Video: Comparing Two-Digit Numbers: Number Lines

In this video, we will learn how to use number lines to compare numbers up to 100 and to find numbers that are greater than or less than a given number.

12:50

Video Transcript

Comparing Two-Digit Numbers: Number Lines

In this video, we’re going to learn how to use number lines to compare numbers up to 100 and to find numbers that are greater or less than a given number.

Here’s part of a number line. In this video, we’re going to be thinking about two-digit numbers. So let’s put some two-digit numbers on there. Should we start at 25? And we’ll count in ones. 25, 26, 27, 28, 29, 30, 31, 32. Are you happy with that? Have we labeled the number line correctly? I’m sure if you saw a number line like this, you’d say this isn’t right. The numbers aren’t in order. Shall we try again?

So we’ll start with 25 again. 26, 27, 28. Have we labeled the number line correctly this time? The numbers are in order. But most often we don’t label number lines like this because the numbers get larger from right to left. Usually, when we look at a number line, the numbers go from smaller to larger in the other direction. Maybe we’ll label it correctly this time. As we make our way from left to right along the number line, each new number on the right of the last number is larger or greater, all the way to 32.

Now, why have we spent the first minute of this video thinking about how to label a number line when you probably knew that all along? Well, by talking about the order that numbers come on a number line, it helps us understand where larger and smaller numbers belong and how to compare them. Let’s think for a moment about the number 27. Which part of the number line shows numbers that are less than 27? As we’ve said already, we know that as we read our number line from left to right, we go from smaller to larger. So, all of the numbers that are less than 27 are in this pink part of the number line here, to the left of 27. We could say the numbers 25 and 26 are less than 27.

And what can we say about the numbers we can see that are greater than 27? Numbers become larger the further to the right we go. So all the numbers to the right of the number 27 are larger than 27. So we could say the numbers 28, 29, 30, 31, and 32 are greater than 27. Can you see what we’ve done here? We’ve used the position of each number on the number line to tell whether it’s less than or greater than another number.

Here’s another number line. This time we’ve labeled it properly, don’t worry. We can see the numbers that are labeled are multiples of 10: 30, 40, 50, 60, and 70. Let’s label two two-digit numbers on our number line to compare. Let’s have the number 45, which is halfway between 40 and 50, and then let’s have the number 60. Now, let’s imagine that we’ve been asked to compare these two numbers. Which symbol would you write in between them? Is 45 equal to 60? Is it greater than 60? Or is it less than 60? There are lots of different ways we could use to find the answer. But remember, in this video, we’re thinking about using the position of these numbers on a number line to help us.

Let’s look at the second number, 60, and think about where 45 is compared to this number. When we look at our number line, if we look at where 60 is, we can see that 45 is in this direction. It’s to the left of 60. We know that all the numbers to the left of a point on the number line are smaller, so we know we can say 45 is less than 60. Now, we just need to choose the correct symbol. We know that symbol that we need to use if two numbers are equal, but it’s sometimes easy to get the other two symbols muddled up. There are two things we need to remember: firstly, that we always read from left to right and, secondly, that the wide part of each symbol always points towards a larger number and the narrowest part points towards the smaller number.

With this symbol, we start with a smaller number, so it means a certain number is less than another number. And with the second symbol, the larger number comes first, so it means that the number is greater than another number. We’ve already said 45 is less than 60. So this is the symbol we need to use. Notice how the narrow part is pointing towards the smaller number and the wide part is pointing towards the larger number. Let’s answer some questions now where we need to compare two-digit numbers. And the way we’re going to compare them every time is by thinking about their positions on a number line.

Scarlett and Victoria are comparing numbers to the right and left of 61 on a number line. Who is correct? And then, we can see two speech bubbles showing what the children are saying. The numbers on the right of 61 are greater than 61. And then, the numbers on the left of 61 are greater than 61.

This question describes two children, Scarlett and Victoria, who are comparing two-digit numbers. And they’re comparing these numbers to the number 61. We’re told in the question, aren’t we, that they’re comparing numbers to the right of 61 and all the numbers to the left of 61. Now, our question asks us, who is correct? And we can see two pictures of the children and speech bubbles showing what they’re saying. Now, they’re both girls, and the pictures aren’t labeled Scarlett and Victoria, so we might not be quite sure which one’s which. When we decide who’s correct, instead of writing their name as the answer, let’s draw a box around them.

