many twos
there are in 18? Should we try skip counting? Two, four, six, eight, 10, 12, 14,
16, 18. There are one, two, three, four,
five, six, seven, eight, nine groups of two in 18. Now we can complete our number
sentence. 18 divided by two equals nine. And we use the bar model to help us
understand what we needed to do. Now, as well as using division to
find a number of equal groups, we did say there was something else we can use
division for, and that’s to find the number in each group. So let’s have a think about a
problem where we need to do this.
Now, maybe you’re feeling hungry,
so let’s stick with the bakery. Let’s imagine that the baker has
baked 15 cupcakes, and she wants to arrange them on three trays. But she wants them to look neat, so
she decides to divide them equally. How many cupcakes will there be on
each of the three trays? Once again, we can represent this
problem using a bar model. The whole bar this time represents
our 15 cupcakes. But we don’t need to draw the
objects every single time. The number 15 will do, and we need
to divide this number 15 into three equal groups. How many will there be in each
group? 15 divided by three equals
what? Can you see that this time we’re
finding the number in each group?
Now that we’ve modeled the problem
using a bar model and also a number sentence, we’re ready to solve it. Can you think of any times tables
facts that might help? We know that three times five
equals 15. And so if we divide 15 into three
equal groups, we know that there’ll be five in each group. We’ve used a bar model to help us
understand what we needed to do to find the answer and then our knowledge of times
tables facts to solve the problem. 15 divided by three equals
five.
We could even complete our bar
model by writing the number five in each of the three bars. If our baker wants to divide these
cupcakes into three equal trays, there are going to be five cupcakes on each
tray. Let’s try putting into practice
what we’ve learned now by answering some questions. And for each of the division
problems we look at, we’re going to draw a bar model to help us understand what we
need to do to find the answer.
Three friends have 24 coins. We can draw a bar model to show how
many coins each one has. How many coins does each one
have?
Did you notice as we read this
problem, there are no operation symbols to tell us what to do? We can’t see a plus or a takeaway
sign or a multiplication or division symbol. How are we going to work out what
to do? Well, the clue is in the pictures
and also in our second sentence where it tells us that we can draw a bar model. Bar models are so useful; they help
us to understand what we need to do to solve a problem. So let’s start at the beginning and
see how this particular bar model can help us here.
In the first sentence, we’re given
two pieces of information with numbers in them. We’re told that three friends have
24 coins. And we’re shown a picture of those
24 coins. I wonder why the coins have been
drawn in a long strip like this. Well, it’s because we can draw a
bar model to help us. Did you notice that the bar in the
bar model is exactly the same length as our strip of coins? It represents the whole amount. And we know this because it’s
labeled with the number 24. Now, what else do we know about
this whole amount of 24 coins? We know that the number of friends
that have these coins is three. And although the question doesn’t
tell us, we do know that each friend must have the same amount of coins. This is because the whole bar has
been split into three equal parts.
Now, our question asks us how many
coins does each of the three friends have. And by looking at the bar model, we
now know what we need to do. We need to start with 24 and divide
it into three equal groups. And our answer is going to be the
number of coins that there are in each group. The bar model has helped us to see
that this is a division problem. What do we get if we divide 24 by
three? We could take 24 counters to
represent our 24 coins and then share them out into three equal groups. Let’s put one in each group. Two, three, four, five, six, seven,
eight. 24 divided by three equals
eight.
And you know we can show this using
the picture of the coins too. If we draw a dotted line up from
each of our three equal bars, we can see that there are eight coins in each
part. We could even label our bar model
to show this. The bar model helped us to
understand what we needed to do to solve the problem. If three friends have 24 coins, to
find out how many coins each one has, as long as they’re equal amounts, we need to
divide 24 by three. And 24 divided by three equals
eight. Each of the friends has eight
coins.
Liam has 35 flowers arranged in
seven rows. How many flowers are in each
row?
With a word problem like this, we
need to think carefully about what we need to do to find the answer. And in this particular word
problem, we’re given something to help us. Can you see what it is? Although we don’t need it to find
the answer, we’re given a bar model, and this really helps us to understand what we
need to do to find the answer. Now our bar model doesn’t show Liam
or any flowers. It’s not a picture, but it is a
type of diagram that can help us. Let’s go through the problem and
see how.
