Assessing understanding of the place value of decimals

What is the relationship between 0.004 and 0.4?

1.35 = 1 + ____ + 0.05

2.532 is equivalent to what?

0.45 can also be represented in which way?

Representing decimals in a variety of ways

﻿Hi, everyone. Welcome back. I hope you're ready to learn. Today's lesson is all about place value to three decimal places. Okay, so just making sure before we start the lesson that you've got everything you going to need. So the lesson agendas today is all about making sure we have a recap of our understanding of place value. We going to then look at representing numbers between zero and one up to three decimal places. When we compare some representations and then we're going to try and use what we've done to then think about a real life context, a real life problem, and help it to help us to solve it. Okay, well, let's get ourselves started then, make sure you've got pencil and paper so you can put some jottings down and you can draw some representations as we go really important in today's lesson. Before we start the main lesson, we've got a bit of a warm up for you thinking about place value. What I'd like you to do is to think about how you would order the numbers that we got here from the smallest to the greatest number now just because we're going from the smallest to the greatest, it doesn't mean you have to go in that order, but that's what I want for when we finish. Okay. Think about your strategy, think about how you're doing it, is it efficient trying to explain how you know that you're right. Okay. Pause the video now and then play when you're finished. Right guys, let's have a look through your answers and we're trying to unpack how we did. So we've got my numbers written out here, don't worry. These aren't in the order. So let's think, first off I want to put my answers in here, but to start with, I'm going to think, right? Let's put them in order. What can I do first? How am I going to order them? Well, I know that I need to know to go to my greatest place value and that's my millions column that I've got here and I can see straight away, I've got three, which have got 4,000,002 numbers, which have got 5 million. So I'm going to actually, although we're going from smallest to greatest number, I'm going to do my 500000 first. I think that's going to be easier. So i can see that one of my 5 million has got 800,000, whereas the other one has only got 400,000. So I know without even looking at the rest of these, the number that this is going to be a greater number, it's going to be my greatest number. So I can put these into my order. I know that I've got two of my numbers then in order. Now looking at the four million numbers, well, this isn't going to help me. So I need to go to my hundred thousands column to support me slightly. I can see that two of the numbers I've got 800,000. Whereas the other number here has got 500,000. So that is definitely going to be my smallest number. So that's going to help me find my smallest number. Now to work out the difference, you know, to two numbers which are four million, 800,000 and something I need to go to my next column. So I can see that I've got my two numbers here. One has got a 50 and one has got 70,000. That's going to then help me where to be able to distinguish between those two numbers order those numbers. So I know that if I've got 50,000 in this column, that's going to be a smaller number than this one. So I can then put these two in order. I've completed doing it. I wonder if you use the same strategy as me, did you go in the same order as me, or did you use a slightly different strategy? It's fine to use a different strategy, maybe yours is more efficient than mine. But what's really great is comparing different strategies with somebody else, with myself and thinking about what's the same what's different. Gives us a deeper understanding of what we're doing to help us. Okay, let's have a better of a review on place value really, really important that we're solid and got a good understanding of this. Hopefully you are familiar with manipulatives use of dieans in order to be able to help us. Now flashing up, here is our traditional use of how we would use dienes normally we've got our one, our 10, a hundred thousands blocks. Now the, the really important thing are these is the relationship between the two different parts. So we can see that from our thousandths to our hundredth, we needed to buy by 10 because 10 of our hundreds are going to go into our 1000. Likewise, 10 of our tenths are going to go into the hundreds. So that was a relationship of divided by or multiplied by 10 depending on which way we're going. And likewise, we've got 10 ones are equal to one 10. Okay. So that's really important that we've got an understanding about relationship. Because that is going to help us if we want to use this to support us with decimal numbers. Because now we want to think actually, if this cube has got a value and represents one, then what would all the other different blocks represent? How would that affect us? So have a bit of a think if you need to pause the video and think about what would the blue, the green and the yellow be worth, if my red is now worth one is my whole. And think about that proportional relationship. Think about the different relationships that we've got. Okay, so if one is my whole, then how many of my blue squares, Hey, would go into this? Yeah, that's right. So there'll be 10 of them. So that's kind of my relationship. So thinking about that, it would be a tenth. So my blue now is worth a tenth because there are 10 of them which are going to make my whole. Likewise, then go into my green block and I know that there, because I've got this relationship here there's going to be 10 of them that make up my 10th. So, actually there's going to be a relationship, but this is a hundredth now not a hundred, a hundredth. And that's because if I go straight from here, there will be hundred of these green sticks would make up my whole. So that's why we call it a hundredth. And they going all the way through to my little yellow square we've got here, my little yellow cube, but that is going to be now a thousandth because, one of them would make up so a thousand of them would make up one whole. So this is why this is a thousand. And we can see that if we look at the relationship between the different parts, that there would be 10 of these making up my hundredth and there'll be a hundred of them which would make up my tenth. Okay. It's really important that we get familiar with being able to reassign dienes like this. Okay. Now we've looked at dean quite closely, but isn't the only way that we can represent decimal numbers. There may be loads of other ways that you would use. So think about possibly other ways that you've represented them. It might be, that you've used place value counters. Now what's the same what's different about these? Well, both of them give us a good understanding of what we've got here in terms of our decimal numbers. However, you might have noticed, well, as a manipulative this is quite hard work this it's quite big, if you've seen a thousands days, they're quite hard work if you've got lots of them. Whereas this is quite efficient. However, you can see that my hundredth here and my thousandth here are my tenth are all the same size. So it doesn't give us that understanding of the scope of how big something is. Which you do get from dienes. So that's worth remembering. We could use something else, what else could we use possibly? Yeah, we could use the bead string Now, if I get one bead string, we know that they split into a hundred parts. So if that is the case, then if that's my whole, then going through, then if I had a pet the bat, it must be one, one of these stacks of tenths that would be tenth, which would mean that a hundred would be this, Oh, that's a bit confusing. Because if I want to represent a thousand using a bead string, then I'm going to have to cut this into 10 parts that isn't particularly useful to me. So what could I do instead? Well, if I did really want to use the bead string, I suppose if I'm representing thousandths, I'm going to have to use and be strangled together to represent one whole. So 10 beats strings representing one whole. And then that would make one bead string worth 0.1 and then would make a one tenth of the bead string 0.0, that's hard work. I don't