Lesson Video: Thousands Mathematics

In this video, we will learn how to model 1000 with place value blocks; define it as 10 hundreds, 100 tens, or 1000 ones; and count in thousands.

17:48

Video Transcript

Thousands

In this lesson, we’re going to learn how to model the number 1000 using place value blocks. We’re going to find out how we can describe it in different ways, like 10 100s, 100 10s, or even as 1000 ones. And once we have understood what a thousand is, we’re going to learn how to count in thousands.

You’ve probably come across the word thousand before. It’s a word that we use when we’re describing numbers, but what is a thousand? If we wanted to model 1000 using place value blocks, we’d use one of these. It’s a cube made from lots of tiny cubes. But what does it represent? How do we get from one of these cubes to one of these cubes? Let’s find out. This here is our place value block with the smallest value. It’s worth one one. And if we put 10 of these together, it’s the same as one of these. 10 ones equals one 10. And using our knowledge of place value, we know that if we put 10 of these together, it would look something like this, and this is exactly the same as one of these. 10 10s equals 100.

Finally, let’s put 10 of these together. 100, 200, 300, 400, 500, 600, 700, 800, 900. But how do we say this number? 10 100. Well, this place value cube that we’ve created does have a value of 10 100s, but it has a name all of its own. 10 100s are the same as one of these. 10 100s equals 1000.

So hopefully you can see now where this 1000s block comes from. And we can describe 1000 by thinking of all the other blocks. As we’ve just said, 1000 is exactly the same as 10 100s. We built it up, didn’t we, to show this? And because each of these 10 100s contains 10 10s, we could even model a thousand out of 10s blocks. 1000 is the same as 100 10s. And finally, if we had enough, we could model 1000 out of ones blocks. Because we know there are 10 ones in each of our 100 10s, we know we’d need 1000 of these tiny cubes to make a 1000 block. 1000 is the same as 1000 ones, which sounds a bit funny when you say it. But if you look at the picture, I’m sure you can see what we mean.

Now, it’s useful that we’ve shown these place value blocks in this order because it helps us understand where thousands belong. Because 1000 is worth 10 100s, we give it a separate place value. So, we have columns for our ones, tens, hundreds, and now thousands. We’re starting to learn about bigger and bigger numbers, aren’t we? And by learning about thousands, we’ve moved on to four-digit numbers.

And to write the number 1000, we simply write the digit one in the thousands place. Of course, if we just wrote the digit one and said it’s in the thousands column, it would be hard to tell. So, we need to do something to show that we’ve got empty hundreds, tens, and ones columns. And I’m sure you know we need to use zero as a placeholder: zero 100s, zero 10s, and zero ones. 1000 is a one followed by three zeros.

Now, I don’t know if you’ve noticed, but we’ve written the number 1000 using digits a couple of times already, one of them still on the screen. Can you see where we’ve labeled 1000 ones? And can you see the way that we’ve written 1,000 isn’t just a one followed by three zeros? We’ve used a comma after the one. Let’s explain why.

When we first start learning to count, we learn one-digit numbers, and they’re quite easy to read and see and recognize. And then, of course, we learn about tens too and we learn how to read and write and recognize two-digit numbers. But as we add more and more places for our digits, numbers that we make are a little hard to read. We can’t always recognize them straightaway. Now, if you keep working hard at maths, it won’t be long before you’ll be able to read a number like this that has seven digits in it.

And to help us read numbers with more and more digits, we need to group those digits to make them easier to read. And the way we do this is to put them in groups of three. We already know about one of these groups of three. They’re the ones, tens, and hundreds. And this first group of three needs to have a name. We can’t call it the ones-tens-hundreds group. That’s too much of a mouthful. So, we just call it the ones group.

But now that we’re learning about thousands too, this is part of the next group of three digits. And these three digits show us how many thousands we have. It’s the thousands group. And whilst we can write a four-digit number like this, sometimes you might see it written with a small gap between the thousands and the hundreds digits. It’s just a way of showing the separate groups. And we then look at this number straightaway and just see the thousands separately and say 1000. But as well as writing all the digits up together or putting a small gap, we can also show these separate groups by writing a comma. And again, it helps us to see that this is 1,000. When we see the comma, we can say thousand.

And in this video, we’re going to be using commas. So, perhaps, we’d better draw some commas into our four-digit numbers at the bottom here. One, two, three. Now that we’ve understood what a thousand is and we know how to write it, let’s try counting in thousands.

This jigsaw is made up of 1000 pieces. Let’s use it to help us count in thousands. 1,000; 2,000; 3,000; 4,000; 5,000. We could use place value blocks to model these numbers. Let’s carry on counting from 5,000. We still got some more boxes of jigsaw pieces to count. 6,000, 7,000, 8,000, 9,000. Now, if we count one more 1000, it’s going to make a five-digit number. And in this video, we’re just thinking about four-digit numbers. So, do you think you could cope with learning about a five-digit number too? Yes, of course you can. 1000 more than 9,000 is 10,000.

Did you notice how counting in thousands is very similar to counting in ones? We just say each number and then the word thousand. One, two, three, four, five. 1,000; 2,000; 3,000; 4,000; 5,000. It’s easy to remember, isn’t it? And hopefully you notice how all the commas that we wrote helped us to read these numbers. Well, we’ve learned a lot about thousands, haven’t we? Let’s put into practice everything that we’ve found out. We’re going to try answering some questions about thousands. Here’s one to start with.

There are six boxes. Each box contains 1,000 pieces of candy. How many pieces of candy are there in total?

