Solving multiplication and division problems using the bar model

Key Stage 2

Maths

Deriving multiplication and division facts

Joshua bought a 4 cinema tickets.  He spent £48.  How much did each ticket cost?

Ellie shared 66 crayons between herself and two friends.  How many crayons did they each get?

﻿Hello, my name is Mrs Behan and in this lesson, I will be your teacher. So we're going to have a look at bar models, and how we can use a bar model to solve multiplication and division problems. And it's all about finding out the known and unknown values. Let's start by taking a look at the lesson agenda. We're going to have a look at partitioning to multiply and divide, something that we should already know how to do, but we will have a recap. We will then use the bar model to solve some problems. There'll be a practise activity. And after that, you will be ready for your independent task. And don't worry, I will make sure to go through the answers with you. There are just two things that you will need for this lesson. Something to write with; so a pencil or a pen, and something to write on. If you don't have those things handy right now, just pause the video whilst you go and get them. And remember to work somewhere where you aren't going to be disturbed for the lesson. So job number one is to have a go at partitioning to multiply and divide. You might want to draw some base 10 or dienes to help you work out the answers to the calculations. So for example, I might show you 36 divided by three. You would be able to work out that that is 12, because of the way that you can partition 36 into three 10s and give them another row each, and six ones. Share those out between three. We have two in each row, recombine it one 10, and two ones makes 12. I could have given you 12 multiplied by three, you would know it is 36 because you would group. One 10 and two ones here, and you would do that three times. So another one here and another one here. Remember multiplication and division have that special relationship. They are the inverse operation. So that might help you too. Okay, let's have a look at the calculations you are going to solve. 22 divided by two is equal to blank. 13 multiplied by three is equal to blank. 48 divided by four is equal to blank. And 11 multiplied by five is equal to blank. So pause the video here whilst you have a go at those questions. And when you're ready, come back to me. Oh, and before I forget, don't forget, you might need more rows and your place value chart or fewer. Okay, I'll wait here, off you go. Okay, are you ready to go through the answers? Let's take one at a time. So 22 divided by two is equal to 11. I'm going to show you how I worked it out in just a moment. 13 multiplied by three is equal to 39. 48 divided by four is equal to 12 and 11 multiplied by five is equal to 55. So let's see how we worked that out. So I've got two rows here on my place value chart because the divisor is two, that tells me I'm going to need to have two groups. Okay, so let's partition 22. So I have two 10s and two ones. So I will share my two 10s between my two rows and my two ones between my two rows. Recombine it, I can see that there is 11 in each group. Let's take a look at 13 multiplied by three. So this time I have three rows because I'm going to make 13, three times. So here's one group of 13 or one 10 and three ones, another group of 13 and another group of 13. I can now recombine it so I have three tens and nine ones, which altogether is 39. I've just turned the camera off for this one because I won't fit on the screen as well as the place value charts. So, how did we work out 48 divided by four is equal to 12? Well, on our place value chart, we have four rows because the divisor is four, so I need four equal groups. I can partition 48 into how many 10s? That's right. Four 10s and eight ones. And then I'm going to share them out along my place value chart. I've got both calculations coming up. So I've got 11 multiplied by five. So we'll have a look at this one first. Okay so we have our four 10s all shared out between the rows. So that's my forty. And then we're going to divide the eight into four equal groups. So there's two in each one. If I recombine a group, I can see one 10 and two ones, that's equal to 12. There are 12 in each group, okay? So we have four groups of 12. Over to this one now. So we've got our place value charts with five rows. Why do we have five rows? That's right, because we are going to multiply by five. So I want 11 groups of five or five groups of 11 or 11 five times, which is actually what I've done. I've made 11 five times. So here's one group of 11, which is one 10 and one. I've done it two times, three times, four times, five times. It was like 11 plus 11 plus 11 plus 11 plus 11. And the total is 55. So we're now going to have a look at some word problems or number stories as I like to call them. The math is hidden inside the story. So we have to do a little bit of detective work to try and find out what the question is actually asking us to do. We need to work out what operation we need to use. So it could be multiplication or it could be division. So we're going to look for the known facts, these things that we can find out from the story that we know are true. And we're going to put that information into a bar model, then using our detective clues, we're going to find out what is it the question wants us to work out, what is unknown? We're also going to add that information into our bar model and we will represent the unknown information using a question mark. So we're going to go to Silverstone, the British racetrack for our first number story. It's quite lengthy so I'm going to read it to you in smaller chunks. Lewis Hamilton supporters created a huge banner to celebrate his Formula One championship. It was 63 metres long, and it needed someone to hold it up every three metres to keep it straight. It was fixed to the Grandstand at one end. How many people were needed to hold it up? So a banner is something that people would put out to go Lewis Hamilton yaaay, well done! To show their support for him, that would be from his fans. So it's a huge banner and it needs, every three metres it needs somebody to hold it up. Otherwise it's going to flop down. So what is the question asking us to find out? What is the unknown information? Well, we're being asked to find out how many people were needed to hold it up? We don't have that information. So let's have a look at what we do know. What are the known values? Well, we know that it was a huge banner and it's important for us to have that in our minds so that we can imagine it. A huge banner. We know that that banner was 63 metres long, so we can try and compare that to something. That's going to be a very long way. Probably the length of the street perhaps. We know that we need somebody to hold it up every three metres to keep it straight. Every three metres. So it's attached to the Grandstand at one end, then three metres in it needs somebody to hold it up, another three metres it needs somebody to hold it up. This is why I call them stories. They're not just word problems. We need to imagine what is actually happening. It's telling us a story. So let's think about what we know and what is the unknown. So let's show our known and an unknown information on our bar model. So we know it is a huge banner. So here I've drawn a huge banner, but it does look like a bar. We know that the length of that banner is 63 metres so I've drawn a line connecting one end to the other. So from here to here and I've shown that that is 63. So we know that value. We know that every three neat metres, we need another person. So I've drawn a small divide here in the bar and a little section and I've written the number three to represent that after this amount of distance, we need another person. So that's going to repeat. So I made a start putting plus three and three more there. So, the unknown information is how many people we need. So really what we're working out is how many times three fits into 63. So I could multiply because we've said how many times can three fit into 63, but I've still got an unknown value. I don't know how many times three fits into 63. So I'm not going to multiply. I actually need to divide. So I'm going to divide by making groups of three. 63 divided by three is a calculation that I'm going to need. Now it's important to point out here that in this lesson, our focus is trying to work out the calculation needed, not the answer itself. So you're going to need your thinking caps on for this next one. So here we have Michael and his friend, Zara and they've been trying to use a bar model to solve this problem. The moles went to buy lunch for the pit crew. They bought 12 burgers for four pounds each. How much did lunch cost all together? This is the bar model that Michael came up with. Michael thinks that this bar model will help solve that problem. Zara doesn't. She does not agree that that bar model will help solve the problem. But what do you think? Pause the video here whilst you have a look over the question and the bar model? Perhaps you could talk to somebody in your house to see what they think too. And when you're ready, come back to me and we'll look at it together. So what do you think? Well, the first thing to do is to find the maths in the story. And it's actually all in this phrase that's underlined on the screen. Bought 12 burgers for four pounds each. So we know the number of burgers that have been bought and we know how much they cost. They each cost four pounds. So does the bar model match the story? Well, yes it does. Michael is right. And we know that because it has 12 equal parts and one part is equal to four. So we actually have two factors to multiply together. So 12 multiplied by four will solve this problem. So because Michael was right in our last number story, he's had to go at another one. So here he is and here is the problem. I'm going to read it to you. It says, Eva won her first go-karting championship after just four months. It took her 10 times longer to win her first F 3000 championship. How long did it take her to be the F 3000 champion? So just have a little look there, what's the known information and what is the unknown? Let's have a look. Okay well, we know the unknown is the total amount of time it took her to be the F 3000 champion. That's our unknown information. But we do know that after four months, she won her first go-karting championship. And then it got, it took her 10 times longer than the four months to win her first at 3000 championship. So this is the bar model that Michael has drawn. Let's just have a look. What do you think that long bar here represents? Well, that's probably going to be the total length of time it's taken for Eva to become the F 3000 champion. And why is it written four up here? Where can we find four in our problem? Here, four months, okay? So we're going to compare this, to this. And we're going to see how many times longer well we know actually how many times longer it's going to take. Let's see if Michael's done that. Okay so he's made a connection here between the four months and the whole length of time. And then he's put multiplied by 12 and then he's decided that the unknown is the whole. We don't know the whole length of time. What'd you think about Michael's bar model? Has he got all of the right information on that? I think Michael has made a bit of a mistake, hasn't he? I'm not entirely sure where he's got 12 from, but it shouldn't be 12 times longer, as this suggests, what should it be? It should be 10 times longer. Because the story tells us it took her 10 times longer to win her first F 3000 championship. So to make the connection, the calculation we need is four multiplied by 10 which you can see written over here. And what is four multiplied by 10? Easy peasy, it's 40. So 40 months altogether is what it took Eva to become the F 3000 champion. Now that we've looked at a couple of different bar models, you're ready for your independent task. I'd like you to match the bar models to the number stories that they show. So I'm going to go through a word problem at a time then I will show you the bar models. A delivery truck has arrived with sets of tyres for the Formula One cars. There are 48 tyres on the truck and each car needs four tyres. How many cars will get tyres from this trip? The moles put the same amount of fuel in an F one racing car and a normal family car. The F one car completed four laps of Silverstone but the family car completed 12 times as many. How many laps did the family car complete? To celebrate winning the world championship the Mercedes Formula One crew went go-karting. The 48 crew was into four equal teams. How many people were on each team? So have a look at the bar models. What I'd like you to do is decide which bar model matches which problem. Pause the video here to have a go at the task. Once you've ready, come back to me and we'll go through the answers together. So let's go through each question. So the important information in this number story, the first one, is that there are 48 tyres on the truck. That's how many are available and each car needs four tyres. Those are our known values. The unknown is how many cars are going to be able to get tyres from the truck. So which one did you choose? Did you choose this one? Because we had 48 and each one has four tyres perhaps? Or did you choose this one here? The correct answer is this bottom one. There are 48 tyres available altogether and each car needs four. Each car needs four tyres. So we need to know how many fours can fit into 48. Let's look at the second one. The most for the same amount of fuel in a Formula One racing car and a normal family car. I underlined or I highlighted same amount of fuel because it's important to know that the parts are equal. The F one car completed four laps of Silverstone. But the family car completed 12 times as many. So I know the F One car completed four laps. So is this the four here? Or is this the four laps here? Well, our unknown information is how many laps the family car completed in total. And we know the family car completed 12 times as many. So actually, this is our unknown value up here, which means our last example is joined to this bar model. Let's just go through how we know. The 48 crew were split into four equal teams. So in our bar model we can see the total of the whole amount is 48 and they were split into four equal parts. The bit we don't know or unknown value is, the size of each part, the size of each team. If you'd like to please ask your parents or carer to share your work on Instagram, Facebook, or Twitter, tagging @OakNational, @LauraBehan21 and #LearnwithOak. Thanks for joining me for this lesson, you've been brilliant. I hope to see you again soon. Bye bye.

Solving multiplication and division problems using the bar model

Solving multiplication and division problems using the bar model

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UnitMaths / Deriving multiplication and division facts

Maths