know whether I want to use bead strings too much here. But it is interesting to think about how we could represent it using bead strings and always thinking about that relationship that isn't going to change no matter what manipulative we are using. Think about, Well, if you are using one compared to another or if you're simply using symbols, if you're using numbers, then think about what's the same what's different throughout this. Okay, now thinking about this, this is something that you consider now. We'd like you to do is we've got a place value chart to help and support you slightly here Hopefully you've got a pencil and paper. How would you start to represent 2.356? So maybe have a go If you don't have the net positives with you, then have a go at drawing part using the manipulatives. How would you go about representing that yourself? So pause the video now and then come back when you're ready. Okay, so how did you come up with it? How did you do it? Well, hopefully we got 2.356. We got it nicely represented there with our numbers. And hopefully you use some sort of manipulative or perhaps you drew out what it could look like. Okay. Moving on slightly then, we've got two different numbers. I want you to consider, if we were going to use one of our symbols here. So we're going to use less than greater than or equal to which would be, be using If we've got 0.34 and 0.304. which one do you think is greater and why? So what you just to think, how would you go about explaining that? And could you draw something, or if you've got manipulatives and make something to help prove it to somebody else. Great. Have a think about that pause the video if you need to, and then we'll come back in a second. Okay, so what did you come up with in order to help you to explain it? Right. Let's have a look then. So, we should know that 0.34 is greater than 0.304, but the really important thing here is why? How do you know that? And that's what we want to explore more. So let's use our manipulatives or our pictorial representations to help us to prove it. Well, first off, I know that both of them have got three tenth. So I can use my dienes to show that they've both got three tenth. However, then got four hundredth in this number. I've got four hundredth in this number I've represented really nicely. Let's have a look at my number over here. Well, I don't have any hundredth, but I do have four thousandth. Now, doing this hopefully helps to illustrate and show why 0.34 is a greater number than 0.304 coz a lot of people might have a misconception and see this as 304, but see this as 34 and think we're 304 is greater than 34. So therefore this must be the bigger number. Now, hopefully that has helped to explain it slightly better for us. What about this then? Now, if we've got one dienes thousand block representing one whole, what does this represent? So have a think, see if you can work out, can you draw it? Can you use your place value counters? In order to be able to explain and show this as a three digit decimal? Okay, pause the video and then when you're done, come back from play. Okay. Let's have a look at what we came up with. Hopefully, now you may have used place value counters. That's fine If you did. We came up with one whole. We came up with three tenths, four hundredths and two thousandths So thinking about that as a number 1.342. Okay. We may have representative plate differently, as I said before place value counters with brown ones, with then our tenths are hundredths and thousandths. Well done If you represent it in different ways. And hopefully again, that better understanding about representing these decimal numbers. Now I've got a statement here that I want you to explore. Elvia says that these representations that we've got here, all show the same number. Do you agree? Now why not looking for here is a yes or no answer. That's too easy. What I want you to do is try and explain what mistake do you think she's made if she's made a mistake and what they do represent. So explain what they do represent in each case and unpack them slightly to pause the video now and think about those different representations that we've got there. Okay, hopefully we've noticed and we've been able to identify that they are not showing the same number. Great, well done if you did. So let's have a bit of a unpack of this then. So we can see here that we've got 2.1353. Okay, so let's have a think about that again. We've got 2.1 coz we've got one tenth, we've got five hundredth and we've got 3000. Okay, so I've used this to help me. You may put this over here, don't worry if you did. Okay, so we can see that this is not the same number as this we've got 2.153 we've got over here 3.512 or they're not the same as each other. And then looking down here. Well, Oh actually yes, I've got 3.512. So hopefully we've seen some connection there. We've got 3.512 So I can see that I've got two different numbers represented in different ways. We've got our ones here and we've got our ones here. Okay, well done if you saw that connection you're able to really explain that. So I would go another one then. So same thing and have a look at these numbers. Elvia is saying these representation share the same number. Do you agree? And try and explore, maybe use and draw some different representations to support your understanding. So pause the video and then come back when you're ready. Okay let's have a look then, as you probably predicted again no they possibly don't show the same representation or do they? I don't know. So we can see that we've got five tenths and two thousandths. Do we have two thousandths? Here we don't, do we? We've got five tenths and we've got two hundredths, not two thousandths there. So these aren't showing the same representation as each other, but here we've got five tenths and we have two thousandths So we can see that obviously that all of the Z whoever's been connecting, has messed up slightly because it can be slightly confusing when we're looking at hundreds of thousands. And it's the same amount of numbers, twos and fives can be slightly confusing. So well done if you spotted that error and then at the bottom here we've got 0.520 So that would be the same as our representation here. Coz we've still got five tenths and two hundredth, but we've just got no thousandths. And we've written that as no thousands. So well done, if you are able to unpick that and explore it. Okay onto your independent task now, while she was in the Amazon, Dr. Drury of MM travel has been tracking some of the local wildlife. And when she's been finding them to make sure that they're all well and healthy, she they've been weighing them. They're really exactly to be able to show how much they weigh in kilogrammes. And you can see that different weights here. Now, one thing to bear in mind is you should notice that some of them are up to three decimal places, whereas others like the river otter is only two decimal places. And that in a second could be confusing. So do make sure that you bear that in mind when you're doing your task. What we want you to do is more than one time, not just once pick two of the animals. And then I want you to use place value counters, or if you don't have place value counters or dienes at home, that's fine. You can use pictorial representations of place value, counters, or dienes to be able to try and represent the different weights. Okay, I want you to show me which of the animals has the greater mass and when you've done that, then pick two other animals and compare that. So you should get lots of different animals compared against each other to be able to show which one has a greater mass than another one. Okay, and really concentrating on using your representations and your deep understanding that we've looked at during the lesson in order to support you. Okay. so hopefully you'll get lots of different representations on your paper to be able to prove your understanding of three decimal places and two decimal places. Hey, well done If you did that guys. If you want to go away and explore it more than by all means, come back this page, pause the play so you can see all the different things and work on it If you've got it done. Well done today, guys, now make sure before you finish that you go away and complete that end of lesson quiz. It was great to have you join us today. Hope you enjoyed the lesson and we'll see you again soon. Bye bye.

