Video: Word Problems: Taking Apart

In this video, we will learn how to solve problems to find the number of objects in one part when one group of up to 10 objects is split into two parts.

08:29

Video Transcript

Word Problems: Taking Apart

In this lesson, we’re going to learn how to solve problems to find the number of objects in one part when a group of up to 10 objects is split into two parts. Let’s think about what we mean by a word problem where we have to take apart to find the answer. Here are seven objects. Three of them are pens. How many of the objects are pencils?

That was an example of a word problem. And we can use those three sentences to label our picture. Here are seven objects. Three of them are pens. How many are pencils? These labels help us to understand what to do to solve the problem. Firstly, we know that the whole amount is equal to seven. There are seven objects altogether. But you know, we can break up the number seven into two parts. And in this word problem, we’re breaking up the amount of objects into pens and pencils.

There are three pens. And so we can say that one of our parts is worth three. And the question’s asking us, how much is the other part worth? How many are pencils? We can find the answer by starting with the whole amount and taking away the part that we know. This is going to leave us with the part that we don’t know. Seven take away three equals what?

We could model our problem using cubes. We can start with seven cubes. Now we need to break apart this whole amount into three and whatever’s left. We’ve broken apart our group of seven into a group of three and a group of another number. How many cubes are there in the other part? There are one, two, three, four. Three and four are two parts that go together to make seven. So we can complete our part–whole model. And we can answer the question. If there are seven objects and three are pens, if we can see the rest are pencils, we know that four must be pencils. Seven take away three leaves us with four.

Let’s have a go at using what we’ve just learned. We’re gonna break up a group of up to 10 objects and split it into two parts to find out what one of the parts is worth.

There are six apples. Some are red and others are green. Two of them are red. How many green apples are there?

This word problem is all about a group. We’re told that this is a group of six apples. Some are red and others are green. But we don’t know to start with how many red and how many green apples there are. And that’s why in the first picture we can see six apples, but they haven’t been colored yet. At the moment, they’re all in shadow. And in our second sentence, we’re told a fact about our group of apples. We’re told that two of them are red. Because the apples are either red or green, we can also say that the rest are going to be green.

Now, the word problem asks us, how many green apples are there? You know, we can represent this problem using a part–whole model. There are six apples altogether, so we can say that the whole amount is six. Now, we can break up the number six into two parts: one representing red apples and one representing green apples. So let’s color-code our part–whole model.

We know that two of the apples are red. And we don’t know how many green apples there are. This is the part we need to find. To find our missing part, we could start with the whole amount, which is six, and take away the part that we know, which is two. Six apples take away two apples leaves us with how many apples?

Let’s model the problem using counters. We’ll start with six counters. We can take away two counters. And this leaves us with one, two, three, four counters. The number six can be broken apart into a group of two and a group of four because two and four go together to make six. If there are six apples — some are red; others are green — and we know that two of the apples are red, then we can say that the number of green apples is four.

There are eight red and green cups. If two of them are green, how many red cups are there?

This word problem is all about taking apart or breaking up a group of objects into two groups. And the group of objects we’re thinking about is a group of red and green cups. And there are eight of them. Let’s use eight cubes to represent our eight cups. Now we can use the information in the first sentence to label our cubes. We know there are eight red and green cups, so let’s label the whole amount eight.

The next piece of information we’re told is about part of the eight cups. And we’re told that two of them are green. Now again, we can use this piece of information to label our diagram some more. Two out of our eight cubes we know are going to be green. Now we’re asked, how many red cups are there?

Well, because we were told to begin with that there were eight red and green cups and only two of them are green, we know that the rest of the cups must be red. Now again, we can show this in our line of cubes. We don’t know how many there are in this part, but we do know that this is the part we need to find. The whole amount is worth eight, and we need to break apart the whole amount into two parts.

Our first part represents the number of green cubes, and we know that this is two. And the second part represents the number of red cubes that we’ve got. So to find the answer, we need to start with the whole amount, which is eight, and take away or subtract the part that we know already, which is two. This is going to leave us with the part that we don’t know.

So to represent our two green cups, let’s take away two green cubes. One, two. Now, how many cubes do we have left? One, two, three, four, five, six. We’ve broken apart the number eight into a group of two and a group of six. So we can complete our part–whole model with this information. And we can write the answer in our number sentence too. If there are eight red and green cups and two of them are green, we can find out the number of red cups by splitting up or taking apart the number eight into a group of two and then counting what’s left. Eight take away two equals six. And so we know that the number of red cups must be six.

What have we learned in this video? Well, we’ve learned how to solve problems to find the number of objects in one part when a group is split into two parts.

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