Lesson Video: Comparing Lengths Indirectly | Nagwa Lesson Video: Comparing Lengths Indirectly | Nagwa

Lesson Video: Comparing Lengths Indirectly Mathematics

In this video, we will learn how to compare the length or height of two objects by comparing them to a third object, either by looking at them or by measuring with square units.

09:40

Video Transcript

Comparing Lengths Indirectly

In this video, we’re going to learn how to compare the lengths of two objects by comparing their lengths to a third object, either by looking at them or measuring with square units. Here are two plants, one in a red pot and one in a blue pot. Now, let’s imagine that these plants are in different parts of our garden. They’re not right next to each other, so it’s difficult to tell which one is taller than the other. We can’t compare the height of the two plants directly just by looking. But there is a way that we can still tell whether one plant is taller than the other. Here’s a third plant. Now, if we compare the height of both of the other plants with this new plant, we could be able to tell which is taller.

First, let’s compare the plant in the red pot with the plant in the orange pot. We can see that the plant in the red pot is taller. Now, we can do the same thing with the plant in the blue pot. If we compare the plant in the blue pot with our third object, which is the cactus in the orange pot, we can see that it’s shorter than the cactus. One of our plants is taller than the cactus and the other plant is shorter. Because we’ve compared both the first and the second plant with the same third object, we know enough to be able to compare the first two plants with each other. We didn’t need to put them side by side, but we can still tell that the plant in the red pot is taller than the plant in the blue pot.

And you know, the third thing that we compare our objects to doesn’t even have to be another object. These two carrots aren’t next to each other, so they’re difficult to compare the length of directly. But instead of using another object, we could use square units. Here’s a chain of six squares. We’ll call our first carrot, carrot A. Let’s compare the length of carrot A with our square units. The length of carrot A is shorter than the six units. Let’s do the same with carrot B. Carrot B is ever so slightly longer than our six square units.

Because we’ve compared both carrots with the same object, we can now say which of the two carrots is longer than the other. Carrot B is longer than carrot A. And we didn’t even need to put them next to each other to tell this. Let’s have a go at answering some questions now where we have to compare the lengths or the heights of two objects. And we’re going to work out the answer by comparing their lengths or heights with a third object.

The blue pencil is longer than the orange pencil. The orange pencil is longer than the green pencil. Which pencil is longest?

In this question, we’re given two statements where pencils are compared with each other. There are three different pencils altogether. There’s a blue one, an orange one, and a green one. And we’re asked, which of these pencils is the longest? So we need to compare these three pencils together. But none of the sentences and none of the pictures show all three pencils at the same time. They only compare two pencils at a time. So we need to use the facts that we’re given to try to work out which pencil is longest.

Our first fact, and the picture underneath it, tells us that the blue pencil is longer than the orange pencil. To help us show this fact, perhaps, we could draw a line like this. We could put things that are shorter towards the left of the line and things that are longer towards the right of the line. To show that the blue pencil is longer than the orange pencil, we could put a blue and an orange counter on our line. Because the blue pencil is longer, we’ve put the blue counter on the right of the orange one. In our second sentence, the blue pencil isn’t mentioned at all.

This time, the green pencil is compared with the orange pencil. And we’re told that the orange pencil is longer than the green pencil. In other words, the green pencil is shorter than the orange pencil. And we can see that from the picture. Because the green pencil is shorter, we’re going to have to put a green counter to the left of the orange counter on our line. If we look at our line, we can see that the blue pencil is the longest. The blue pencil is longer than the orange pencil, which is longer than the green pencil. The longest pencil is blue.

Matthew is taller than Daniel and shorter than Benjamin. Who is the shortest?

In this question, we need to compare the heights of three different boys. There’s Matthew, Daniel, and Benjamin. The question asks us, who is the shortest? But we aren’t given any pictures or measurements to help us. How can we compare these three children’s heights? Well, we’re given one sentence to help us here. And in this sentence, we’re given two facts. We know what two children’s heights are compared with Matthew. And we can use this to help us find the answer. To help us solve the problem, let’s draw a line. And we’ll go from left to right, shorter to taller.

So the first part of our sentence compares Matthew with Daniel. And we’re told Matthew is taller than Daniel. There we go. So we’ve written the letters M and D on our line. Because we know Matthew is taller than Daniel, we’ve written the M to the right of the letter D. The second fact that we’re told is also to do with Matthew. But this time we’re comparing Benjamin’s height with Matthew. So Matthew is taller than Daniel. But he’s shorter than Benjamin.

Now, if Matthew is shorter than Benjamin, we’re going to have to write the letter B for Benjamin somewhere here. Benjamin is taller than Matthew. And because Matthew is taller than Daniel, Benjamin is the tallest. But our question asks us, who is the shortest? We can use the diagram we’ve drawn to help us. The shortest out of the three boys is Daniel.

Complete the following statements with taller or shorter. The rabbit is what than the eight blocks. The carrot is what than the eight blocks. The rabbit is what than the carrot.

This is a comparing problem where we’re comparing the heights of different objects. And in the final sentence, we have to either say that the rabbit is taller than the carrot or the rabbit is shorter than the carrot. But unfortunately, we haven’t got the rabbit and the carrot side by side in one of the pictures. To find the answer, we have to compare both objects, the rabbit and the carrot, with a third object. And the third object, as we can see from the picture, is eight blocks. And these eight blocks are in the tower.

Let’s start by comparing the rabbit with the eight blocks. Is the rabbit taller or shorter than the eight blocks? We can see that the top of her ear comes above the tower, doesn’t it? The rabbit is taller than the eight blocks. Now, let’s compare the carrot with the same eight blocks. And if we compare the height of the carrot with the height of the blocks, we can see it doesn’t reach all the way to the top, does it? We have to use the word shorter to complete this sentence. The carrot is shorter than the eight blocks.

So if the rabbit is taller than the eight blocks and the carrot is shorter than the eight blocks, we now know which is taller out of the rabbit and the carrot. The rabbit is taller than the carrot. The rabbit is taller than the eight blocks. The carrot is shorter than the eight blocks. And that’s how we know the rabbit is taller than the carrot. The missing words are taller, shorter, and taller.

Now, what have we learned in this video? We’ve learned that we don’t always need to see two objects next to each other or measure them to know which is longer or shorter. Instead, we can compare the lengths or heights of two objects by comparing each one to a third object.

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