Video: Adding Hundreds to Three-Digit Numbers

In this video, we will learn how to model adding a multiple of one hundred to a three-digit number and investigate which digits in the number change.

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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.

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