Worded problems about converting between metric units of length

In a long jump I achieve 1.4 m and my friend achieves 10 cm less than me. How far did my friend jump?

It takes 8 km to get to my nan's house and half the distance is where my cousin lives, how far away does my cousin live?

Which of the measurements below is likely to be the length of my bedroom?

Which of the measurements below seem to be correct for a kitchen in my sister's doll house?

Ribbon A is 3.4 m long and ribbon B is 200 mm shorter than ribbon A. How long is ribbon B?

Solving problems involving converting between metric units of length

﻿Hi there, my name is Miss Darwish. And for today's math lesson, we are going to be looking at the context of perimeter in converting lengths. So before we get started, if I could just ask you to take yourself to a nice, quiet, peaceful environment, somewhere where you can be ready to learn. Okay, so the agenda for today's lesson is, first of all, we're just going to be recapping on what perimeters of shapes, how to find the perimeter of a shape. And then we're going to be looking at finding the perimeter, and then we're going to be adding some constraints, a bit of problem solving. And then at the end, there will be a quiz for you to complete as always. So for this lesson, if you could just grab yourself a pencil, something to write on and a ruler, and we can get started. Okay, let's talk about perimeter. Hopefully, you remember what perimeter means. If you don't, don't worry, we'll just recap. So we are finding the perimeter of a shape. For example, of a bedroom, of our living room, a kitchen, we're finding an area, we're finding the perimeter, sorry, of a shape. So we are finding all the way around. We want to know the measurements all the way around that shape, okay? And that is what we call finding the perimeter. So all the way around the shape, no cutting corners. So we can find the perimeter of a shape. So have a look at this question. Can you find the perimeter of this shape for me? Can you find the perimeter? If you need to do some jottings, go for it. Okay, have you found the perimeter? Should we have a look? So 2.5 metres, add 1.3 metres, add 0.9 metre, add 1.9 metre, add 1.6 metre, add 3.2 metres add the end which equals 11.4 metres. Is that what you got? So the perimeter of this shape is 11.4 metres. Okay, well done, if you got that right. Now let's have a look at question two. What's the same and what's different between question one, the one I just showed you, and this question? In the first question, can you see that? I gave you the dimensions. We have the length and the width in metres. This time we've got some in centimetres and some in metres. So we might have to do a bit of converting, some conversions. So finding the perimeter. Again, I'm just going to give you a few seconds. Just any jottings if you want to do some conversions, have a go and then we'll look through it together. Sometimes I find it easier to grab a highlighter, if you have a highlighter, or just underline, and all the ones in metres, do it in one colour, or you can do it with a coloured pencil, and all the ones in centimetres do it with another colour, but that's just me. Okay, let's have a look together. So step one is definitely to convert. Your first step in finding the perimeter is to convert. We want it to look like question one. Either all of it in metres or all of it in centimetres, in order to find the perimeter, okay? So we want it to look like question one, that was nice and easy, right? Because it was all in metres. We just added it up together. This time, some are in centimetres and some are in metres. So we want to decide to be stick to metres? Do we stick to centimetres? Either is fine, of course. So step one would be to convert. So 225 centimetres is equivalent to 2.25 metres. 0.95 metre stays the same. 1.9 metres stays the same. 0.75 metre stays the same. 35 centimetres is equivalent to 0.35 metres. And then 170 centimetres is equivalent to 1.7 metres. Now it looks nice and easy. So now it's easier. Of course, step two just to add it all up to find the perimeter. Make sure you do your lining up correct. 1.7 add 2.25, add 0.95, add 1.9, add 0.75, add 0.35. So to find the perimeter, we're just adding all the way around the shape. Of course, making sure it's either all in centimetres or all in metres, or if it was something else, all in millimetres. Okay, and did you get 7.9 metres as your answer? Okay, 7.9 metres or 7.90 metres. Okay, now let's have a look at another word problem, bit of problem solving now. So the Olympic Planning Committee need your help. Now the pole vaulting athletes need a room. So they need a room to be in. It must have a total perimeter of 14 metres. So the total perimeter must be 14 metres. And in order to safely fit the athletes' pole volt, because they've taken it in the room with them, one length, just one length, has to be at least four metres. So one of the lengths of the room has to be at least four metres. And of course this room is large, it's not a doll's house. We're talking in metres, okay? So I'll read that again. The Olympic Planning Committee need your help. They need you to have a think and design a room and it must have a total perimeter of 14 metres. And in order to safely fit the athletes' pole volt, one length of the room must be at least four metres. So four metres, five metres, 5.5 metres is okay. I'm going to give you some thinking time just to read that and jot down and make any notes. Okay, let's have a look at this together. So there are lots of possible answers. So we're saying it must have a total perimeter of 14 metres. It can't be 15, it can't be 14.1. And in order to safely fit the athletes' pole vault that one length must be at least four metres. Okay, so there could be many possible answers. So this is one possible answer. So first of all, because one of the measurements has to be four metres, at least four metres, I'm going to do that bit first. So there's my four metres, okay? So it's like I've ticked the last part. In order to safely fit the athletes' pole vault, one length must be at least four metres. So I've done that bit first. Now what's left for me to do? Make sure that the perimeter is equal to, do you remember? Okay, back 14 metres, okay? So if I say that that's 2.8 metres, then this bit has to be 1.2 metres. Can you see why? The length at the top is four metres. So the length of the bottom is also four metres. So 1.2, add 2.8, has to be equal to four metres. Okay. And then I'm going to add 1.5 and 1.5, which is equal to three metres and that shows it on the side. And I'm going to add it up just to check. So I've got three metres, add four metres, add 1.5 metres, add 2.8, add 1.5, add 1.2 is equal to 14 metres, phew. Let's go back to the constraints that we had. It must have a total perimeter of 40 metres. Can I tick that bit off? Absolutely, it had a total perimeter of exactly 14 metres, thank God. And then in order to safely fit, one length has to be at least four metres. Did we have that? Absolutely, so I've ticked both constraints. Now let's have a look at a different shaped room. So they haven't actually specified, they haven't told us what the room needs to look like. So this is one example. And now let's have a look at another example. What's the perimeter here? 14 metres, well done. Four add four add three, add three metres is equal to 14 metres. And one length has to be at least four metres. Is it? It is. Okay, so that could be another possible answer. So we've got two different designs for a room and either one of these athletes would be happy with, because it satisfies the criteria. Okay, well done. Now it's time for you to pause the video and have a go at your own problems. And then, so I've got an independent task for you with a similar word problem to the one we've just had a go at. So good luck. Give it your best. And then once you've finished, come back and we'll go through the answer together. Okay, welcome back. How did you find those? Okay, shall we go through the answers together now? So this is the question that I left you with. Draw two different designs for an Olympic boxing ring that satisfy the criteria below. So you had to come up with two different designs for an Olympic boxing ring. Now let's see what the criteria is for the boxing ring. So, the first thing is it must have a total perimeter between 14 and 24 metres. So 16 metres allowed? Yes, 'cause it's between 14 metres and 24 metres. Is 13.9 metres allowed? No, because it's less than 14 metres. Okay, the perimeter has to be between 14 and 24 metres. And the second criteria is that the length and the width of the ring cannot have a difference of more than two metres. So if I have a width of seven metres and a length of 11 metres, that's got difference of four metres and it can't have a difference of more than two metres. So these are two things to bear in mind and to be careful about when doing the two different designs for the Olympic boxing ring. Okay, should we have a look at some possibilities? So this is what I've done. So I've got my three possibilities. Let's have a look at the purple one. The first possibility is that I've got six metres and five metres. So a length of six metres and a width of five metres. Does that work? Six add six, add five, add five is equal to 22 metres? That works that's between 14 and 24 metres. So I've got that right. And the length and the width cannot have a difference more than two metres. What's six take away five? It's one, it's not more than two, phew. The first one is safe. It's passed the Olympic Committee. Let's have a look at the second one. You might have something similar to me, the same as me, or you might have something different. But if I go through my options and show you how I check by reading through the criteria, then you can do the same with your options if you have something different. So the second one, I've got a length of seven metres and width of five metres. So seven add seven, add five, add five, I'm just going to check the perimeter is 24 metres. And it has to be between 14 and 24 metres. So that's allowed, okay? And it can't have a difference of more than two. Seven take away five is two exactly. They say it can't be more than two. It's not more than two. So again, we are safe. We're good to go. So the first two designs are fine, phew. Now let's check the last design. 5.5 metres and 4.5 metres. Let's check the perimeter first of all. 5.5 add 5.5, add 4.5, add 4.5 is equal to 20 metres. So that's the perimeter. And then the length and the width cannot have a difference of more than two metres. Do they? 5.5 take away 4.5? No, just one metre, phew. So again, it meets the criteria. So if I presented any of the three designs here, they would be happy with it. Okay, so again, I want you, maybe you can discuss with someone in your family or someone at home, what your plans come up with, if it's different from any of mine, and see if they agree that it would pass. Okay, well done. Now if you would like to share your work with us here at Oak National, then please do ask your parent or your carer to share your work for you on Twitter, tagging @OakNational and to use the hashtag #LearnwithOak. Now it's time for you to go and complete the quiz. So I'm just going to leave you there and say, "Well done, with all the brilliant, fantastic learning that you have done on today's lesson and good luck with the quiz."

Quiz about finding the perimeter of shapes

A rectangle has a width of 4 m and a length of 20 m. What is it's perimeter?

If a rectangle has a width of 4 metres and a length of 700 cm, what is the perimeter of the shape?

A living room has a perimeter of 26 m in total. Which of the below show its possible dimensions?

A games room has a perimeter of 36 m in total. Which of the options below cannot be the dimensions of the game room?

Which of the dimensions below does not have the same perimeter as the rest?

Converting Between Units of Length in the Context of Perimeter Quiz

In this lesson, we will model problem solving activities where we must work out the perimeter of shapes with different units and then create designs involving constraints.

Maths

Y5 Maths

Key Stage 2

Year 5

Miss

Converting between units of length in the context of perimeter

Converting units of measure

Number

THEME

UNIT

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Converting between units of metric mass

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Solving problems involving various units of measure

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Lesson overview:Converting between units of length in the context of perimeter

Core Content

Converting units of measure: