### Video Transcript

Comparing Three-Digit Numbers

In this video, we’re going to learn
how to compare numbers up to 1000 by comparing the number of hundreds, tens, and
ones.

Now there are all sorts of ways we
could represent three-digit numbers. Let’s start by comparing some
objects. And let’s imagine that in a
stationery store, notebooks are sold in big bundles of 100, smaller packs of 10, and
also on their own in ones. And let’s imagine there’s this many
blue notebooks and there are this many red notebooks. Now we know that we’ve got two
three-digit numbers represented here because we’ve got a number of hundreds as well
as tens and ones. And if we want to compare the blue
notebooks with the red notebooks, these two three-digit numbers, where are we going
to start? Should we start by comparing the
number of ones, the packs of 10, or the bundles of 100?

When we compare numbers, we’ve got
to start somewhere. Now perhaps you know already which
part of the number we need to start comparing. It’s the part of the number that
has the biggest value. In a way, it’s the part that
matters most. Now without doing any counting,
just imagine that you’ve been given the job of lifting these notebooks to put them
in the back of a van. And let’s imagine that they’re as
heavy as they look. So the bundles of 100 are really
heavy. The packs of 10 are not really very
heavy at all. And the individual notebooks on
their own are quite light really. And your boss says to you, do you
want to take the blue notebooks or the red notebooks? Which would you choose? Or here’s another question. Which part of the number would you
be looking at before you made your decision?

Would you make your decision based
on the individual notebooks, the packs of 10, or the bundles of 100? Well, if you don’t fancy doing any
heavy lifting, I think you might make your decision based on the number of hundreds,
don’t you? And this is a rule we can remember
whenever we’re comparing numbers together. We always start by comparing the
part of the number that’s worth the most. So let’s start by looking at these
hundreds. If we have to, we’ll go into the
tens and ones, but we might not have to. If we look at the blue notebooks to
begin with, we can see two hundreds bundles. So this number contains two
hundreds. It’s going to be 200 and
something.

But if we look over at the red
notebooks, we can see there’s only one bundle of 100. This number is going to be 100 and
something. So straightaway we can say which
number’s the greatest, can’t we? We can say that there are more blue
notebooks than there are red. Even though we know which number is
going to be larger, let’s just quickly look at the rest of each number so we can
write them down as three-digit numbers. So the blue notebooks are made up
of two 100s, one 10, and three ones. This is the number 213. And then the red notebooks are made
up of one hundred, five tens, and five ones. This is the number 155.

By the way, before we move on, look
at how if we’d have started by comparing the ones, we might have been tempted to say
that there were more red notebooks. Good job we started with the bundle
that had the biggest value, isn’t it? 213 is greater than 155.

Now there are lots of different
ways to represent three-digit numbers, not just with objects. Let’s generate some random numbers
by spinning this spinner. There we are. So our first number is going to be
made out of place value counters. Okay, and let’s spin again to
generate another number. Our second number needs to be
represented in words. Okay, now let’s compare our two
numbers together. Do you notice something interesting
about our first number? There aren’t any place value
counters that represent hundreds, are there? We’ve just got tens and ones. So we can say this is going to be a
two-digit number not a three-digit number. And if we look at our number that
we’ve modeled using words, we can see that there are some hundreds in it. This is a three-digit number.

So we’re comparing a two-digit
number with a three-digit number. Now, as we’ve said already, we
always start by comparing the part of the number that has the most value. And in the three-digit number,
that’s the number of hundreds that we have. But our first number doesn’t have
any hundreds. So we don’t need to count
anything. We don’t need to even look at the
rest of the number. We know which number’s largest. A number with three digits is
always larger than a number with two digits because a number with two digits is less
than 100 and a number with three digits is 100 or more. So we could use this symbol in
between both of our numbers. And let’s quickly write them using
digits to show what we mean. Six 10s and two ones is 62. 62 is less than 221.

