Lesson Video: Comparing Masses Indirectly | Nagwa Lesson Video: Comparing Masses Indirectly | Nagwa

# Lesson Video: Comparing Masses Indirectly Mathematics

In this video, we will learn how to indirectly compare the masses of two objects by using scales or nonstandard units to compare them to a third object.

14:51

### Video Transcript

Comparing Masses Indirectly

In this video, we’re going to compare how heavy two objects are. We’re going to do this by comparing their masses to a third object. Let’s imagine you’re out shopping for a new mobile phone, and there are two phones that you like the look of. There’s this black one here with a big screen or this brightly colored red one with the buttons. Now, let’s imagine one of the main things that’s gonna help you decide which one of these phones to buy is not the price or what it can do, but how heavy it is. You want it to feel light in your pocket. And so, you ask yourself, “Which phone is the lightest?” Which one weighs less?

Now, of course, the quickest way to answer this question will be to get a set of balancing scales like this and put one phone on either end. And we’d be able to tell, just by looking at how the scales move, which phone is the lightest. But let’s imagine that we can’t compare the phones directly like this. Maybe they’re in different shops. Whatever the reason, we’re going to need to compare them, but not side by side. Is there a way we could work out which phone is lightest without putting them on the same set of scales? Well, there is, and it involves using a third object. Let’s use this mug.

Now, if we compare the mass of both mobile phones one by one with the mug, it might help us see which one is lightest. Let’s see if it helps. Here is a set of scales. And to begin with, we’re going to compare the black mobile phone and the mug. Oh! Can you see what’s happened here? The end with the mobile phone on it has gone down. And this is meant that the end with the mug on it has gone up. Now, we can look at these scales and in a way we can read them. We can tell something about both objects. We can see that the black phone is heavier than the mug.

Now, let’s compare the red phone with the mug. Something different happened this time. This time, the end with the mug on it has gone down, and this has made the end with the red mobile phone on it go up in the air. Again, we can look at this set of scales, and we can read it. What does the picture tell us? It tells us that the red phone is lighter than the mug. We’ve compared both mobile phones to a third object, and now we can see which phone is lightest. It’s the red one, isn’t it? The black phone is heavier than the mug, but the red phone is lighter than the mug. And so, we can say that the red phone is lighter than the black phone.

Another way we could compare the masses of two objects without putting them directly on the same set of weighing scales is by using units of measurement to help us. Let’s compare this blue mobile phone with the black one. But instead of using a third object to help, let’s use these plastic blocks. The blue phone weighs the same as three plastic blocks. We know this because the scales are balanced. But the black phone only weighs the same as two plastic box. We know that two blocks are going to be lighter than the three blocks, and so the black phone is lighter than the blue phone. Again, we’ve managed to work out which phone is lighter without having to compare them directly.

Let’s practice now what we’ve learned, and we’re going to answer some questions where we need to compare the masses of objects.

Which item is lightest, the bottle of milk or the apple?

In our question, we’re asked to find the item that’s lightest, in other words, the object that weighs the least. If we had a set of scales and we put the bottle of milk on one end and the apple on the other, we’d see straight away which item was lightest. But in this question, we’re not comparing these objects directly. Instead, we’re using a third object to help. Can you see what it is? It’s this pot of strawberry jam. By comparing both objects with the pot of jam, we should be able to work out which one’s the lightest.

Let’s look at the pictures. In the first picture, we can see that we’re comparing the bottle of milk with a pot of jam. The bottle of milk has pushed that end of the scales right down, hasn’t it? And this has lifted the pot of jam in the air. So, what can we say about the bottle of milk? The bottle of milk is heavier than the pot of jam. Now, let’s look at our second picture. This time, we’re comparing the apple with the pot of jam. And this time, it’s the end with the pot of jam on it that’s weighed down, and it’s the end with the apple on that’s moved upwards. So, what can we say about the apple? The apple is lighter than the pot of jam, isn’t it?

We’ve compared both our objects with a pot of jam. And we can use the information we’ve got to work out which item is lightest. We know that the bottle of milk is heavier than the pot of jam, but the apple is lighter than the pot of jam. So, we know that the apple must be lighter than the bottle of milk. The lightest item is the apple.

Which item is heaviest? Is it the watermelon or the pot of jam?

In this question, we need to spot the heaviest item. We know that the word “heaviest” means that it weighs the most. And If we had a set of balancing scales like these and we put a watermelon on one end and that pot of jam on the other, we’d be able to see straight away which item was heaviest. But in this question, we’re not comparing the masses of these two objects directly like this, even though it’d be easier. We’re comparing both objects with a third object. Can you spot it? It’s a bottle of milk. First, we’re going to compare a pot of jam with the bottle of milk. And then, we’re going to compare the watermelon with the bottle of milk. And we’re going to use this to help us work out which is heaviest out of the watermelon and the pot of jam.

So what can we see in the first picture? Well, in this picture, we’re comparing the pot of jam with the bottle of milk. And we can see that the end of the scales that has the bottle of milk on it has gone down. This has meant that the end with the pot of jam on it has gone up in the air. And this tells us something about how heavy these items are, doesn’t it? What can we say about the pot of jam? The pot of jam is lighter than the bottle of milk.

