Lesson Video: Dividing Numbers Using Bar Models Mathematics • 3rd Grade

In this video, we will learn how to draw bar models and write equations to represent one-step division problems with numbers up to 100.

16:29

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.

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