Representing Number

Key Stage 3

Maths

Numbers and numerals

﻿Hello everyone, it's Mr. Millar here. In this lesson, we're going to be representing number. So first of all, I hope that you're all doing well. And if you haven't watched any of my videos on Oak before, as I said, I'm Mr. Millar. I teach maths at a school in central London, and I'm really excited to be doing this particularly because these four lessons, I think you're going to enjoy a lot. We're going to be looking at different number systems, starting off with our number system, but then looking at some different ways that people count numbers and group numbers together. So it should be really interesting. Anyway, let's start off with the, try this task. You'll need some paper and a pen with you. And for the try this task, you're having a look at four representations. And the question is which of these representations would be the most helpful to explain this number to an alien and why? So all of these four representations represent the same number. And I want you to write one sentence describing how this representation represents that number. So pause the video now. One sentence on each of these four representations And then we'll go through it. Okay, great. So I hope that you all saw that this number was 32 and let's go through each of these representations. So the first one, the one that has 32 individual dots, well, we can think of this as just 32 dots or 32 ones. Nice and straightforward. And it's pretty obvious what the number is, but you probably took some time as I did counting up all those dots. So maybe not the most efficient way of representing them. What about the second one? Well, you might see something like this on a tally chart. If you come across those before, where you group numbers in groups of five, and we can see that we've got one, two, three, four, five, six groups of five. And two ones leftover. So two ones. And we can add those up. So six groups of five would be equal to 30 and the two ones would just be equal to two. And if we add them up, we have got 32, same as before. What about the two on the right hand side? What do they have in common? Well, they're both using what we call the base 10 number system. Which is the number system that you're very familiar with. It's the number system that we use. The first one, the one at the top. Well, we can see that we've got three groups of blocks of 10, so three blocks of 10. And then two ones as well, the three blocks of 10, give us 30. And the two ones give us two, add them together. And I get 32 again. And the one on the bottom is exactly the same thing, but this is the 32 in the place value system that you've probably seen many, many times before. So we could just read it off, straight away as 32. But the reason why it's 32 is because it's three times by ten, which is 30, and two times by one, which is two add them together as before, and we get 32. So lots of different ways of representing 32. And you probably found that either the third one or the fourth one was most useful because grouping together numbers in 10, it makes it really, really easy to find out what that number is straight away. Okay. Let's have a look at a few more examples of our number system. Okay, so here is a different number that three students are discussing. The number that they're discussing is two hundreds and 22 tens. And each of these three students is thinking about this number in a different way. So the first student, Antoni is thinking of it as two, lots of 100 and 22 lots of tens. So two lots of 100, you could think of as two times by a hundred. And I'll let you think of what 22 tens mean. The second student, Bihn is thinking about this number in terms of a diagram. And she's got two blocks of 100 and 22 blocks of 10. And she's thinking that I can group together some of the tens to make hundreds. So how do you think about how you might do that? And the third student Cala is saying I can write each part in the place value system. Think about how you might write both of these parts in the place value system. So three different ways of thinking about this number for you to have a think about. Again, pause the video and see if you can express the number in these three different ways. Pause video now. Okay, great. So this is a little bit more of a difficult one. Compared to the first one, but again, by thinking about the place value system with base 10 number system in different ways we can be successful. So the first one I can think about as two lots of 100, well, two, lots of 100 is, as I said, two times by 100, which is 200. And 22 tens we can think of it as 22 times by 10. That's really important. 22, lots of 10 is 22 times by 10. And we know that to times by 10, we add a zero at the end of a number, which is 220. And then adding those numbers together, well, we get 420. Let's see if we get the same number thinking of it in the other two ways. So the second student, having a think about grouping some of these tens together, well, what happens if I group these 10, lots of 10 together, I know that 10, lots of 10 makes 100. And I can do the same thing for this lot of 10 tens got 100 here. And then I've got remaining two lots of 10 so 20 here. So I've got 100, 100, 100, 100 and 20, add those all up. And I get 420. Finally the place value system again should be pretty straightforward. First of all, how do I write two hundreds in the place value system? Well, I put the two in the hundreds column, and then if I want, I can put in the zeros here, anything to the right of the number is essentially a placeholder. So I can put zeros in there as a placeholder. And then 22 tens. Well, I need to have the 22 here because I want 22 tens. And then, I can again have a placeholder there and then If I add both of these numbers together, I'm going to get 420 again. So a number of different ways to think about this number, they're all useful. And now let's have a look at the independent task. Okay so two different questions for you to do the first question, you've got four statements. They are either true or false. And the second question, put these in ascending order. So starting off with the smallest, there might be two, which are the same, So just be prepared for that. A number of ways that you can think about this, a number of ways that we've looked at so far, you can have a look at.. think about this in terms of the place value system, if you want to, or you can think of it, for example, you can think of 40 hundreds in the first one as 40 lots of 100, which you can work out. So a couple of different ways to think about this. So anyway, pause the video now to copy down these questions and to see how many you can work out then we'll go through them. Great, let's go through them. Nice and quickly then. So the first one is true because 4,000 we can write as a four followed by three zeros and 40 lots of 100 is going to be 4,000 as well. Next one is going to be false because I've got 8,000 here and 800 ones. Well, that is 800 lots of one, which is just 800. So that's false. the next one, 4,000 plus 200. Well, that's going to be 4,200 and 420 tens. Well, that's 420 times by 10, which is the same thing. So that is true. And then the final one, well, 300 plus 15 ones is going to be 315. And 315 tens is 315 times by 10, which is 3,150, so that is false. You could have thought about this in terms of the place value system, and hopefully you would get the same answers. Okay. Question number two, ascending order. Well, let's just work out each of these workout, which is the biggest, which is the smallest. So 204 tens is going to be 2040. 2004 ones is just 2004. 2 thousands and 40 ones is also 2040 And 24 hundreds. Well, that is going to be 24 times by 100 which is 2,400. So we can see that the second one is the smallest. And then followed by the first one and the third one equally. And then the final one is the largest. Great hope that you've found that nice and straightforward. Let's take a look at the final task today, the explore task. Okay. So here is the explore task. It's an interesting one. It should be challenging. So let's have a look at what we need to do. So form each number by placing the cards into the place value grid. So what does that mean? Well, form each number, we've got four different numbers to form 3,184, 3,127, et cetera. And we need to form each of these numbers by using the cards below and putting them in some kind of order into the place value grid. Let's just have a look at one example to see how we might do this. So I'm going to take the second example, we need to make the number 3,127 by putting the cards seven, 12, and three into the place value grid. So I could do this for example, by putting the three in the thousands column, the 12 in the hundreds column and the seven in the ones column. That's one way I could do it, but now we need to check to see if we actually get the number 3,127. So how do we do that? Well, the three thousands is simply by itself, just 3000. The 12 in the hundreds column. What's that? Well, that is 12 lots of 100, which is 1,200. And the seven in the ones column is just seven. So I got 3,000, 1,200, and seven. And I need to check, do these, add up to make 3,127? Well, if I order them under each other, as I should do, I will see if I add all of these up, I'm going to get 4,207, which is not what I want. So I need to put the numbers three, 12, and seven in a different place to get the number 3,127. So you have got four numbers to do four numbers to find out. It might take you a while by trying different combinations, but make sure that you set your working out nice and neatly so that when you calculate the value of each number, you get that right. Okay. Pause the video now for five, six, or maybe more minutes and see how many of these four you can get. Okay, so hope that you had a good go at that and let's go through this now. So the first one was actually really nice and straightforward. All you needed to do was rearrange these number cards into three, one, eight, four, and then you get the number that you want, really nice and straightforward. The next one you needed, I'll write it up in the place value grid, you needed a three in the thousands column, the 12 in the tens column and the seven in the ones column. Because that would get you 3000 and then 12 lots of 10 is 120, and seven ones is seven. And that gets you 3,127. So that was the second one. I'm going to rub it out now. So make sure you pause the video, If you need to, to get it down. The third one, 2,904. You needed the two in the thousands column, the eight in the hundreds column, the 10 in the tens column, and the four in the ones column. And then that will give you 2,000, 800, 10 tens is 100. And four ones add them all up, you get 2,904. And the final one. Well, there's actually two different solutions here. So did you find one of them? Well done. if you only found one of them, pause the video now and see if you can find a different way of getting 4,444. And I'll just tell you the two ways of getting them would be a four, a three, a 13 and a 14. And a three, a 13, a 14, and a four. So really well job. really nice job if you've got those and that is it for today's lesson, I hope that you enjoyed it. And next time we're going to be looking at number systems in the base five system. So it's going to be a really interesting lesson, hopefully. Thanks very much for watching. Have a great day. See you next time, bye.

Representing Number

Representing Number

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UnitMaths / Numbers and numerals

Maths