On the second set of scales, we’re comparing the watermelon with the bottle of milk. This time, it’s the end with the watermelon on that’s gone down, and this has lifted the end with the bottle of milk on it up in the air. What can we say about the watermelon then? The watermelon is heavier than the bottle of milk. And we can use what we’ve found to compare our two objects. Because we know the pot of jam is lighter than the bottle of milk but the watermelon is heavier than the bottle of milk, we can tell which item is heaviest. It’s the watermelon. The watermelon must be heaviest.

Order the animals on the scales, a duck, a penguin, and a rabbit, from lightest to heaviest.

And if we look at the bottom of the question, we can see that we have three possible answers to choose from. In this question, we’re shown some animals on some sets of weighing scales. There’s a duck, which appears twice. Then, we have a penguin and a rabbit. And although we don’t weigh all three objects at the same time, we’ve got enough information here for us to be able to put these animals in order from lightest to heaviest.

Let’s draw a line to help us. Because we’ve been asked to go from lightest to heaviest, let’s put the word lightest on the left and heaviest on the right. Now, the idea behind this line is it is going to work a little bit like a number line. But instead of putting numbers in order, we’re going to be putting these animals in order. Let’s look at our first set of weighing scales. What can we see? We can see the end with the penguin on it has gone down, and this has pushed the end with a duck on it upwards. Although we’ve only compared two animals so far, we can tell which one’s heavier, can’t we? The penguin belongs somewhere at this end of our comparing line because it’s heavier than the duck. And we’ll put the duck at this end because it’s lighter than the penguin.

Now, let’s look at our second set of scales. On these scales, we’re comparing the rabbit and the duck. This time, it’s the end with the duck on that’s moved downwards, and the end with the rabbit on is lifted up. We can say then that the duck is heavier than the rabbit. And if we look at our line and we know that the duck is heavier than the rabbit, we’re going to have to draw the rabbit to the left of the duck towards the lighter end of our line, aren’t we? The rabbit is lighter than the duck, and the duck is lighter than the penguin.

Now that we’ve put our animals in order from lightest to heaviest, can you spot the correct order in the answers? It’s this one. We found that the penguin was heavier than the duck, but that the duck was heavier than the rabbit. And so, if we order the animals from lightest to heaviest, the correct order is the rabbit, then the duck, then the penguin.

Here are three objects. The feather is lightest, and the car is heaviest. Which scales represent the correct masses?

In this question, we need to compare the masses of three objects. There’s a ball, a feather, and this toy car here. Now, we don’t need to weigh these objects to be able to put them in order of mass. We’re given some clues to help us. Firstly, we’re told that the feather is lightest. We could draw a line to help us here. At this end, we can put the objects that are lightest and at the other end the objects that are heaviest. So, our line goes from lightest to heaviest. Now, we’re told that the feather is lightest, so let’s sketch our feather in the correct place. It belongs here, doesn’t it?

The next piece of information we’re given is that the car is heaviest. Let’s sketch the car on our line then. It belongs at this end. Now because we know the feather is lightest and the car is heaviest, we know where to draw the ball too. We know that the ball weighs somewhere in between. It must be heavier than the feather but also lighter than the car. Now, we know what order to put our objects in according to their mass. We can look at the sets of scales that we’re shown. We’re asked which scales represent the correct masses. Sketching that line was useful, wasn’t it? So, let’s do the same as we compare these scales.

On the very first set of scales, we can see that the end that has the toy car on it has gone down and the end with the ball on it has lifted up. This tells us that the toy car is heavier than the ball. So wherever we draw the ball on our line, we need to draw the car to the right of it. It’s heavier than the ball. The second set of scales compares the ball and the feather. And we can see that the end that has the ball on it has gone down and this has lifted the end with the feather up in the air. We can say that the feather is lighter than the ball. This means that we need to draw the feather to the left of the ball, don’t we? We’ve used our first picture to put the objects in order.

Now, let’s look at our second picture. On the first set of scales, we’re comparing the ball with the feather. And the end with the feather on has gone down, and this has lifted the end with the ball on up in the air. We can see in this picture the feather is heavier than the ball. So wherever we draw the ball on our line, we need to draw the feather to the right of it. In this picture, it’s heavier. The second set of scales compares the ball with the car. This time, it’s the end with the ball on that’s gone down, and the end with the car has been lifted up. We can say then that the ball is heavier than the car. Or If we say it in a different way, the car is lighter than the ball. So, we need to draw the car now to the left of the ball.

We were told to begin with that the feather was lightest and the car was heaviest. And we used these two facts to put the objects in order from lightest to heaviest: feather, ball, car. By looking at all the sets of scales, we can see that only one picture represents the correct masses. Because the car is heavier than the ball and the feather is lighter than the ball, if we put the objects on these scales in order, it matches the facts we already know. The feather is lightest, and the car is heaviest.

What have we learned in this video? We’ve learned how to compare the masses of two objects by using scales to compare them to a third object.

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