Represent decimal numbers in a variety of ways

Key Stage 2

Maths

Multiplication and division

﻿Hi everyone. And welcome to today's lesson. As you can see today's lesson is about representing decimal numbers in a variety of different ways. So we're going to explore how we can represent and look at decimal numbers. Let's have a look at what the lesson will look like today. So as we can see, we're going to review our understanding of place value first, 'cause that's really important. We're then going to understand the place value of decimal numbers then start representing those decimal numbers in lots of different ways as we said and then look at the value of each digit. Okay, well let's get started. So make sure that you've got a pencil and a paper can be really useful in today's lesson just to make some jottings or draw some diagrams. Okay, so let's have a bit of a warm-up just to get our brains working a little bit, have a look at the representation I've got here. Now I'm just going to make that slightly bigger for you. So looking at this representation what four-digit number is being represented with dienes here? And so maybe 10 seconds or so. Okay, so shout the answer now don't be scared. Shout the answer out. Okay, what did we get? So hopefully we got 3,251. Now, if I'm able to do this, what am I using to support me? It might be that you've got place value chart that to be able to help you to think about each different blocks. So we've got a red here so we can see that there's a thousands dienes and there're three of them so three thousands, we've got two of the hundred slabs so two hundreds, we've got five of the 10 sticks that's 50 and then we've got one dienes on its own that's worth a value of ones so 3,251. Okay, let's continue. In our new learning today we want to look at the relationships between different numbers 'cause that's going to really support us during this lesson. So I want you to think about different statements you can make to think about the relationship between these different numbers so a thousand, a hundred, ten and one. Think about how many times smaller one is than the other or how many times greater one is the other. So for example, I can say that 10 is 10 times greater than one and one is 10 times smaller than 10 because it goes up this one will go into my 10 stick 10 times, okay? So think about the other ones maybe moving from one to a thousand or 10 to a hundred and think about what you can say about that, okay? It's going to be a few seconds, pause the video if you need to, to have a bit of a discussion. Okay, so hopefully you've had some time to discuss that and this should be some understanding we already have from previous years. So thinking about some examples you've got there lets just have a look. So we've got a thousand here and we can say that a hundred and we can put it in 10 times here so we'll have 10 hundreds would make up 1000, okay? So likewise we can use our knowledge of division if we've got thousands, I would divide it by a hundred, we would have 10 of them because we'd need 10 of these to go into one thousands block. So it's really important that we're able to be really flexible and be able to describe the relationship between these 'cause they're going to be really useful in today's lesson. We can also think of them in rather than normal value start thinking of them in a decimal value and now we've re-assigned the value of the dienes. Now this is really important to have a really good understanding of whereas before we had our dienes worth 1000 can now say that the value of that in thousand block is worth one, so this is now worth one whole. And if this is what worth one whole, our proportional relationship has not changed. So you can now say that a hundred block we have here is now worth a 0.1, okay? So there're still, it's still a tenth of our whole. So we still got that same relationship and we've now got our stick here which is now worth 0.01 'cause we could fit 100 of them into one whole or we could fit 10 of them into one 10th. Okay, so we can see the relationship is still the same and likewise a thousand is worth a thousandth of a whole because 1000 of them would make up our whole block or we would have 10 of them making up a hundred or a hundred of them making up our 10th, okay? Lots of really important bits of that company there so do feel like if you need to pause the video and have a bit of a practise saying those words and thinking about those relationships. But just remembering from our different dienes lots that we're going to be using today. Although we may have an understanding of the value normally that we use the relationship between those dienes blocks is going to stay the same, that isn't going to change at all. So that's the thing to focus on. We'd still go back to divide it by 10 between each four of them. So that's going to be really useful in today's lesson. So we can think of this if the cube is representing one then we've got all those different values of 0.1, 0.01, 0.001 so 1000th at the end, okay? So that's really useful to bear in mind as we go through this lesson and to use during the lesson. Okay a bit of a practise for you then. I want you to have a look at these and think what would I have to do in order to be able to show these relationships? So I've got 0.01. What would I have to multiply that by to get to 0.1 here? So how many times would my stick here go into my square here? So have a look that and have a bit of a think and then likewise, if I have the whole here, my whole cube, how many of my hundredth sticks here would make up that? How many could I divide my whole into? Great, so have a bit of a think. What would you have to do? Look at those