Let’s try one more example. Our first number is going to need
to be written as a numeral, which means using digits. There we are. And then a number written in
expanded form. And if you remember, expanded form
means we need to separate out the hundreds, the tens, and the ones and write it as
an addition. Here we’ve done it using arrow
cards. Right, so let’s compare our
numbers, shall we? And once again, we’re going to
start with the part of the number that has the greatest value. In this case, it’s the
hundreds. Our first number is written as a
numeral, which means we’ve used digits to write it. Now to help us remember which
digit’s which , shall we label them? Now you might think this is a
little bit like a place value grid, isn’t it? But it’s going to help us.

So our first number has a four in
the hundreds place, which is worth 400. But if we look at the number of
hundreds in our second number, we can see that there’s 400 there too. So we’ve compared the part of the
number that’s worth the most, but they’re the same. What we do now? Well, we carry on moving through
the number comparing the part of the number with the next highest value, which, of
course, is the tens. Our first number has a seven in the
tens place. We know that seven 10s are worth
70. But the tens in our second number
are also worth 70. When we compare three-digit
numbers, we don’t always have to go to the ones, but we do in this case because our
hundreds and our tens are exactly the same.

Our first number has two ones, but
our second number has four ones. And now finally, we can see which
number’s the greatest. It’s the second number. The first number is less than the
second. And if we read them both as
numbers, 472 is less than 474.

Now in a moment we’re going to
answer some questions where we need to practice our skills of comparing numbers. But before we do, here’s a quick
game for you to see whether you’ve learned what you need to. Let’s imagine you’ve got six digit
cards and we’ve used them to make two three-digit numbers. But at the moment, they’re upside
down. Now you could compare these numbers
by turning over all six cards. But the aim of the game is to
compare these two numbers by turning over as few cards as possible. So your question is this. In which order would you turn over
the cards to make sure that you can compare the numbers by turning over as few cards
as you need to? Would you turn over each of the
cards in the first number and then go through the second if you need to? Or maybe you’d compare each type of
digit starting with the ones first and so on. What would you do?

Well, hopefully, if you can put
into practice what you’ve learned in the video already, you’d start by comparing the
digits that are worth the most, the hundreds digits. And if those two hundreds digits
are different, we can answer the question in two moves. We can compare the two numbers
without turning over anything else. 600 and something is less than 900
and something. And can you see if we’d have
started with the ones digits, it wouldn’t really have told us very much. We know eight ones are larger than
one one. And we know five 10s are larger
than zero 10s. But it’s not until we see those
hundreds that we can really compare these numbers.

Right, let’s have a go at answering
those questions then.

Compare 251 and 234. Which number is greater?

In this question, we’re given a
pair of three-digit numbers, 251 and 234. And we’re told to compare them. We need to find which number is
greater. In other words, which is the
largest number? Now underneath the question, we can
see a place value grid. And place value grids are really
helpful when we’re comparing numbers. Do you know why? It’s because they help us to see
numbers in terms of the value of their digits, in this case, the hundreds, the tens,
and the ones. Now which digit should we start
comparing first? Is this like column addition and we
need to start with the ones and move from right to left? Should we start with the hundreds
and work from left to right? Or doesn’t it matter?

If we think for a moment about the
value of each part of our number, we know that the hundreds are worth a lot more
than the tens or ones. And because they’re worth a lot
more, we need to start by comparing them. They make the biggest difference to
our numbers. So let’s start by comparing the
hundreds digits in our numbers. We can see that both of our numbers
begin with the digit two. They’re both 200 and something. And because the hundred digits are
exactly the same, we can’t separate these numbers. We can’t see which one is greater
yet. And so this is why we move along
down the number to the place with the next greatest value. And that’s the tens digits.

The number 251 has five 10s, and
the number 234 has three 10s. These are different, so they’re
gonna help us compare the numbers. We know five 10s are greater than
three 10s. And now we can see which number’s
greater. It doesn’t matter what the ones
show us. We’ve compared the hundreds and
they were the same. So we moved on to the tens, and we
saw that one lot of ten was greater than the other. 251 is greater than 234. The number that’s greater is
251.

Pick the symbol to compare the
numbers. 377 what 731.

