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.
