Lesson Video: Three-Digit Numbers on a Number Line | Nagwa Lesson Video: Three-Digit Numbers on a Number Line | Nagwa

# Lesson Video: Three-Digit Numbers on a Number Line Mathematics

In this video, we will learn how to locate and represent three-digit numbers on number lines with different scales.

16:28

### Video Transcript

Three-Digit Numbers on a Number Line

In this video, we’re going to learn how to show and to find three-digit numbers. We’re going to do this on number lines that have different scales. Oh, dear! It looks like somebody’s altered the title of our video. Now, who could that be? But, you know, showing three-digit numbers on a washing line might not be such a bad idea. It’s a good place to start.

Here’s a washing line with some blank cards pegged on it. Let’s turn it into a number line by writing a three-digit number at the start. What about 260? What number do you think we need to write on the second card? Well, that depends on what we call the scale of the number line. In other words, what are we going to count in?

When we first start learning about numbers, the scale that we use is to count in ones. So after 260 would come 261, 262, 263, 264, 265, 266, 267, 268, 269. We can see that where the red bird is standing on the washing line is above the number 266. But this is when we count in ones. What if we change the scale? What number is the red bird standing next to now?

Well, whatever number it is, we can see that it comes in between the numbers 310 and 330. We could use this fact to help us, but also we could look at the scale of the number line. What are we counting in this time? To get from 260 to 270 is a jump of 10. Can you see how the number’s gone from six 10s to seven 10s and then from seven 10s to eight 10s in 280, 290, 300? Can you see how we’re counting in 10s each time? 310. This means our missing number must be 320, 10 more than 310. And we can see that 320 does fit in between 310 and 330, doesn’t it? And if we carry on counting in 10s from 320, we can see that it fits with the rest of the number line. 330, 340, 350.

So this number line had a different scale than the first one, didn’t it? We knew that we had to count in 10s. Shall we try one more scale? This time, we’ve got two missing numbers to think about. The red bird is on a number that is halfway between 600 and 700. We’ll use this clue to help us in a moment. And the second missing number is halfway between 750 and 850. What’s the scale of this particular number line?

To find out, we can look at two numbers that are next door to each other. Let’s look at these two, 500 then 550. Can you see how much we have to count on to get from 500 to 550? It’s 50, isn’t it? And then if we count on another 50, we get to 600. We can see that this is the scale all the way along the number line. So we know our first missing number is not only halfway between 600 and 700, it’s also 50 more than 600. 400, 450, 500, 550, 600, 650. And as well as being halfway between 750 and 850, our second missing number is 50 more than 750. Let’s count from the red bird onwards. 650, 700, 750, 800.

The scale this time was to count in 50s. Each new number on our number line was worth 50 more than the one before it. And as well as counting in ones, 10s, or 50s like we’ve done already, we could also count in fives or even 100s. To be able to show and to find three-digit numbers on number lines, we can’t just look at where the arrow’s pointing. We need to also look at the scale, in other words, how the numbers change.

Let’s answer some questions now where we need to practice these skills. None of them are going to feature birds or washing lines. But we are going to see some number lines that have different scales in them and some numbers that we need to recognize.

What number is missing from this number line?

We’re given a number line here, which is just a line with lots of numbers written in order. And we’re asked, what number is missing from the number line? Now, to find the answer, we need to do two things. Firstly, we need to look at where the missing number is. And then once we’ve done that, we need to think carefully about what the number line shows.

Now, our missing number is here, isn’t it? That’s why we’ve got this empty box. It’s the number that comes after 913 but before 915. In fact, we could say it’s in between 913 and 915. Now that we’ve looked at the position of our missing number, let’s look at the whole number line. What do we notice? We can see that it starts with the number 900. It goes all the way up to 920. And if we count along the number line, we can see that we’re counting in ones. 900, 901, 902, 903, and so on. We could say that the scale of this number line is to count or jump in ones each time.

So if we come all the way across now and look at our missing number, we know that it’s going to be one more than 913. We know that one more than 13 is 14. And so one more than 913 is 914. And if we count the numbers around our missing number, we can see that it fits in perfectly. 913, 914, 915, and so on. The number line shows a scale where we’re counting in ones. And we know then that our missing number is going to be 914.

This line shows a sequence of whole numbers. What numbers are missing?

The first sentence of this question is a really good way of saying what a number line is. It’s a line that shows a sequence of numbers or, in other words, it’s a way of showing numbers in order. And we can see with this number line that our numbers get bigger. We start with 100, and it goes all the way up to 900. But can you see there are two missing numbers along the way? What are they?

Let’s look at our first number to begin with. The first thing we can say about this missing number is that it comes after 100. But that’s not really much of a help. We could be counting in ones, in which case our missing number is 101. Or maybe we’re counting in 10s. 100, 110.