relationships down in the grey box, so they going to help you here? Great, so pause the video if you need to and then we'll have a look. Okay, so let's have a look at some of these then so a 0.01, what would I need to multiply it by? What I can see that if this is one here, about two, three, four, five, six, seven, eight, nine we would have 10 of them. So zero point zero one multiplied by ten is equal to 0.1. And likewise this is going to be slightly more difficult here but you can see that we've got the one stick here and I'm dividing it. How many times I can divide it? we'll have 10 of them here and then I'd have 10 locks of that. I'd need to divide it by 100, 100 of my hundredth sticks will make up the one whole. Okay, so hopefully we're getting a little bit familiar with the way we've re-assigned our dienes values to be able to represent decimals. Let's have another go this time is over to you. So pause the video and see if you can work out what you would multiply the first one by and what we divide the second one by. Okay, so 0.001, my thousandth what would I multiply it to get to 0.1? Hopefully you can see that here we'd have to multiply by 10 to get to one of these to make my hundredth stick and then again by 10 to make this. So I have to multiply it by 100ths. and here, well actually this is similar to the one we did before. So you can say that one divided by a hundred would equal 0.01, okay, great. So hopefully you've got a great understanding of that. Now we can try and apply a little bit more. Okay, so over to you now we're going to pause the video and I want you to have a go at this one. Okay, so let's go through those answers. So 0.001 multiplied by what is equal to hundred oh, yes. Well done is multiplied by 1000 and then 0.1 divided by what is equal to 0.01 we can see quite nicely that is going to go into here 10 times. Okay, so well done if you've had to go that much better understanding now. Now we're going to have a think about how we can represent these numbers. So looking at the number I've got here, I've got one whole, I've got two tens, I've got three hundreds. So how could we represent this number? The different ways I can represent it apart from my my dienes I've been representing it with so far. Well, have a think, pause the video and see which different ways you can write down to be able to represent this number and then we going to come back together. Okay, so which ones did you come up with? I wonder if you've got any of mine, we could represent it as a number so in this case we've got one whole, we have got two tenths and we've got three hundredths, so 1.23. We could represent it using our place value counters here. So not quite the same as dienes actually they're slightly more efficient in some ways because we don't have all this cumbersome huge thousand blocks, we can just represent it nice and easily using these place as onces we've got, solid understanding. We could represent that using fractions so you've got the whole, we've got two tenths and three hundredths. We could represent it by drawing, sorry, writing out the words or we could represent it in a different way so we could think about it in terms of how many hundredths there're as a total. And then we're saying that almost. So one hundred and twenty three hundredths in that case. So lots of different representation we use that and then I've got written version of that written as a fraction. So lots of different ways that we can connect and see what's the same? What's different about these things? Okay, so over to you then. I'm going to let you say we've shown you some examples, how many different ways could you represent this? So let's have a bit of a think. Can you try and work this out? Okay, what do we come up with? Some of these part? Okay, so 0.35 we've got in the way we can write it, we've written it as a fraction, we've got our place value counters there, we've written it down, lots of different ways that we could go about representing this number. Now, looking at that then we want to now move on and think about well, which one of these two is correct? So I've got representation here using my dianes and I want you to look at this so somebody said, this is worth 2.13 and someone also said, this is worth 2.31. Now, which of these two is correct? So have a think, which one of these two do you think is correct? And if there's a mistake, what could the mistake be? Okay, so maybe we've had a bit of a think about this we can see that we've got 2.31 here, so we've got two wholes, we've got 0.3 so you can see that there are three tenths and then we've got one hundredths. So we've obviously got a little bit confused somewhere along the line with the tenths and the hundredths. So we can see this is 2.31. Okay, so some ideas of what we could do here. Now, which one of these do you think is correct? Have a look at the two values, it's the same principle as the last one, which of these two is correct? And perhaps can you work out what the mistake was? Okay, so which one did you come up with? Okay, we've got three ones here, we've got two tenths and we've got four hundredths. Now as you can see here there's already a bit of an error because we know that we shouldn't be representing the hundredths here and the tenths here. So obviously I think where somebody's got confused with this being normally representing a 10, they might have represented as a 10 and got slightly confused, okay? Hopefully you're able to explain that really clearly. So well done. Now, a task for you, what we want you to do is using these different ways of representing fractions and decimals. Can you now find the matching cards of these? So we're going to pause the video, which ones are matching and then maybe circle them in different colours and then when you're ready, un-pause the video and we'll have a look at the answers. Okay guys, thank you very much. Hopefully you've got that finished. So let's have a look at those all important answers to see how we did. Okay, so I've put them in different colours, have a look through these and try and work out where you right. Were there any that you didn't quite get right there? If you did maybe have a look again try and represent them in other ways to see if you can work out what errors have happened there. Okay guys, we're going to move on slightly and develop the learning a little bit more. So as I kind of mentioned before, we've been using dienes and we've been re-assigning the dienes however it isn't quite the most efficient way of doing it because actually if we've got place value count as I said before these can be a little bit more efficient in terms of representing it because I've got a one here rather than having a big dienes, thousand block which you may not all have in our homes. We can use these and it's really, really efficient. So I'm going to think about trying to represent it here. So now I've got three ones, I've got my one tenth, two hundredths, and my five thousandths. And I've also represented it as a fraction here. So a different way of representing it. Now, as we can see here, I've then thought just think about well, how could I start to represent this? So I've got, as you can see one tenth, three hundredths, and I've got four thousandths. But what would that be as a fraction out of 1000. Okay, so maybe you've got a bit of a clue here, re-write it down as 0.134 as a decimal, would that be as a fraction? Yes, that's right. We'd have a 134 over 1000 out of 1000. Okay, because it's not whole is there a whole would be one, so that's out of a thousand, that's a whole so we've got 134 out of 1000. Okay, so let's move us on slightly further. I want you to pause the video now and this time taking the number 1.432. Can you use place value counters? I know you don't have place value counters at home, perhaps you can just draw them in 'cause that's nice and efficient. And can you represent it? So you might want to represent it as that can you then represent it as a fraction as well as we've just practised doing? Okay, so pause the video and I'll have a go at that and then play whenever you're ready. Okay, so hopefully you're able to do that. Let's have a look at what we could have come up with. So we have 1.432, we should have represented that with one whole, should have had four tenths, three hundredths and two thousandths. Okay, well done if you've got that. We could then if we think about it as a decimal number, we've got one whole, 0.4, 0.03 and 0.002. Wooh, headache. And that is 1.432 all together. And then thinking about it as a fraction, we've got one whole or you might've written one out of one and then four tenths, three hundredths and two thousandths. It's okay, so brilliant if you've done that. Lots of different ways that we're at presenting it, we're getting a deeper understanding of our decimal numbers now. Okay, so our independent we're going to be doing much the same as we've been doing before, we've been representing fractions in lots of different ways. So looking at the thing we've got here, we've got the number is said as 1.203. What I want you to do is fill in the missing parts here. So if there's anything missing or anything that hasn't been completed, I want you to complete it. So let's have a look at how we might complete an example. Well, it's 1.203, I've written it that as my decimal number, and that would be one plus 0.2 plus 0.003 my thousandths, and then looking through, we've got one plus two tenths plus three thousandths, and we've got it written as my fraction as well. So, what I want you to do now is you can either do it by pausing the video on this all you've got it as your task in your worksheets. Go to this, have a go at completing the next two examples. So you've got one here and remember we've got some missing values here as well, a bit more challenging for you to try and piece it together. And we've got another example here with our place value counters to help you out a bit, have a look at these different examples and see if you can complete them. Okay, so want you to pause the video now, go and complete your task and then we'll come back and have a look at the answers. Okay, great job guys. So let's have a look at some of those answers then. And the first one, the number is set as, so there's missing values is 2.132, and we can see that written here as a decimal and we've got our parts as we then look and partition that as well and we've got it in here in dianes or you could might've drawn it as dianes possibly and we've also written it as a fraction here as well. So well done if you did that, that wasn't an easy one and our second one now a little more challenging numbers and is 31.02 and we've got it written as 31.02 is equal to 30 plus one plus 0.02, we've got our representations here and we've also written it out as a fraction here. So well done if you did that. So great job so far guys hopefully you've been keeping up, well done today. Really, really good lesson, lots of exploring and lots of going through those different fractions. Now hold on today guys. Make sure before you finish you go into that final quiz and complete that. Okay, so make sure you complete the quiz. Thank you very much for your time stay guys. Have a good day. Bye bye.

Represent decimal numbers in a variety of ways

Represent decimal numbers in a variety of ways

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UnitMaths / Multiplication and division

Maths