The first piece of information that we’re given in this question is that there are six boxes, and we can see these in the picture. Next, we’re told how many pieces of candy are in each box. This is an interesting number. It has four digits. This number is made up of zero ones, zero 10s, zero 100s, and one 1000. When we see the digit one followed by three zeros, we know it’s 1,000. So, each box contains 1,000 pieces of candy, and there are six of them.

We’re asked how many pieces of candy are there in total. We can find the answer by counting in thousands six times, one for each box. 1,000; 2,000. Look at how the thousands digits changed in our place value grid. 3,000; 4,000; 5,000; 6,000. We read that each of these boxes contained 1,000 pieces of candy. And because there are six boxes, we knew that we could find the total number of pieces of candy by counting in thousands six times. 1,000; 2,000; 3,000; 4,000; 5,000; 6,000. And we can write the number 6,000 using digits as a six in the thousands place. We can use a comma to separate the thousands and the hundreds digits and then zeros in the hundreds, tens, and ones places. There are 6,000 pieces of candy in total.

What is the number represented below?

The number that this question’s talking about is represented by the place value grid that we can see. Let’s take a moment to look at it carefully. What can we say about this grid? Well, firstly, we can see that it’s made up of four columns. This means that the number that we can see is a four-digit number. Do you remember what place value each one of these four columns represents? We’ve got our ones, tens, hundreds, and then this final column here which represents thousands. And each 1000 is shown by one of these green cubes here. They’re made by putting 10 100s together, 100 10s, or even 1000 ones.

And we can see if we look at our place value grid, we’ve modeled our number using two 1000s blocks and nothing else. There are no little red ones blocks in the ones column. Let’s write a zero to show there aren’t any. And there are no tens rods in the tens column. Again, let’s show a zero to show that we haven’t got any tens or any hundreds. But we can see that we do have some 1000s blocks, and there are two of these. So, we can write the digit two in the thousands place. Two 1000s have a value of 2000, and that’s how we say our number, 2000.

Now we don’t have to do this, but when we write a number in thousands, we can use a comma after the thousands and before the hundreds digit to separate out the thousands. So instead of writing our answer like this, we can write it like this. It’s just a way of helping us read large numbers quickly. In the place value grid, we saw that there were two 1000s blocks, and there wasn’t anything else. And that’s how we know the number that’s represented in the place value grid is 2,000.

Find the missing number in the following sequence. 1,000, 2,000, 3,000, what, 5,000.

We’re given a sequence of five numbers, but one of them is missing. We need to find it. And to find the missing number in a sequence, we need to look at how the numbers change. So, let’s begin by looking at our first number. It’s the number 1,000. We write it using a one in the thousands place and then three zeros to show our empty hundreds, tens, and ones places.

The second number in our sequence is 2,000. And if we want to write 2,000 using this place value grid, we just need to change the one digit in the thousands place for the digit two. We’ve got one more 1,000. Do you think that our sequence might be to add 1,000 each time? It’s always important to look at the next number along too, because this could be a doubling sequence. Now, if we’re right and we need to add 1,000 each time, the next number after 2,000 won’t have a two in the thousands place. It’ll have one more than two; it’ll be three. And that’s exactly what we do have. In the sequence, we need to count in thousands. 1,000, 2,000, 3,000. And now if we add one more 1,000, we’re going to have 4,000. And we write the number 4,000 with a four in the thousands place followed by three zeros.

Now there’s one more thing we need to include, because the numbers in this sequence have a comma between the thousands and the hundreds digits. This is just a way of separating digits into groups to make numbers easier to read. All our thousands numbers in this sequence do have one of these commas, so we’re going to include it for 4000. Let’s read our sequence then, and we’ll model it using place value blocks as we say each number. 1,000, 2,000, 3,000, 4,000, 5,000. The missing number in our sequence of counting in thousands is 4,000.

How many hundreds are there in 1,000?

This question mentions two numbers. The first number is hundreds. Let’s remind ourselves what a hundred is. It’s a one followed by two zeros, isn’t it? It has a one in the hundreds place, a zero in the tens place, and a zero in the ones place. And we can model 100 using one of these place value blocks. The second number in our question is written using digits. It’s made up of a one followed by three zeros this time. This time, the one is in the thousands place, and it has zeros in the hundreds, tens, and ones places. And because of that one in the thousands place, we read this number as 1,000. And 1,000 using place value blocks looks like one of these.

And our question asks us, how many hundreds are there in 1,000? Let’s go through two ways to find the answer. Firstly, we could use a place value grid to help us, and we need to use what we know about each column. The lowest-value column, of course, is the ones. And we can have anywhere from zero ones up to nine ones. But because each column only contains one digit, if we want to show 10 ones, we have to move to the next column along because 10 ones is the same as one 10. And the same is true of the tens. This place can only contain one digit. So again, we could have anything from zero all the way up to nine 10s. But as soon as we have 10 10s or even more, we can’t show this. Again, we move up to the next column. 10 10s are the same as 100.

Perhaps you can see where this is taking us. Each time we find 10 of something, we move to a new place value. A number can contain anywhere from zero hundreds up to nine 100s. But as soon as we get to 10 100s, we start a new column. 10 100s are the same as 1,000.

So that’s one way to find the answer. But we could also use place value blocks. We could ask ourselves, how many of these could we put together to make one of these? Let’s find out. We’d need one, two, three, four, five, six, seven, eight, nine, 10. We’ve used a place value grid and place value blocks to work out how many hundreds there are in 1,000. But there are other ways we could’ve found the same answer. For example, we could’ve shown how we can count in hundreds 10 times before we get to 1,000. There are 10 100s in 1,000.

So, what have we learned in this video? We’ve learned how to model 1,000 using place value blocks. We’ve also seen how we can describe 1,000 in different ways as 10 100s, 100 10s, or 1,000 ones. Finally, we’ve practiced counting in thousands.

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