To decide what our missing number is, we need to look really carefully at our number line to see what the scale is, in other words, to see what we’re counting on in each time. Let’s look at some numbers that are in a row that we know already. 300, 400, 500, 600. Can you spot what we’re counting in? This number line shows jumps of 100. So if we go back to the very beginning and we start with 100 and make a jump of another 100, we can see that our first missing number is going to be 200. And this fits in with the sequence, doesn’t it? 100, 200, 300, 400, 500, 600.

What’s the next missing number going to be? What’s 100 more than 600? It’s 700. Let’s count along the whole number line. 100, 200, 300, 400, 500, 600, 700, 800, 900. We worked out that the scale of this number line was to count in 100s. And that’s how we know the two numbers that are missing are 200 and 700.

What are the missing numbers in the given sequence?

In this question, we’re given a number line. But unfortunately, this number line has got two missing numbers on it. Can you work out what they are? Let’s look at our first missing number to begin with. Now, one of the ways that we can find a missing number on a number line is to look at the scale of the number line, in other words, how the numbers change. But another way that we can find numbers is to think about the numbers either side of our missing number.

In this example, we can see that our missing number is exactly halfway between the numbers 300 and 400. Now, let’s imagine that we’ve got a really strong magnifying glass and we can zoom in just on this little part of the number line. It would look like this, wouldn’t it? Now, what number comes halfway between 300 and 400? It’s 350. This means that the scale of our number line or, in other words, the amount that we add each time is 50. Each new number is 50 more than the last. So if we look at our second missing number, we can use this idea of counting in 50s to help us.

Let’s start from the number 500. 500, 550, what, 650. What number is 50 more than 550? It’s 600. Let’s read our way along the whole number line and see whether our two missing numbers fit in. 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800. The missing numbers in this sequence are 350 and 600.

Which arrow is pointing at the number 670?

We’re given five different number lines here. And can you see? On each one, there’s a blue arrow pointing out a position. But only one of the blue arrows is pointing where the number 670 belongs. Let’s go through each number line to try to find out which one it is.

Now, if we look at our first number line, we can see that not all the marks on the number line have got a number by them. We start with the number 600. Then we make one, two, three jumps before we get to the number 630. Now, we know 630 is 30 more than 600, and 30 is the same as three 10s. So each jump that we’ve made must be worth 10. 600, 610, 620, 630. The numbers fit. And we’ve worked out that the scale of the number line is to count in 10s.

Let’s count on in 10s from 660 to find out what number the blue arrow is pointing to. 660, 670. This is the number we’re looking for, so we can see straightaway that the arrow isn’t pointing to it. And then 10 more than 670 is 680. The first arrow doesn’t show 670; it shows 680.

Let’s try looking at our second number line. This number line is a little bit similar to the first one in that the first number we can see labeled is 600 and the last number is 690. But we can see that there are a lot more notches on this number line, aren’t there? The scale must be different.

Let’s try and work out what the scale is. If we start at 600, we make one, two, three jumps before we get to 615. Now, on the first number line, we made three jumps and we got to 630. That was by adding 10 each time. But this time, we’ve only got to 615. So it seems like we’re adding less than 10. Let’s try counting in fives. 600, 605, 610, 615. It works! And so we know that, on this number line, each interval or mark is worth another five.

Now that we’ve worked out the scale of the number line, we can work out the value of the arrow. Is it pointing to the number 670? Let’s start with 660, which is the notch before it, and we’ll count in fives. 660, 665. Oh dear, we can see that the number the other side of the arrow is the one we’re looking for, 670. On this number line, the arrow is pointing to 665, not 670.

This next number line is a really quick one to understand. 100, 200, 300. We can see that the scale is to count in 100s. And the blue arrow on this number line is pointing halfway between the number 500 and 700. We know that this arrow is pointing to the value 600. We’ve only got two more number lines to look at. Which arrow is pointing to the number 670?

Now, can you see a similarity between this number line and the first one we looked at? Each of the intervals is worth 10. On the first number line, not all the numbers were labeled, were they? But on this one, they are, all except the one with the blue arrow. 600, 610, 620, 630. Just like the first number line then, we’re counting in 10s. And we can see that the blue arrow is the number that comes after 660. And 10 more than 660 is 670. It looks like this is the answer we’re looking for.

Let’s just check our final number line. Well, if we look at where the blue arrow is pointing on this number line, we can actually use some number sense to realize it’s not pointing to the number 670 at all. It’s pointing to a number that comes after 675. And because we know 675 is more than 670, we know that the blue arrow must be pointing to a number more than 675. We don’t even need to know the scale on this one. We can see straightaway it’s not going to be 670.

The correct number line is the one that shows a scale that goes up in 10s each time. And it shows the arrow pointing to the number that comes after 660. We know this because the number that is 10 more than 660 is 670.

What have we learned in this video? We’ve learned how to show and to find three-digit numbers on number lines that have different scales.

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