Identifying known and unknown relationships

Key Stage 2

Maths

Deriving multiplication and division facts

﻿Hello, my name is Mrs. Behan, and for this lesson I will be your teacher. In this lesson, you are going to learn how you can use the bar model to help your solve different problems, problems that might come up in our everyday lives. We're going to use our skills of addition, subtraction, multiplication and division, pull everything together to do some problem solving. Let's begin by looking at the lesson agenda. We're going to start by identifying unknown values in problems. We'll then go into much bar models to problems, there will be a practise activity, and after that you will have an independent task to have a go at. And don't worry, I know you'll want to know how you got on so I will make sure I go through the answers with you. There's three things you will need for this lesson, a pencil or a pen and some paper to write on. If you haven't got those things in handy, just pause the video here whilst you go and get them. Remember to work in a quiet space where you aren't going to be disturbed during the lesson. So we're going to begin by naming the four operations. Do you know what we mean when we say the four operations? All it means is addition, subtraction, multiplication and division. Nothing new there, but if you didn't know that, that's what we meant when we said the four operations, now you do. So say them again with me. Addition, subtraction, multiplication and division. When we solve math problems, these are the things we need to know. We need to be able to use and we need to choose which operation to use. So in a math problem, what is it that helps us understand what the maths that we've got to do? So what helps us understand what the maths in a problem might be? Just have a moment to think. I have some thoughts and this is what I came up with. Understanding the relationship between the known and unknown values helps us to work out what kind of math is involved. When we look at a word problem or a number story, we have to figure out what the known facts are, and then what is the question is asking us to solve, what the problem actually is, which bits of information is unknown. The bar model is helpful in representing these relationships in problems. So as I always say, you tell a number story and you make your bar model as you go along, and it starts to build the story with you. And the bar model can help us to see the relationship between the parts and the wholes or differences. So then, when we've got that information, we'll be able to figure out which operation is that we need to use, whether it's addition, subtraction, multiplication or division. So let's put our ideas to the test. Here is a word problem or a number story as I like to call them. Will you read it with me? Let's go. The pit crews at Silverstone counted all the tyres used by their drivers during the British Grand Prix. In total, they use 264 tyres. 176 was soft tyres, and the others were all wet-weather tyres. So how many wet-weather tyres were used? I'd like you to have a go, just a first go at drawing out a bar model. Think about what information we know and think what information we don't know. And then that will help you construct your bar model. I'll wait here for a couple of moments whilst you have a go. Okay, so you've had time now to have a go at your bar model and I'll show you mine, okay? So I've just moved the word problem up into the corner of the screen to make room for my bar model. So this is how I got my bar model to look like this. I looked at the information in bold, which I had already highlighted I've made it bolder to make it more obvious what the known values are. It says in total, they use 264 tyres. So I know a total is 264 tyres. So I've been able to draw a long bar here with this information on top 264, and that 264 represents the number of tyres in total. 176 was soft tyres, so I know a part of that whole I've been given, a part of it was soft tyres, and that part was 176. So I put a line down my bar, I divided it into two parts. And this part I know is represented by this 176 and that's the amount of soft tyres they were. Now I've been told that the rest, all of the others were wet-weather tyres, there were no more parts, if they told me that summer wet-weather tyres and some other sorts of tyre, I would have had to make more parts, but on this occasion, I only have two parts. But I don't know how many wet-weather tyres there are, that is my unknown value. So as you can see here, I've represented that with a question mark. So now if I look carefully at my bar model, I can think right, how am I going to work out what this missing part is? I have a whole and I have one part, but I don't know the rest. So I'm going to need to subtract 176 from 264, and that will help me find the difference between the two. That will help me work out the size of this other part. So the calculation I had to do was 264 subtract 176, and when I calculated it, the difference was 88. So I know that 88 wet-weather tyres were used. So here is the same word problem, but now you can see three bar models up on the screen. And know we have already worked out what the bar model should look like, I've already shown you in the last slide. But here you'll be able to or won't see any numbers. We've just got boxes and question marks. So the question marks represent which value, the known or the unknown? Of course it's the unknown. But the box, the orange box represents the values that we know, that's the information we can take from the word problem. But on these examples, the numbers have just been replaced by an orange box. Can you tell me which of these three bar models was the one that we ended up drawing to solve this problem? That's the one, it was the third example and that's because we could see we had a whole all together, we wrote in there which number, we put the total in there which was 264. We had the value of one of the parts which were the soft tyres, so we represented the 176 there, and we didn't know this value. So the other part was unknown. Well, let's just think about why this one and this one does not represent our story. Well, when we look at this one, we have a whole here so we've drawn a bar, and we could put 264 tyres in there, because we know the total. However, how many parts does this bar model have? That has four parts, but how many types of tyres were there? They were just two, wet-weather tyres and soft tyres, so we don't need four parts. So this bar model does not represent the problem that we need is not showing us the kind of maths we need to work out the answer to this problem. So let's look at this second example. So, this one is suggesting with a bar here, we don't know the whole. Well, that's wrong because we do know the whole. And let's unpick this a little bit more as well. This is a sort of module that we would use if we were comparing two sets of something. Because you can see there is a gap. So the shorter bar, compared to the longer bar shows us that there is a difference, there is a gap. The two sets are not equal. That has nothing to do with the story about tyres, two types of tyres, 264 in total, it has nothing to do with it at all. So we were right when we drew this bar model down here. Over to you now. So, here are some word problems or number stories. And I'm going to read each one to you, I'm then going to show you three bar models and you need to try and match the problem to the correct bar model. Let's start with the first one. There were 450 Union Jack flags waving in the crowd at the Grand Prix, but there were only 157 German flags. How many more Union Jack flags were being waved than German flags. The second question, a pit crew has 48 tyres. How many times could they use them to change all four wheels on their team's cars? And the final question, tickets to watch the Grand Prix qualifying session on Friday cost 55 pounds each. Michael's dad buys three tickets, how much did he pay in total? So here are the bar models, so pause the video here whilst you have a go at matching up the correct bar model to the number problem. take as long as you need and when you're ready, come back to me and we'll go through the answers together. Okay, so you've had a go at matching up the bar models with the problem, so let's take the first one. There were 456 Union Jack flags, so we're looking for something that where we have a known value of the total. So the orange boxes represent the known values, don't they? So that would be this one, or it would be this one. So we've got a choice of two. There were only a 157 German flags, how many more Union Jack's flags were being waived than the German flags. So this tells me we've got a bit of a difference problem. We're not sure which one it is. So it's this one over here because like I said, we need to work out this gap. The two parts would make the whole, well actually on here, we've not got a part halfway. This is obviously the Union Jack amount of flags, and this represents here the German flags only 157. So what operation would we need do to find the difference? That's right, it is a subtraction. So 456 subtract 157 is equal to 299. So you would answer there are 299 more Union Jacks than German flags. Okay, let's look at the second question. A pit crew has 48 tyres, how many times could they use them to change all four wheels on their team's cars? So it's either this one or this one. Do we know the whole amount? Well, yes we do, we know that the team has got 48 tyres to use, and we need to see how many times four goes into 48. So is it going to be this middle bar model here. And the calculation we would need would be 48 divided by four equals 12. So they could do it 12 times, they could change the tyres on the car 12 times before they run out of tyres. So that means that this last question matches up to the first bar model, and that's because we know the size of one equal part is 55 pounds. Michael's dad buys three tickets, and each ticket is going to cost the same amount, so this is going to help us see the maths in this problem. So we know now that 55 multiplied by three is equal to 165. I very nearly didn't give a full answer then for the last question so how much did Michael's dad pay in total, Michael's dad paid 165 pounds for three tickets. For your independent task, I'd like you to read some word problems and draw a bar model to go with it. That's going to help you work out what kind of math you need to do to solve the problem. I'm going to show you an example and take you step by step how to do it because it can be a little bit confusing. So here's my word problem or my number story. Polly is playing RoboBlasters, she has a total of 272 points and she's trying to catch up with a friend Harold, who is 320 points ahead of her. How many points does Harold have? So step number one, we need to identify the known and the unknown values in the problem. So we're going to be a bit like a detective now, we're going to scan through to find out some information. So relevant to us now is that she has a total of 272 points. That's Polly's amount. So one part of this Polly's amount is 272 points. We know she's trying to catch up with Harold, and he is 320 points ahead of her. So I'm starting to think well, he must have what she has which is 272, and he's got some more, he's got 320 points more. So starting to work out how our known values can help. But the unknown value is how many points Harold has, we haven't been told that. So now we've talked about the relationships between them, we can draw a bar model, so this is the bar model that I have drawn. So I know that this bar here at the bottom, I actually did first, this is how much Polly has. So this bar, shown here with 272 represents Polly's points. Harold has a different amount of points okay? So this top bar represents Harold's points. He's got the same number of points as Polly, plus 320 points more. We know that because