Lesson Video: More and Less: One, Ten, One Hundred, or One Thousand Mathematics

In this video, we will learn how to use place value to add or subtract 1, 10, 100, or 1000 from four-digit numbers and complete number patterns.


Video Transcript

More and Less: One, 10, 100, or 1,000.

In this video, we’re going to learn how to use place value to add or subtract one, 10, 100, or 1,000 from four-digit numbers. And we’re going to use what we found out to help us complete number patterns.

A video of these penguins singing has been posted online. The counter in the top corner shows how many people have watched it already. Let’s model this number using place value blocks. The number on the counter shows two 1,000s, four 100s, eight 10s, and seven ones. 2,487 people have watched this video already.

Now let’s imagine one more person starts watching the video. Firstly, how would we expect our place value blocks to change? Well, one more person is worth one more ones block. So we could model one more person watching the video by adding this ones block here. By adding one, it’s the number of ones that has changed. Instead of 2,487 views, the video has now had 2,488 views. If we add one, the ones digit changes. Let’s carry on counting in ones and watch how this digit changes.

So we’ve got 2,488, and if we count on one more, we’ll have 2,489. It’s only that ones digit that’s changed here, isn’t it? And if we count on one more — wait, what’s happening here? We’ve only added one more one, but this time it’s had more of an effect on our number. Both the ones digit and the tens digit have changed. And of course, if we put our minds to it, we know why this is, don’t we? If we have nine ones and we add one more, we cross what we call a tens boundary. We make another 10. And with our place value blocks, we exchange 10 ones for one 10. So 2,489 became 2,490.

And this is an important fact to remember about adding or subtracting ones. The ones digit will always change, but at times this will have an effect on some of the other digits too. We’re quite close to a good example of this because if we carry on counting in ones up until we get to 2,499 and then add one more, not only there’s a number of ones change, as we’d expect, but also the number of tens and hundreds. The number that is one more than 2,499 is 2,500.

Let’s imagine now that the number of views of this video have gone up quite a lot, and we’re now on 5,138. And as soon as the counter gets past 5,000, it starts behaving a little bit differently. Instead of showing each individual person or counting in ones, it now counts in tens. Let’s count forwards in tens and see what happens. 5,138, 5,148, 5,158, 5,168. Can you see what’s happening here? As we’re finding one more 10 each time, the tens digit is changing. But is the tens digit the only digit that changes? Well so far, it has been. But eventually, we’ll get to a number where other digits are going to change too.

Let’s reset our counter back to 5,138. And let’s look at the numbers that have come before this. Let’s count back in tens. 10 less than 5,138 is 5,128 then 5,118. So far, it’s just the tens digit that’s changing again. This time it’s going down by one, 5,108. But now there’s a zero in the tens place. How can we show one more lot of 10 less than this? Well once again, we’re going to need to cross a boundary, and this time it’s a hundreds boundary. In other words, our hundreds digit, which is at the moment one, is going to change. 10 less than 5,108 is 5,098.

This time, both the tens digit and the hundreds digit have changed. And if we carried on counting in tens, eventually the thousands digit would change too. And it doesn’t matter how far we count in tens forwards or backwards. The ones digit will never change. Can you see how all of our numbers have eight ones in them? And just to include the other digits, the tens digit will always change. And eventually, the hundreds and thousands digits will sometimes change. Let’s try answering a question now where we have to practice what we’ve learned about counting 10 more and 10 less.

What is 10 more than 1,212? What is 10 less than 1,212?

This question is all about how numbers change when we find 10 more or 10 less than them. And it’s the same number we’re starting from each time: 1,212. Now because we’re counting in tens here, finding 10 more or 10 less, we can use our knowledge of place value to help us because one of the digits in a four-digit number is worth tens. 1,212 contains one 1,000, two 100s, one 10, and two ones. In the first part of our question, we’re asked to find 10 more than this number. Well, as we’ve just said, 1,212 contains one 10. And if we find 10 more than this number, we need to add one more 10. We’ve added another 10s block, and now we have two 10s. None of the other digits have changed. We still have one 1,000, two 100s, and two ones. But instead of one group of 10, we now have two. 10 more than 1,212 is 1,222.

Now let’s use the same idea, but this time we’re going to find 10 less than our number. So, just like before, we can start with 1,212. And which part of our number do you think is going to change if we need to find 10 less than this? Well with a question like this, we always need to start by looking at the tens digit. Our number contains one 10. So if we find 10 less than this, we’re going to need to take away this 10. Instead of one 10, we now have zero tens. Once again, the thousands digit, the hundreds digit, and the ones digit in our answer are exactly the same. They haven’t changed at all. However, because we have 10 less instead of one 10, we need to write a zero in the tens place.

We’ve used our knowledge of place value to find 10 more and 10 less than the same number. 10 more than 1,212 is 1,222, and 10 Less than 1,212 is 1,202.

At the start of this video, do you remember which numbers we said we were going to be adding or subtracting? We said there were going to be one, 10, 100, or 1,000. These are the four place values in a four-digit number, and this is why we don’t always have to model numbers using place value blocks or counters. We can find an answer just by looking at the digits in a particular column, just like what we’ve discussed already when talking about tens and ones. If we want to find 100 more or less than a number, we know the digit in the hundreds place will definitely change because, of course, we’re finding 100 more or less.

And depending on how many hundreds we have, the digit to the left of this, so that’s the thousands digit, may sometimes change. But the two digits to the right of the hundreds place, that’s that tens and the ones, will stay the same. They’re not going to change at all. So that’s what happens if we add or subtract 100. For example, if we find 100 more than our number, instead of having a six in the hundreds place, we simply need to alter that digit to one more 100, 700. It was the hundreds digit that changed. The thousands digit this time didn’t change, and neither did the tens or the ones. They’re never going to change.

And using this idea, what do you think is gonna happen if we find 1,000 more or 1,000 less? We know that the digit in the thousands column itself will definitely change. But the digit in the columns to the right, that’s the hundreds, the tens, and the ones digit, are never going to change. For example, if we find 1,000 less than our number, we just look to the thousands digit and we say to ourselves, “Well, there’s 3,000 at the moment, our number is 3,747, and we need to show one less 1000.” So instead of 3,000, we now have 2,000. We have gone from 3,747 to 2,747. And hopefully, you can see that those last three digits haven’t changed at all.

Now that we’ve looked at all four place values, let’s have a go at answering some more questions. Each time we’re going to use our knowledge of place value to help us work out how the numbers are going to change.

Find the number that is 1,000 less than 2,599.

What skills do you think you need to have to be able to find 1,000 less than a number? Perhaps you may think that the main skill is subtraction. After all, we need to find 1,000 less than a four-digit number here. But in a way, the most important skill that we need is a knowledge of place value. We know there’s such thing as a thousands column or a digit in a number that’s worth 1,000. And if we know where that thousands digit is in a number, we can work out how our number is going to change.

In this question, we’re given a number 2,599. Now you’ve probably heard as we’ve read that how many thousands we’ve got and which digit is in the thousands place, but let’s write this number in a place value grid just to help us. This number contains two 1,000s, five 100s, nine 10s, and nine ones. And if we want to find the number that is 1,000 less than the number in our grid, we need to be looking at the digit in the thousands place. At the moment, our number contains two 1,000s as we’ve just said. But if we want to find the answer that is 1,000 less than this, instead of two 1,000s, we’re going to need to show 1,000.

In this example, we found 1,000 less than a number by subtracting one from the digit in the thousands column. 1,000 less than 2,599 is 1,599.

Complete the following table:

Let’s start by taking a moment to look at the table that we’re given. In the first column, we can see a four-digit number, 2,370. And then our next four columns tell us what we need to do to this number. First, we need to write down how our number is going to change if we take away one then if we take away 10, 100, or 1,000. To help us understand how our number is going to change, we can think about the place value of each digit. 2,370 is made up of two 1,000s, three 100s, seven 10s, and zero ones.

Now, before we start, here’s a quick question that’s quite interesting to think about. Which of these four columns is going to be most difficult to fill in, taking away one, 10, 100, or 1,000? I’m guessing a lot of you will think either 1,000, because it’s larger, or even they’re all going to be just as difficult as each other. You know, I wonder whether the trickiest subtraction is actually the first one. If we want to take away 10, 100, or 1,000, we can see that in each of the tens, the hundreds, and the thousands places, we have a digit. We’ve got something to take away. But if we want to take away one and we already have zero ones, we need to give it a little bit more thought. We need to look at the next column along to the left.

Our number contains seven 10s and zero ones. In other words, it’s something thousands something hundreds and seventy. And if we take away one from 70, we get 69, don’t we? The ones digit has changed, which we’d expect it to, but also the tens digit has changed too. Let’s go back to our starting number, and this time we’re going to think about how it’s going to change if we take away 10. This time, we already have some tens in the tens place. This is going to be a little bit easier to do. We have seven 10s. And so if we take away 10, instead of seven 10s, we’ll be left with six 10s. By finding 10 less than our number, the tens digit has changed.

Back to our starting number, this time we’re going to take away 100. Again, we already have a digit greater than zero in this column, so it’s going to be fairly straightforward. We have three 100s in 2,370, and if we subtract one of these hundreds, we’ll be left with two 100s. Again, it’s only one digit that’s changed, this time our hundreds digit. Finally, we need to take away 1,000, so we’ll look to our thousands digit, see that we’ve got two 1,000s there. And one less than this is 1,000. 1,000 less than 2,370 is 1,370.

To help us answer this question, we used a place value grid, and this helped us think carefully about how each digit in our number was going to change as we took away one or 10 or 100 or 1,000. We also found that the subtraction we needed to think about most was when we took away one because we had a zero in the ones place. So taking away one also affected the tens digit. We’ve completed the table using the following numbers: 2,369, 2,360, 2,270, and 1,370.

So what have we learned in this video? We’ve learned how to use place value to find one, 10, 100, or 1,000 more or less than a four-digit number.

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