Did you notice when we read both statements, there’s only one difference between them. Both children are trying to tell us which numbers are greater than 61. The first character says the numbers on the right of 61 are greater than 61. And we can see them labeled in green on their number line, can’t we? 62, 63, 64, 65, and 66. The second character also talks about numbers that are greater than 61. But they say the numbers on the left of 61 are greater than 61. And again we can see these labeled in green on their number line too. 56, 57, 58, 59, and 60. So to solve the problem, we need to think about directions on a number line.

If we want to find the numbers that are greater than 61, are we going to look at the numbers to the right of 61? Or are we going to look at the numbers to the left of 61? Well, we know as we read a number line from left to right, we go from smaller to larger. So if we start at the number 61, the numbers that are larger or greater than 61 are to the right of 61. We can see that the first character here has got it right. We know that the numbers to the right of any number on a number line are greater than that number. And so, the numbers to the right of 61 are greater than 61.

Compare the numbers on the cards. Which symbol is missing? 84 what 48. Hint: use the number line.

At the very bottom of this problem, we’re given three symbols. We’ll go through what each one means later on. We use these symbols to compare numbers together. And we’re given two two-digit numbers. We need to decide which of the three symbols goes in between these numbers. The two numbers that we need to compare on the cards are 84 and 48. We need to think about whether 84 is less than 48, whether it’s greater than 48, or whether the two numbers are the same.

Now, there are different ways we could do this. But in this particular question, we’re told how to find the answer. We’re given a hint and it says, use the number line. Now, when we’re given a hint in a question, it usually means “do this.” So let’s use the number line to help us. I can’t see the number 84 on this number line, can you? Where do you think it belongs? Well, I can see the number 80 here. The number 90 comes after this, and we know that 84 is in between 80 and 90. Can you see this notch halfway between 80 and 90? Because it’s halfway, we know that it stands for 85. And 84 comes just before 85.

So let’s draw an arrow just before this middle notch. And we’ll label it 84 just to remind us what we’re labeling. Now, let’s label our second number. Where’s the number 48 on the number line? Can you see the number 40? And we can see the number 50 after it. The halfway point in between must be 45. And we know that 48 comes after 45. It’s nearly 50. So let’s draw an arrow just before 50, and we’ll label it 48. This is a good question, isn’t it, because it’s already got us thinking about number lines and we haven’t even started comparing these two numbers yet.

But now that we’ve labeled our numbers, we can compare them. Where’s the number 84 compared to 48? We can see that it’s in this direction. It’s to the right of the number 48. We know as we move to the right along this number line, we go from smaller to larger. We can see this if we look at the numbers as a label, can’t we? We start at zero, and as we move to the right, we go on to 10, 20, 30, 40, and so on. These numbers are getting bigger and bigger. So because 84 is to the right of 48, it’s a larger number. 84 is greater than 48.

Now, we just need to choose the correct symbol to use in between the two numbers. Which symbol means is greater than? Well, we know that this symbol means is equal to or is the same as. So let’s cross out this symbol. We know this isn’t right. Now, we’re left with these two symbols that look a little bit like arrows. It’s often easy to get confused. Which one means is greater than? The way we can remember which is which is that the narrow part of each arrow always points to a smaller number, the wider part of each symbol always points towards the larger number. And the other thing to remember is that we always read from left to right.

So if we look at this first symbol, we can see that we start with a smaller number, end with a larger number. The smaller number is less than the larger number. So this symbol means is less than. And if we read the second symbol from left to right, we can see that we start with a larger number. The larger number is greater than the smaller number, so this symbol means is greater than. Hopefully, we’ve reminded ourselves which symbol we need to use. 84 is to the right of the number 48 on our number line. And we know that all numbers to the right of another number are larger numbers. The correct symbol to use in between 84 and 48 is the one that represents is greater than. 84 is greater than 48.

What have we learned in this video? We’ve learned how to use number lines to compare numbers up to 100. We’ve also found numbers that are greater or less than a given number.

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