Video Transcript
Adding Hundreds to Three-Digit
Numbers
In this video, we’re going to learn
how to model adding a multiple of 100 to a three-digit number. And as we do this, we’re going to
investigate which digits in the number change. Now let’s imagine you’re playing a
computer game and you’ve got one more level to go. And your score at the moment is
247. And to finish the level, you’ve got
to burst this green bubble, which is going to give you another 200 points. Let’s think about this number 200
for a moment. What do we know about it? Well, we know if we were going to
model it, we’d only need two 100s blocks. We wouldn’t need any tens or ones,
would we?
And if we were to show it using a
place value grid, we’d only really need to think about the digit two in the hundreds
place. We’d still need some digits in the
tens and the ones to show that they’re there, but they’d be zeros. 200 is what we call a multiple of
100. In other words, it’s a sort of
number we get when we add hundreds together. 100, 200, 300, 400, 500. These are all multiples of 100. And they’re all the sort of numbers
that we’re going to be adding to three-digit numbers in this video. So that’s why that bubble says 200
on it. It’s because to find the answer, we
need to add together our score, which is 247, and this multiple of 100.
So let’s begin by thinking about
the three-digit number that we have already. Because it’s got three digits in
it, we know it’s made up of some hundreds, tens, and ones. It has two 100s, four 10s, and
seven ones. But how are these digits going to
change if we had some more hundreds to it, like we’re about to do? Let’s find out. We could start by modeling our
score using place value blocks: two 100s, four 10s, seven ones. Now when we burst that bubble,
we’re going to need to add 200 to our score. And as we’ve said already, because
200 is a multiple of 100, we don’t need any 10s or ones blocks. We just need to add two 100s. What is 247 plus 200? Well, if we put all of our place
value blocks together, we can see that instead of two 100s blocks, we now have two
more. So that’s four 100s blocks
altogether.
The total is made up of four
100s. But the number of tens and ones
hasn’t changed at all, has it? We still have four 10s and seven
ones. 247 plus 200 equals 447. And we can actually hear how the
hundreds digit is the part that changes when we read the numbers: 247, 447. So our total score when we complete
this level is going to be 447. You know, we don’t always have
place value blocks with us as we’re playing computer games, do we? So thankfully, there are other ways
to add hundreds to three-digit numbers.
A different method is using a
number line to help us. Let’s imagine we’ve been asked to
add together 629 and 300. So we think to ourselves, right,
I’m going to use a number line to help. I’m gonna start by drawing a
line. And I don’t really want to start at
zero because I’m adding on from 629. So I’ll draw an arrow to show that
my number line goes backwards and I’m going to label 629 at one end of my number
line. And perhaps I’ll draw an arrow at
the other end to show that it continues on. Now, next, what I’d do is have a
look at the number I need to add on to 629 and I might think to myself, that’s a
multiple of 100. It’s a number that only contains
hundreds. There are no tens or ones to worry
about, just three 100s. So I can use my number line to
count on three lots of 100.
Now what we can do to represent
this on our number line is to draw each jump by showing an arrow line like this. And because we’re adding hundreds,
we could label it plus 100. And we’re going to do this for
every jump of 100 that we make. 100 more than 629 is 729. Then we have 829 and then finally
929. We’ve made three jumps of 100,
which is the same as adding 300, and we’ve ended on the number 929. Did you notice how the last part of
our number didn’t change? 629 and then 729, 829, 929. Because we’re adding a number of
hundreds, the tens and the ones digits don’t change.
And that’s why if we have a
calculation like 492 plus 400, for example, it never really makes sense to use
something like the column method. We’d still have to start by adding
the ones, two plus zero, then the tens, nine plus zero. A bit of a waste of time really
because we know that these digits aren’t going to change. It’s only the hundreds digit that
is going to change. So that’s why we’re not looking at
things like the column method here. We’re looking at ways where we can
add the hundreds and almost forget about the tens and the ones because they’re just
zeros.
So we’ve looked at using place
value blocks and number lines. Let’s just try one more method by
breaking this number apart. Now although you could probably do
this breaking apart in your head, let’s use a part–whole model to show what we’re
doing. And our whole amount is 492. Now, as we’ve just said, we want to
wait and work out the answer where we almost forget about the tens and the ones and
we just think about the hundreds. So let’s break off our
hundreds. And we can see that in the number
492, there are four 100s. So we’ll write the number 400 in
our first part here, and then the tens and the ones at the left are worth 92. So we’ll put this part over on the
left here. We won’t worry about that.
Now, to the number 492, we’re
adding 400. We already have four 100s, so we
just need to add another four 100s. And 400 plus 400 equals 800. So let’s rub out our part that says
400. And let’s change it to 800. Now of course, this part–whole
model doesn’t make sense anymore, does it? So we’re going to have to change
the whole amount at the top. In other words, we’re gonna have to
put our two parts together, 800 and 92. And of course, this is the
answer. This is the total we’ve made,
892.