What is the relationship between one hundredth and one thousandth?

If one bead on a bead string represents one thousandth, how many beads would you need to represent one?

When you are comparing the decimal numbers 1.234 and 1.256, which place value column is the most important to decide which is the largest?

If I am representing the decimal number 3.609 using place value counters, which place value column will be empty?

Place Value to 3 Decimal Places Quiz

In this lesson, we will explore a variety of ways of representing numbers up to three decimal places.

Maths

Y6 Maths

Key Stage 2

Year 6

Place Value to 3 Decimal Places

Multiplication and division

Number

THEME

UNIT

Represent decimal numbers in a variety of ways

Multiply and divide by 10, 100 and 1000 involving decimals

Multiply and divide by 10, 100 and 1000 with in context

Understand the terms 'common factor' and 'common multiple' as properties of a number

Identify properties of numbers

Multiply a decimal number by a whole number

Solve multiplication problems using known and derived facts

Use efficient strategies to multiply numbers, including decimals

Practise multiplication and division skills

Use formal written methods for short multiplication including multiplying decimals

Multiply by a two-digit number using long multiplication

Use formal written methods, including long multiplication, to solve a range of problems

Explore efficient mental strategies for division

Use the formal written method for short division

Use the formal written method of long division to solve appropriate calculations

Solve problems involving division with remainders (Part 1)

Solve problems involving division with remainders (Part 2)

Represent remainders in different ways depending on the context of the problem (Part 1)

Represent remainders in different ways depending on the context of the problem (Part 2)

Lesson overview:Place Value to 3 Decimal Places

Core Content

Multiplication and division: