Lesson Video: Converting Mass: Kilograms and Grams Mathematics • 3rd Grade

In this video, we will learn how to measure masses using mixed units, convert between masses using partitioning, and compare masses given in grams and kilograms.

18:22

Video Transcript

Converting Mass: Kilograms and Grams

In this video, we’re going to learn how to measure masses using mixed units, in other words in both kilograms and grams. We’re also going to learn how to convert between masses using partitioning and to compare masses given in grams and kilograms.

Now I don’t know if you knew, but the average three-eyed, hairy, blue monster weighs three kilograms. We can see this from the one sitting on the set of scales, can’t we? Let’s think about what our set of scales show for a moment. Like with any measurement, we’ve got a number. In this case, it’s the number three. And then we’ve got a unit of measurement. We always need a unit of measurement, don’t we? And in this example, our unit of measurement is represented by the letters kg. And we know these letters represent a unit of mass, don’t we? Kilograms.

Just to remind us, a kilogram is about the same mass as a liter of water, just helps us picture how heavy it is. But you know, kilograms aren’t the only way that we can measure the mass of this monster. If we zoom in on our set of scales, we can see two buttons. One’s labeled kg, which we can see is lit up. But the second one is labeled with the letter g. Can you remember what units of measurement is represented by the letter g when we’re talking about mass? g stands for grams. And as a little reminder, a gram is about the same mass as a paper clip. So it’s very light.

Now what do you think is going to happen if we press the button that represents grams on our set of scales? We’ve already said that the monster weighs three kilograms. Surely, we can’t measure its mass in grams too. But you know, we can. If we think about measuring time for a moment, if somebody asked you how long it takes you to get to school, you might give them a number in minutes. But that doesn’t stop you measuring how long it takes you in seconds. It’ll just be a really big number, that’s all. And usually we try to avoid really big numbers if we can help it.

And in the same way, we can use different units of measurement to measure the mass of this monster. It’s just if we use grams, it’s going to be a bigger number, that’s all. Now before we press this button, let’s try to predict how many grams our monster weighs. And to help us do this, let’s try to remember a fact about grams and kilograms. Do you remember how many grams make up a kilogram? One kilogram is the same as 1,000 grams. This is a really important fact that we need to remember. It’s one we’re going to be using again and again in this video. Let’s draw a bar model to represent it.

One kilogram is exactly the same as 1,000 grams. Now our monster doesn’t weigh one kilogram. As we’ve seen already from the set of scales, it weighs three kilograms. And because we know that each of these kilograms is exactly the same as 1,000 grams, we can say that the monster weighs three lots of 1,000 grams, which is the same as 3,000 grams. And so if we press the second button, the monster might not have changed, but the way that we’ve measured its mass has. We can say that it weighs three kilograms or 3,000 grams.

Now the mass of this monster is interesting. Can you see why? It weighs five kilograms and some more. And that some more that we’re talking about isn’t quite enough to take it to six kilograms, so we have to write this in grams. That’s why our scales say that it weighs five kilograms and 250 grams. Do you remember, at the very start of this video, we said we’re going to learn how to measure masses using mixed units? Well, just like if you’re measuring your height, you might measure one meter and then some more centimeters, we can also measure mass in mixed units too. And this monster has been weighed in kilograms and some more grams.

But what if we want to write this mass using one unit of measurement? How many grams is the same as five kilograms and 250 grams? We can use partitioning to help us here, so let’s draw a part–whole model. And the whole amount is going to be the mass of our monster as it is at the moment in mixed units. So that’s five kilograms 250 grams. And we can partition this amount into the number of whole kilograms that we have, so that’s five kilograms, and also the number of extra grams that we have, which is 250 grams.

Now we want to change this whole amount so that we give the measurement in grams only. And can you see that one of our parts is already in grams? We don’t need to worry about this part here, do we? The unit of measurement that we’re using in this part is exactly what we want, 250 grams. But when we look at our other part, we can see we need to do some thinking. It’s in kilograms. We’re going to have to change those kilograms into grams before we carry on. And to do this, we’re going to need to recall that fact that we said earlier on that was going to be so important.

One kilogram equals 1,000 grams. And so if we have five kilograms, like we have in this part–whole model, then we know that this is the same as five lots of 1,000 grams, or 5,000 grams. We’ve converted our five kilograms into grams. They both weigh exactly the same. It’s just a different way of saying it. So let’s change our part–whole model. Let’s erase five kilograms. And instead, let’s write this amount in grams. And hopefully, you can see that both of our parts are now written using the same unit of measurement. They’re both in grams.

Now, although our part–whole model is true, these two amounts do weigh the same as five kilograms 250 grams. We’re going to erase the whole amount and now express it in grams. In other words, we’re going to put our two parts back together again. We know that 5,000 plus another 250 equals 5,250. And so whilst we could measure the mass of this monster in mixed units, in other words, some whole kilograms and then some more grams, we can also convert this measurement so that we write it just in grams. The monster weighs five kilograms and 250 grams, or 5,250 grams.

If you remember at the start of the video we said we’re going to convert between masses using partitioning. That’s exactly what we’ve done over here. This part–whole model helped us do that, didn’t it? Now so far in our introduction, we’ve converted kilograms to grams. And then we converted a measurement that was made up of kilograms and grams into grams. But we can use what we’ve learned in other ways, too. We could go from grams into kilograms and grams. We could also use what we’ve learned to order different masses that are written in different ways. So what we’re going to do now is we’re going to try answering some questions where we have to put into practice what we’ve learned. And we’ll try using it in some of these different ways. So watch out for them.

Convert two kilograms to grams.

When we measure the mass of something, how heavy it is, we can do so using different units of measurement. And in this question, there are two units of measurement mentioned. Can you see them? We’ve got kilograms and grams. In fact, there’s a number next to the word kilograms. We’ve actually got a measurement, two kilograms. Now we know that a kilogram is about the same mass as a pineapple, but a gram is a lot lighter. Something like a pen lid might weigh one gram.

But just because grams are a lot lighter, doesn’t mean we can’t weigh heavier objects with them. It just means that the number of grams that they’ll measure will be a lot more. In this question, we need to convert the mass two kilograms into grams. And we’re expecting that number then to get a lot larger.

Now for us to be able to convert from a unit of measurement to another one, we need to know what one of those units is worth. Do you remember how many grams are worth the same as one kilogram? One kilogram is worth 1,000 grams. And this fact is so important. We’re going to use it to help us here. Now if we know that one kilogram is the same as 1,000 grams, can you see what two kilograms are going to be worth? If we double the number of kilograms, the number of grams will be doubled too. We could’ve shown the same thing on a bar model as well if we’d wanted too. One kilogram is exactly the same as 1,000 grams. And so two kilograms are the same as two times 1,000 grams, or 2,000 grams.

So just like we predicted, because a gram is worth a lot less, it’s a larger number. We’ve used the fact one kilogram equals 1,000 grams to help us convert two kilograms into grams. The answer is 2,000 grams.

Complete the following model.

The model that’s being talked about in this question is the part–whole model that we can see underneath. And it’s labeled with some different measurements of mass. Let’s have a look at what we’ve got. The whole amount at the top here is 2,435 grams. And the two parts that it’s been split or partitioned into are interesting. Firstly, we’ve got two kilograms. This is interesting because it’s a completely different unit of measurement, isn’t it? We’ve started off with an amount of grams, and we’ve split it into a number of kilograms and some more grams. And this part is interesting too because this is the missing number we’re looking for.

Now can you see what makes this part–whole model tricky? It’s the fact that one of our parts is in kilograms. If all the parts were in the same unit of measurement, it’d be fine. We could find out the missing number quite quickly. So perhaps the first thing we should do to help ourselves is to convert these two kilograms into grams. And we can use a fact about kilograms and grams to help us.

There are 1,000 grams in a kilogram. And so one way to find the number of grams that there are in two kilograms is to take the number of kilograms that there are, which is two, and to multiply it by the number of grams there are in one kilogram, in other words, find out the answer to two multiplied by 1,000. Now there are different ways we could use to help us multiply by 1,000. But because we’re only multiplying it by two, it’s quite quick to do in our heads, isn’t it? Two lots of 1,000 are worth 2,000.

So now to make this part–whole model a little easier to understand, we could cross through our two kilograms. And we could write it in a different way. We’ve converted our two kilograms into grams. Two kilograms are worth 2,000 grams. And now we should be able to work out what our missing answer is. The whole amount is 2,435 grams. One of our parts is worth 2,000 grams. So that’s all our thousands used up. And we’re just left with our hundreds, tens, and ones. Our part–whole model started off by having mixed units of measurement. So the first thing we did was to convert kilograms into grams. And this helped us see more easily that 2,435 grams can be split into 2,000 grams and 435 grams. Our missing number is 435.

Order the given masses indicated on the cards from lightest to heaviest. 1,674 grams, one kilogram 825 grams, 1,324 grams, and one kilogram 647 grams.

We’re given four colored cards here. And on each one, we can see a mass. And the question asks us to order the masses from lightest to heaviest. Now perhaps we’d normally expect if we were looking at some measurements of mass that something that weighs a very small amount might have a small number and something that’s a lot heavier would have a larger number. But there’s a slight problem with thinking like this. Can you see what it is?

The measurements that are written on the cards are not all using the same unit of measurement. We’ve got mixed units. We’ve got two measurements in grams. And then we’ve got two measurements that show a whole number of kilograms and then some more grams on the end. And so if we were just looking at the numbers on the cards, we might say that the blue card shows the smallest numbers and 1,674 is definitely the largest number we can see. But we can’t actually say these are the lightest and heaviest masses. The only way we can compare these measurements together is by converting some of them so that they’re all in the same unit of measurement.

Now there’s two ways we could do this. One way is that we could take these two measurements and convert them from grams into mixed units, so a whole number of kilograms and then some more grams. That way, all the measurements on the cards will be written in kilograms and grams. Or we could leave those two as they are and instead take the red and the blue cards and convert them from mixed units, kilograms and grams, into just a number of grams. And that way, all the cards will be written as so many grams.

Now either of these two methods would work. It doesn’t matter which one we do. But perhaps in this question, we’ll go with the second option. The reason is it’s going to give us one number at the end rather than two. And it’s a bit easier to compare if we just have one large number.

So first of all, let’s take our red card. Let’s convert one kilogram 825 grams into just grams. And as we can see, part of our number is already in grams. We know we already have 825 grams. So we just need to convert our kilograms into grams, too. We know that one kilogram is equal to 1,000 grams. And remembering this fact is really useful because that’s all we need to convert here. We have one kilogram. And so we just need to write 1,000 grams. So the mass on the red card is worth 1,000 grams and another 825 grams. Put the two parts back together. And what have we got? 1,825 grams.

Let’s cross out the mass that’s written at the moment. And we’ll write what it’s worth in grams above. Now we just need to do exactly the same thing with the blue card. At the moment, it reads one kilogram 647 grams. As before, part of it is written in grams already. That’s the 647 grams. And once again, it’s quite quick to convert our kilograms into grams because we’ve only got one of them. That’s 1,000 grams again. And if we add together 1,000 grams and also 647 grams, we have 1,647 grams. So we can cross through these mixed units and write the exact same thing just in grams.

And now that all the masses are in the same units of measurement, we can just look at the numbers. Each number has the same number of thousands, so we’re going to need to move on and look at the hundreds digits. The smallest number of hundreds is on the yellow card. It’s three. So our lightest weight is 1,324 grams. But we can see that the largest digit is eight 100s, so the mass on the red card must be heaviest.

Now what about the two masses in between? Unfortunately, we can’t split them up by looking at the hundreds. They both contain six 100s. So we need to look at the tens digits. And seven 10s on the green card is greater than four 10s on the blue card. So that’s how we know 1,674 grams is greater than one kilogram 647 grams. The masses in order from lightest to heaviest are 1,324 grams, one kilogram 647 grams, 1,674 grams, and one kilogram 825 grams.

So what have we learned in this video? We’ve learned how to measure masses in mixed units. We’ve also learned how to convert between masses using partitioning.

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