Now as we say, we could’ve done
that in our heads. We could’ve looked at 492 and
thought to ourselves, “Well, there are four 100s. I need to add another four
100s. That’s gonna make eight 100s. The answer is 892.” So there are all sorts of methods
we could use to add hundreds to three-digit numbers. And we’re going to try using these
as we answer some questions now. Let’s see whether you remembered
what we’ve learned.
Fill in the blank: 207 plus 500
equals what.
In this question, we’ve got two
numbers to add together. Now they’re both three-digit
numbers. But if we look carefully at our
second three-digit number, we can see that it’s a little bit of an easier number to
add. This is because although it
contains a number of hundreds, five 100s, it doesn’t contain any tens or ones. It’s what we call a multiple of
100. And because it’s made up of five
100s, we can count in five 100s to find the answer. Let’s start with the number
207. And let’s count on it hundreds five
times.
And we’ll find out which number we
say is the last number. So we’ll start with 207 and then
307, 407, 507, 607, 707. We know that the number 500 is made
up of five 100s but no tens and no ones. So that’s why as we read each
number, they always ended in seven. 207 becomes 307, 407, 507, and so
on. We counted on five 100s from
207. And the last number we said was the
answer. 207 plus 500 equals 707.
Count in hundreds to find the
total. 433 plus 300 equals what.
In this question, we need to find
the total of 433 and 300. Now the number that we’re adding on
here, 300, is a multiple of 100. It’s worth three 100s, and that’s
why we’re told to count in hundreds to find the total. Now underneath our question, we can
see a number line, and we can use this to help us find the answer. In other words, we can use it to
count in hundreds. Now the first number that’s marked
on our number line we can see is the first number in our addition, 433. And then we’ve got one, two, three
intervals until we get where we want to get to. So we can see that to add 300, we
could use these intervals as jumps of 100. Three jumps are the same as adding
300.
Now the number 433 is made up of
four 100s, three 10s, and three ones. But as we’re adding hundreds, we
don’t need to think about the tens and the ones. We just need to think about how our
four 100s are going to change. So let’s count in hundreds three
times, 433 and then 533, 633, 733. We counted in hundreds three times
to find the answer. And we used a number line to help
us recall this. Because we were adding a multiple
of 100, we knew that the tens and the ones in 433 were not going to change. Our answer was going to end in 33
too. And so we found that 433 plus 300
equals 733.
Find the total by first adding the
hundreds. 265 plus 300 equals what.
In this question, we’ve got an
addition and the first number is a three-digit number, 265. And the number that we need to add
to it is a three-digit number too, 300. Now because the number that we’re
adding here ends in two zeros, we know that it’s a multiple of 100. In other words, it’s a number that
we get if we count in hundreds. We wouldn’t need any tens or ones
if we wanted to model it using place value blocks, just hundreds. And if we were to model it using
arrow cards, we’d only need a 100s arrow card, again, not tens or ones. And this is why our question tells
us we can find the total by first just adding the hundreds. And if you look at our first number
265, can you see that it’s been written with a sort of part–whole model
underneath?
Now we can complete this to show
how we can break up the number 265 because as we said already all we need to do is
to think about the hundreds. And we know 265 is made up of two
100s. So we could break apart our two
100s and we put them in this part here. And then of course, what’s left is
65, our tens and our ones. And we’ll leave these behind over
here. We’ll come back to them in a
minute. Now that we’ve broken up our number
so we can see these two 100s separately, we can just add the hundreds together. Two 100s plus another three 100s
makes 500.
So our answer is gonna be made up
of 500 and the tens and the ones that we had from before, which is 65. And if we combined 500 and 65 back
together again, we get the answer 565. Because we were adding a multiple
of 100 here, we found our total by adding the hundreds together. There are two 100s in 265 and by
splitting our number up, we could just add these two 100s with the three 100s. Our tens and our ones didn’t change
at all. 265 plus 300 equals 565.
If there are 342 boys and 200 girls
in a school, how many students are there?
In this question, we’re given two
parts of a whole amount. If there are 342 boys and 200
girls, to find the number of students there are, we know we need to add these two
amounts together. In other words, what is 342 plus
200? Now there’s something interesting
about the number that we’re adding on to 342 here. Can you see what it is? 200 is a multiple of 100. It’s what we get when we count on
in hundreds twice: 100, 200. And so to add 200 to 342, all we
have to do is to think about the hundreds digits.
And you know, before we even start,
we can make a prediction here. We can say that the number of tens
and ones are going to stay the same. 342 has four 10s and two ones. And that’s why we know that our
answer is going to have four 10s and two ones, too. We just need to think about
combining our two 100s together. That’s 300 and another 200. Now we know three plus two equals
five. So 300 plus another 200 is going to
make 500. We found the answer quickly here,
simply by adding on the hundreds that we needed to. If there are 342 boys and 200 girls
in a school, the number of students that there are altogether is 542.
So what have we learned in this
video? We’ve learned how to model adding a
multiple of 100 to a three-digit number. We’ve also investigated which
digits in the number change when we do this.
