Lesson Video: Adding and Subtracting Lengths: Numbers up to 20 Mathematics

Video Transcript

Adding and Subtracting Lengths: Numbers up to 20

In this video, we’re going to learn how to measure objects in centimeters using numbers up to 20 and then use these to find the sum or the difference between the lengths of the objects that we’ve measured.

Here, we have two pieces of string. Let’s measure them to see how long they are. First, we’re going to need a ruler. And this ruler shows centimeters. Next, we’re going to need to move it so that it is next to our first piece of string. Is it lined up correctly? Well, at the end of this video, we’ll see that we can actually measure like this. But things are much clearer if we start measuring from zero. So, let’s line up zero with one end of our piece of string.

Is this right? We’ve matched up one end of our ruler with one end of our piece of string. No, even this isn’t right. We need to match up where the number zero is on the ruler. If you look, it’s a little bit in from the end. Not all rulers are the same, so we need to always look for the scale and look for zero on it. That’s better. Now, we can start measuring from zero.

And if we look at the other end of our piece of string, we can see that it’s six centimeters long. Let’s measure our second piece of string. It looks longer. First, we’ll line up our ruler. So, zero on the scale is level with one end of our piece of string. So, we can start measuring from zero. And if we look at the other end, we can see that it’s level with number eight. This piece of string is eight centimeters long.

Now, in this video, we’re going to use what we’ve measured to help answer questions, questions like, what is the total or what is the difference? To find the total, we need to add our two lengths together. Six plus eight equals 14. And so, the total of both lengths of string is 14 centimeters. If we put them both end to end, this is how long it would be.

To find the difference between both lengths, we could start with the longest length and take away or subtract the shortest length. We know that eight take away six is two. And so, the difference in length between both pieces of string should be two centimeters. You know, we can use our rulers to show this. If we draw a line down from six centimeters, we can see how long the first piece of string is compared with the second. And this shows us that there’s a difference of two centimeters. The pink piece of string is two centimeters longer.

First, we measured our objects. And then, we used our measurements to find the sum, or the total, and the difference. Now, let’s try some questions where we have to measure and then either find the sum or the difference.

If I stack these cubes on top of each other, what will the total height be?

In the picture underneath the question, we can see two cubes. At the moment, they’re side by side. But our question wants us to imagine stacking the cubes on top of each other. And if we do that, they’re going to become taller, aren’t they? And our question wants us to work out what the total height would be if we put one on top of the other. To find the answer, we’re going to have to measure these cubes. And to help us, we’ve got two rulers.

The way the first ruler has been positioned, we can see that zero on the scale is level with the bottom of the cube. So, we start counting at zero. And if we look at the very top of the cube, this is level with the number eight on our ruler. So, the first cube is eight. But eight what? If you turn your head and look at the ruler, you might be able to see the letters cm near the number zero. These letters stand for centimeters. Our first cube is eight centimeters tall.

Now, what about our second cube? Looks like it’s going to be a little bit smaller than eight, doesn’t it? To begin with, we need to check that our ruler is matched up so that zero is level with the bottom of our cube. So, we can start counting from zero. And if we look, the top of our cube is level with the number six. This cube is six centimeters tall.

Now that we’ve measured both of our cubes, we need to use what we’ve found to find the total height. Eight plus six equals what? Eight counters plus six more equals nine, 10, 11, 12, 13, 14. And because eight plus six equals 14, we can now use this to answer the question. If we stack the cubes on top of each other, their total height will be 14 centimeters.

How much longer is the bigger pencil than the smaller one?

Our picture shows two pencils, a red one and a yellow one. Now, if we look at how these pencils have been lined up, we can see that the pointed end, which is the end that we write with, are both level with each other. This makes it easier for us to measure and also to see which pencil is longer. If we look at the other end, which is the end with the rubber, we can see some dotted lines which clearly show us the red pencil is the bigger.

But our question wants us to find the difference between these two lengths because it asked us, how much longer is the bigger pencil than the smaller one? And to find out this, the first thing we’re going to have to do is to measure these pencils.

Let’s start with the red one. We can see that the pointed end of the pencil is level with the number zero on our ruler. And if we look carefully, we can see the letters cm. Which means that we’re measuring in centimeters. And the red pencil goes all the way from zero to the number 19 on our ruler. It’s 19 centimeters long. Now, let’s measure our yellow pencil. Again, we’re starting measuring from zero. But this time, the pencil only goes as far as the number 16. It’s 16 centimeters long.

Now, we can use what we’ve found to answer the question. How much longer is 19 centimeters than 16 centimeters? One way of finding the answer is to use our ruler as a sort of number track or number line. All we have to do is to count how many centimeters there are in between our two lengths. To get from 19 to 16, we can count one, two, three centimeters. It looks like the bigger pencil is three centimeters longer than the smaller one.

Another way we can find the difference is to subtract. So, we start with the longer length, which is 19, and we’re going to take away 16. So, we’re going to take away one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16. We’re left with three.

We found the same answer in two different ways. The bigger pencil is three centimeters longer than the smaller one.

How long are these worms altogether?

Now, before we answer this question, do you remember right at the start of the video, we talked about how it was much clearer if we start measuring from zero on a ruler. Just makes things a lot easier. But we also said that it was possible to measure things if they’re not starting from zero. To measure the first worm in our picture, we’re gonna have to start measuring from the number three.

Can you see how the tail end is level with three centimeters? And we’re going to have to start measuring out the second worm from one. Let’s look at the first worm first. Its length is from three centimeters all the way to nine centimeters. And we can use these two measurements to help us work out how long the worm is. How many centimeters is it from three to nine?

We could find the answer by counting on from three centimeters. One, two, three, four, five, six. Even though we haven’t measured from zero, we know this worm is six centimeters long. Our second worm goes from one on the ruler all the way to 10 centimeters. Now again, we can use these two measurements to help us find out how long he is.

Just like before, we could start at one and count on all the way to 10. Or another way to find the difference would be to use subtraction. 10 centimeters take away one centimeter leaves us with nine centimeters. The length of our second worm is nine centimeters.

So, to solve our problem, all we have to do now is to add our two lengths. Nine plus six equals what? Here’s part of a number track we could use to help us. We’ll start at nine, then count on one, two, three, four, five, six. Nine plus six equals 15. The length of our worms altogether is 15 centimeters.

Now, what have we learned in this video? Firstly, we’ve learned how to measure object in centimeters and then find the sum or the difference between the lengths we’ve measured.