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Comparing Two-Digit Numbers: Number Lines
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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.
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Here’s part of a number line.
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In this video, we’re going to be thinking about two-digit numbers.
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So let’s put some two-digit numbers on there.
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Should we start at 25?
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And we’ll count in ones.
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25, 26, 27, 28, 29, 30, 31, 32.
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Are you happy with that?
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Have we labeled the number line correctly?
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I’m sure if you saw a number line like this, you’d say this isn’t right.
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The numbers aren’t in order.
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Shall we try again?
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So we’ll start with 25 again.
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26, 27, 28.
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Have we labeled the number line correctly this time?
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The numbers are in order.
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But most often we don’t label number lines like this because the numbers get larger from right to left.
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Usually, when we look at a number line, the numbers go from smaller to larger in the other direction.
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Maybe we’ll label it correctly this time.
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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.
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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?
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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.
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Let’s think for a moment about the number 27.
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Which part of the number line shows numbers that are less than 27?
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As we’ve said already, we know that as we read our number line from left to right, we go from smaller to larger.
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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.
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We could say the numbers 25 and 26 are less than 27.
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And what can we say about the numbers we can see that are greater than 27?
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Numbers become larger the further to the right we go.
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So all the numbers to the right of the number 27 are larger than 27.
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So we could say the numbers 28, 29, 30, 31, and 32 are greater than 27.
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Can you see what we’ve done here?
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We’ve used the position of each number on the number line to tell whether it’s less than or greater than another number.
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Here’s another number line.
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This time we’ve labeled it properly, don’t worry.
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We can see the numbers that are labeled are multiples of 10: 30, 40, 50, 60, and 70.
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Let’s label two two-digit numbers on our number line to compare.
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Let’s have the number 45, which is halfway between 40 and 50, and then let’s have the number 60.
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Now, let’s imagine that we’ve been asked to compare these two numbers.
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Which symbol would you write in between them?
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Is 45 equal to 60?
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Is it greater than 60?
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Or is it less than 60?
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There are lots of different ways we could use to find the answer.
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But remember, in this video, we’re thinking about using the position of these numbers on a number line to help us.
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Let’s look at the second number, 60, and think about where 45 is compared to this number.
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When we look at our number line, if we look at where 60 is, we can see that 45 is in this direction.
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It’s to the left of 60.
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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.
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Now, we just need to choose the correct symbol.
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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.
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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.
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With this symbol, we start with a smaller number, so it means a certain number is less than another number.
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And with the second symbol, the larger number comes first, so it means that the number is greater than another number.
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We’ve already said 45 is less than 60.
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So this is the symbol we need to use.
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Notice how the narrow part is pointing towards the smaller number and the wide part is pointing towards the larger number.
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Let’s answer some questions now where we need to compare two-digit numbers.
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And the way we’re going to compare them every time is by thinking about their positions on a number line.
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Scarlett and Victoria are comparing numbers to the right and left of 61 on a number line.
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Who is correct?
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And then, we can see two speech bubbles showing what the children are saying.
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The numbers on the right of 61 are greater than 61.
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And then, the numbers on the left of 61 are greater than 61.
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This question describes two children, Scarlett and Victoria, who are comparing two-digit numbers.
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And they’re comparing these numbers to the number 61.
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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.
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Now, our question asks us, who is correct?
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And we can see two pictures of the children and speech bubbles showing what they’re saying.
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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.
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When we decide who’s correct, instead of writing their name as the answer, let’s draw a box around them.
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Did you notice when we read both statements, there’s only one difference between them.
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Both children are trying to tell us which numbers are greater than 61.
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The first character says the numbers on the right of 61 are greater than 61.
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And we can see them labeled in green on their number line, can’t we?
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62, 63, 64, 65, and 66.
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The second character also talks about numbers that are greater than 61.
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But they say the numbers on the left of 61 are greater than 61.
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And again we can see these labeled in green on their number line too.
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56, 57, 58, 59, and 60.
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So to solve the problem, we need to think about directions on a number line.
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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?
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Or are we going to look at the numbers to the left of 61?
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Well, we know as we read a number line from left to right, we go from smaller to larger.
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So if we start at the number 61, the numbers that are larger or greater than 61 are to the right of 61.
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We can see that the first character here has got it right.
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We know that the numbers to the right of any number on a number line are greater than that number.
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And so, the numbers to the right of 61 are greater than 61.
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Compare the numbers on the cards.
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Which symbol is missing?
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84 what 48.
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Hint: use the number line.
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At the very bottom of this problem, we’re given three symbols.
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We’ll go through what each one means later on.
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We use these symbols to compare numbers together.
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And we’re given two two-digit numbers.
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We need to decide which of the three symbols goes in between these numbers.
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The two numbers that we need to compare on the cards are 84 and 48.
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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.
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Now, there are different ways we could do this.
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But in this particular question, we’re told how to find the answer.
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We’re given a hint and it says, use the number line.
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Now, when we’re given a hint in a question, it usually means “do this.”
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So let’s use the number line to help us.
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I can’t see the number 84 on this number line, can you?
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Where do you think it belongs?
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Well, I can see the number 80 here.
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The number 90 comes after this, and we know that 84 is in between 80 and 90.
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Can you see this notch halfway between 80 and 90?
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Because it’s halfway, we know that it stands for 85.
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And 84 comes just before 85.
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So let’s draw an arrow just before this middle notch.
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And we’ll label it 84 just to remind us what we’re labeling.
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Now, let’s label our second number.
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Where’s the number 48 on the number line?
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Can you see the number 40?
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And we can see the number 50 after it.
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The halfway point in between must be 45.
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And we know that 48 comes after 45.
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It’s nearly 50.
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So let’s draw an arrow just before 50, and we’ll label it 48.
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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.
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But now that we’ve labeled our numbers, we can compare them.
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Where’s the number 84 compared to 48?
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We can see that it’s in this direction.
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It’s to the right of the number 48.
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We know as we move to the right along this number line, we go from smaller to larger.
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We can see this if we look at the numbers as a label, can’t we?
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We start at zero, and as we move to the right, we go on to 10, 20, 30, 40, and so on.
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These numbers are getting bigger and bigger.
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So because 84 is to the right of 48, it’s a larger number.
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84 is greater than 48.
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Now, we just need to choose the correct symbol to use in between the two numbers.
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Which symbol means is greater than?
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Well, we know that this symbol means is equal to or is the same as.
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So let’s cross out this symbol.
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We know this isn’t right.
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Now, we’re left with these two symbols that look a little bit like arrows.
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It’s often easy to get confused.
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Which one means is greater than?
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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.
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And the other thing to remember is that we always read from left to right.
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So if we look at this first symbol, we can see that we start with a smaller number, end with a larger number.
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The smaller number is less than the larger number.
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So this symbol means is less than.
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And if we read the second symbol from left to right, we can see that we start with a larger number.
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The larger number is greater than the smaller number, so this symbol means is greater than.
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Hopefully, we’ve reminded ourselves which symbol we need to use.
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84 is to the right of the number 48 on our number line.
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And we know that all numbers to the right of another number are larger numbers.
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The correct symbol to use in between 84 and 48 is the one that represents is greater than.
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84 is greater than 48.
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What have we learned in this video?
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We’ve learned how to use number lines to compare numbers up to 100.
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We’ve also found numbers that are greater or less than a given number.