Firstly, we’re told that Liam has
35 flowers. Now, as we said already, there
aren’t any pictures of those 35 flowers, but can you see them on the bar model? The number 35 is here, and the way
that it’s labeled it shows us that the whole bar is worth 35. Now, we’re told that Liam’s flowers
are arranged in seven rows. Can you see the number seven
represented on this bar model? Well, it’s not labeled, but we can
see that the whole bar of 35 has been split into one, two, three, four, five, six,
seven equal parts. These are just the same as the
seven equal rows that Liam’s flowers have been arranged in.
So by looking at our bar model, we
can see what we need to do to find the answer. We need to split up 35 or divide it
into seven equal groups. And our answer is going to be the
number in each group. And in this particular problem,
it’s going to show us the number of flowers in each row. So what is 35 divided by seven? Let’s use our knowledge of times
tables to help here. Seven lots of what equals 35? Seven times one equals seven, seven
twos are 14, seven times three is 21, seven times four is 28, and seven times five
equals 35. And because we know seven lots of
five equal 35, we can say 35 divided by seven equals five.
We’ve used a bar model to help us
understand what we needed to do to solve the problem. If Liam has 35 flowers and they’re
arranged in seven equal rows, we know the number of flowers in each row is going to
be the answer to 35 divided by seven. And 35 divided by seven equals
five. There are five flowers in each
row.
Olivia has 30 crayons, and each box
holds five crayons. Find the number of boxes she’ll
need for all the crayons by finishing the bar model. 30 divided by five equals what?
We’re told that Olivia has 30
crayons, and she’s obviously sorting out all these crayons into boxes because we’re
told that we need to find the number of boxes she’s going to need for all of the
crayons. Now, in the first sentence, we’re
also given another fact to help us. We are told that each box holds
five crayons. So to find the answer, we know we
have to divide 30 into equal groups of five, and we need to find out how many groups
there’ll be. Now, we’re given a bar model to
help us understand the problem. But this bar model is only partly
completed. We can see the top bar is labeled
30. This represents the first number in
our number sentence and the 30 crayons that Olivia has to begin with.
Now we can also see that underneath
this first bar there are three smaller bars; all three are the same size. The main reason we know this is not
because they look the same size; it’s because they’re all labelled five. They all have the same value. And each of these little bars
labeled with a number five represents another box of five crayons that Olivia has
split her 35 crayons into. Now the way our bar model looks at
the moment, she’s only made three boxes of five crayons. The bar model is only partly
finished. We need to see how many fives there
are in 30.
Let’s find the answer by finishing
the bar model. We could use a number line and skip
count in fives to help: five, 10, 15. So, so far, Olivia has split up 15
crayons into equal groups of five, and she’s made three groups. Let’s continue drawing this bar
model: 20, 25, 30. We skip counted in fives and we
found that it took six jumps of five to get to 30. And so we used the bar model to
help us understand what we needed to do to answer the question. 30 divided by five equals six. And so if Olivia has 30 crayons and
she splits them up into boxes that hold five crayons each, the number of boxes that
she’s going to need for all of the crayons is six.
A girl wants to share 45 oranges
equally among five people. How many oranges will each person
receive?
Now, sometimes in a word problem,
we might see a word that’ll give us a clue as to what we need to do to solve the
problem. And in this problem, there is one
of those words. Can you spot it? It’s the word share. And we could also include this word
equally here because when we share or split something up equally, this is the same
as dividing it. It looks like this might be a
problem that we need to use division to solve. But you know, one of the best ways
we can model a problem like this to work out exactly what we need to do is to use a
bar model. So let’s use a bar model here.
The first thing we know about the
girl in the question is that she has 45 oranges. This is the number she begins
with. It’s the whole amount. So we can start sketching our bar
model by drawing one long bar, and this can represent the whole amount of 45
oranges. Now what does this girl do with
these oranges? She wants to share them or divide
them equally among five people. In other words, she wants to split
up this whole amount of 45 into five equal parts, and we could show this on our bar
model. Here’s the whole amount, and we can
divide it into one, two, three, four, five equal groups. And our question is asking us, how
many oranges will each person receive? In other words, what’s each one of
these groups worth? What is 45 divided by five?
Perhaps we can think of some times
tables facts that could help us here. How many fives make 45? We know that 10 fives are 50. 45 is one lot of five less than
50. So instead of 10 fives, 45 is one
lot of five less. It’s nine fives. 45 divided by five equals nine, and
we could complete this bar model to show this. Each of the five bars is worth
nine: nine, 18, 27, 36, 45. We’ve used our bar model to show
that 45 divided by five equals nine. And so if a girl wants to share 45
oranges equally between five people, each person will receive nine oranges.
What have we learned in this
video? We’ve learned how to represent
division problems by drawing bar models, writing equations, and using these to help
solve the problem.