In this question, we’re given two
numbers to compare. And because we can see that they
both have the same number of digits, we can’t just compare them by counting the
digits. We need to look at what those
digits are. These are both three-digit numbers,
so they both contain a number of hundreds, tens, and ones. And we’re told that we need to pick
the symbol to compare these numbers. Do you remember which symbols we’re
talking about here? Remember that when we use
comparison symbols like this, we always read the numbers and the symbols from left
to right. And also the widest part of the
symbol, the open end, always points towards the larger number. So if we used this symbol, we’re
saying that the first number is less than the second or we could say the first
number is greater than the second. And if we think they’re both the
same, then we’d used this symbol here.

Now, for many of you watching this
video, you might already know which number’s the least and which number’s the
greatest. You might have even spotted as we
read the question, we read those numbers out. But before we go through how to
find the answer, think for a moment: How do you know which is the greatest? What did you look for? Which part of the numbers did you
look at or listen for as they were read aloud? When we compare two numbers
together like this, we always look at the part of the number that’s worth the most
first. And in three-digit numbers like
this, that means the hundreds digit.

Our first number has a three in the
hundreds place. This is worth 300. But our second number has a
different digit. It has a seven in the hundreds
place worth 700. And because these two digits are
different, this is all we need to do to compare the numbers together. We know that three 100s are less
than seven 100s. And so a number that’s 300 and
something is always going to be less than a number that’s 700 and something, isn’t
it? 377 is less than 731. The correct symbol to use to
compare these two numbers together is the one that represents less than.

Choose the correct symbol to
compare the given numbers. 246 what 264.

Here are two three-digit numbers
that we need to compare here. And we need to choose the correct
symbol to write in between them to compare them. Do you remember what our three
symbols mean? The widest part of these arrow-like
symbols always points towards the greater number. So with this symbol, the greater
number’s going to come first. This symbol means is greater
than. Our second ~~number~~
[symbol] is facing the opposite direction, so we can see the smaller end of the
arrow comes first. This helps us remember that the
first number is less than the second. And, of course, when there is no
wide end or thin end and both lines are exactly the same distance apart, this is the
equals sign. And it means that they’re both the
same.

Now that we’ve reminded ourselves
about the symbols, let’s compare the numbers. Do you remember which part of the
number we need to compare first? It’s the part with the greatest
value. There’s no point looking at the
ones first and deciding that one lot of ones is greater than the other because the
number of hundreds might be different. The digits with the greatest value
are the hundreds digits. But we can see that both numbers
have a two in the hundreds place. They’re both 200 and something. So far, the numbers are equal,
aren’t they?

We need to keep comparing, so we
need to look at the digit that has the next greatest value. And this is the tens digit. Our first number has a four in the
tens place, which is worth 40. And our second number has a six in
the tens place, which is worth 60. Now that we’ve got two different
digits to look at, we can see straightaway which number is larger and which is
smaller. Four 10s are less than six 10s. So our first number is less than
our second, and we need to use the less than symbol. Although the number of hundreds in
our numbers was the same, the number of tens was different. And we used this to compare our
numbers together. 246 is less than 264. And so the correct symbol we need
to use to compare the numbers is the one that means is less than.

Which is greater, 91 or 736?

Now perhaps by seeing these numbers
or listening to them as they were read out, you could spot which of these two
numbers was greater. But stop for a moment and ask
yourself, how do you know? What was it about these two numbers
that told you which one was greatest. Let’s look at each number for a
moment and think about it. Our first number is made up of two
digits, a nine and a one. In other words, it’s made up of
nine of these, or tens. And, of course, we know it’s made
up of one of these, a one. But when we look at our second
number, we can see it’s longer, isn’t it? It contains more digits.

As well as a tens digit and a ones
digit, this number contains a hundreds digit too. There are seven 100s in this
number. Now often when we compare numbers,
we might look at the digits, compare the nine 10s with three 10s and so on. But here we’ve got a two-digit
number and a three-digit number. And we can see straightaway which
number’s greater. It’s the number with more
digits. The number with three digits is
greater than the number with two digits. The greater number out of 91 and
736 is 736.

What have we learned in this
video? We’ve learned how to compare
numbers up to 1000 by comparing the number of hundreds, tens, and ones.