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.