he's 320 points ahead of her, so now I can think about the calculation I need, which is 272 plus 320. And the last step as you can see over here is to solve the problem using an efficient calculation strategy. Now I know to get to this point, you will be a wiz at calculating especially with addition, so you choose something that is most comfortable for you. I found out that the total of 272 and 320 is equal to 592 points. You have all the information you need now to have a go at your independent task, so let's take a look. So on the screen you can see remainder of the steps you need to take in order to draw the bar model correctly to match the problem. Firstly, identify the known and unknown values in the problem, then identify the part-whole relationships and draw or make an appropriate bar model to identify the calculation needed. Solve the problem using an efficient calculations strategy. So here's the first problem you're going to take, there's three problems coming up and you will take each problem in turn and draw a bar model. In one section of the Luffield Grandstand there are five rows with 47 seats in each row. How many Formula One fans can sit in this section? Problem number two. The catering team served 398 meals to the pit crews at lunchtime, and a further 536 in the evening. How many meals did they serve in total? I word that is a lot of meals to be serving in one day. And the last problem, when slowing down at the village turn, a car's brake temperature measures 985 degrees celsius. This decreases by 395 degrees celsius when the car passes through Woodcote. What temperature is measured in the brakes at Woodcote? Pause the video here to complete your task. Once you're ready, come back to me and I'll go through the answers step by step with you. Take as long as you need. How did you get on? Let's go through the first problem together. In one section of the Luffield Grandstand, there are five rows with 47 seats in each row, how many Formula One fans can sit in this section? To my mind I can picture that, lots of people sat in five rows 47 seats on each row. Okay, first job, identify the known and unknown values in the problem. So I've underlined five rows, that's a known fact and 47 seats in each row, also a known fact. I'm now going to think about the relationship between those, oh, I also need to find out the unknown value. Unknown is how how many fans can sit in this section. So starting to think how I'm going to work out, I can see five rows, 47 people on each. So I draw my bar model now that I figured out the relationship. So I know that in one row 47 people can sit there. That has to be multiplied by five, doesn't it? Why? Because there are five rows. So now I need to work out what the product is, because it's clear now that I will need to multiply. So five, five groups are 47, five multiplied by 47 is equal to 235. Let's take the second problem. The catering team served 398 meals to the pit crews at lunchtime, and a further 536 in the evening. How many meals did they serve in total? So starting to think about that in my mind, some we serve at lunchtime and some more was served in the evening. It's really important to think about what's happening in the story. let's identify the known values and the unknown values. We know that 398 meals have been served. We know that a further or another 536 meals were served. So I've got two parts, haven't I? The meal served at lunchtime and the meal served in the evening. My unknown value is how many meals the team served in total. So and you think about the relationship, I understand that I've got one part of 398 and another part of 536. When I draw out my bar model, I can see the two parts side by side, and I know the value of each. One to be 398, the other would be 536. The unknown value is up here, what is the total? Well, when I'm finding the total I must add, so 398 plus 536, you use a strategy that you are comfortable with, but when I calculated it, I came up with 934. So 934 meals were served in total. And finally, when slowing down at the village turn a car's brake temperature measures 985 degrees celsius. This decreases by 395 degrees celsius when the car passes through Woodcote, what temperature is measured in the brakes at Woodcote? So these are different turns on the track. So what are the known values? Well, we know that the temperature at the village turn is 985 degrees celsius, it then decreases. Now I understand the word decrease means to go down. So, that's really really important, understanding the vocabulary in the story as well. So I know when I draw my bar model, oh, there's the underlined unknown value. What is the temperature that's measured in the brakes at Woodcote? So when I draw the bar model, I have got some missing information, because I'm going to compare the two temperatures. This longer bar here is the temperature of the brakes and the village turn, so that will be 985 degrees celsius, we could put that value in that box there. When it gets to Woodcote the value of the sorry, the temperature of the brake is different. What is it now, what is it decreased by? Well it's decreased by 395 degrees. We don't actually know what that leaves us with, but we do know the difference is 395 degrees. So I have a whole and I have the amount of difference, but I don't know what the other part is. So I know I'm going to have to subtract. So my calculation is 985 subtract 395 is equal to 590. If you'd like to please ask your parents or carer to share your work on Instagram, Facebook or Twitter, tagging @OakNational @LauraBehan21 and hashtag learn with Oak. It's been great working through some pretty tricky stuff with you for this lesson so well done, give yourself a big pat on the back and keep up the hard work. I'll see you again soon, bye bye.

Identifying known and unknown relationships

Identifying known and unknown relationships

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UnitMaths / Deriving multiplication and division facts

Maths