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.