### Video Transcript

Word Problems: Comparison
Problems

In this video, we’re going to learn
how to solve comparison problems that we need to use addition or multiplication to
solve. And we’re going to use bar models
to help us choose the correct operation each time. Now, if you were asked to list some
superheroes, I’m sure you could think of a few names, but have you ever thought,
these are the superheroes that are around now. What about those superheroes that
have gotten a bit older and have retired? What does they do with their
time? Well, they mostly sit around
drinking cups of tea or knitting and looking back at the good old days, talking
about what they used to get up to, comparing what they can do now with what they
could do back then.

For example, if we look at what
this superhero is saying, she’s saying, “When I was younger, I could clear six more
buildings in a leap than I can do now.” Can you see the comparison that’s
going on in this sentence? She’s comparing what she could do
then and what she can do now. Let’s imagine that now she can
clear only two buildings in a single leap. We could draw a bar model now to
help show the comparison. We’ll draw a bar to represent what
she can do now, and that’s to leap over two buildings, and a bar to represent what
she could do back in the good old days. And we can see that the top bar is
longer than the bottom bar, can’t we? We know this because she could
clear six more buildings in a leap than she can do now.

And now that we’ve drawn this bar
model, we can see how to find out what this superhero could do when she was
younger. To find the value of the top bar,
we need to add two and then six more. Back in her prime, this superhero
could clear eight buildings in one leap. We solved this comparison using
addition. And the bar model helped us
understand that it was addition we needed. It showed us which operation to
use. And did you notice there was also a
clue in what the superhero was saying. The words six more give us an idea
that we’re going to have to add, don’t they?

Let’s have a think about another
type of problem. Let’s imagine that this particular
superhero is looking back and saying, “Back in the good old days, I could lift five
times as many cars as I can now.” And let’s also imagine that we know
that now he can only lift three at a time. Again, we could use a bar model to
help us work out what this particular superhero used to be able to do. We could draw a bar to represent
what he can do now, and we’ll label it three to represent the number of cars he can
lift. Now, we know by looking at what
he’s said that this particular superhero used to be able to lift five times as many
cars, so that’s five times as many as three. This is the same as five lots of
three.

In our last problem, we used
addition to compare the amounts. But can you see we might use a
different operation this time? Although you could possibly find
the answer by working out three plus three plus three plus three plus three, it will
be a lot quicker to calculate five times three. And so we can write an equation now
that’s going to help us to solve this problem: five times three equals what. And it’s not just the bar model
that we can use to help us. If we look closely at what the
superhero has said, he said he could lift five times as many. And that little phrase five times
tells us that we’re probably going to need to use multiplication to find the
answer.

Now we can complete the equation
and use it to help us solve the problem. We know five times three is 15, and
so we can say that back in the good old days, this particular superhero could lift
15 cars. You can see now why he’s
complaining about only being able to manage three now. So once again, we’ve solved the
problem that needed us to compare two values together. But this time, we needed to use
multiplication to solve it. And the bar model was really useful
again in helping us to understand which operation to use. We’re going to try some questions
now that are all about comparing values together. And to solve each word problem,
we’re either going to need to add or multiply. To help us choose which operation
to use, we’re going to be drawing bar models whenever we can. Let’s see if we can apply what
we’ve learned.

Select the problem that can be
solved by the equation five times 18 equals 90. Noah is 18 years old. Sophia is five years older than
Noah. How old is Sophia? Or Noah is 18 years old? Sophia is five times as old as
Noah. How old is Sophia? Or finally, Noah is 90 years
old. Sophia is five times as old as
Noah. How old is Sophia?

In this question, we’re given three
problems. And they’re all very similar,
aren’t they? They’re to do with the ages of Noah
and Sophia. These are what we call comparison
problems because we’re comparing one person’s age to the other. Now, one of the things we do when
we’re solving a word problem is to work out what we need to do to find the
answer. And often, we can write an equation
that’s going to help us to find it. And in the first sentence, we’re
told that one of these problems can be solved by working out five times 18 equals
90. So, in a way, this is a sort of
backwards question, isn’t it? We’ve got the answer. We just need to work out what the
problem was.

One thing that we know can be
really helpful when we’re trying to solve a word problem is sketching a bar model to
try and show what the question is asking. So let’s read through each of our
possible answers really carefully and try sketching bar models. In the first problem, we’re told
that Noah is 18 years old. And then comes the comparison,
Sophia is five years older than Noah. So we could draw a bar to represent
Noah’s age and label it 18 and another bar to represent the five years that Sophia
is older than Noah. And then we can see how to find
Sophia’s age. This is an addition problem. And to find Sophia’s age in this
problem, we will need to add together 18 and five.

Our second problem begins in the
same way. We’re told that Noah is 18 years
old. But something slightly different
comes next. Instead of Sophia being five years
older than Noah, we’re told that she’s five times as old as Noah. Now, this means something
completely different. If we draw a bar labeled 18 to
represent Noah’s age again, we can show Sophia’s age by drawing five times this
amount, in other words, five bars all the same length labeled 18. Can you see this is no longer an
addition problem, is it? We solve this problem by using
multiplication. We’d need to find the answer to
five lots of 18, five multiplied by 18. This is the equation we were
looking for, and we know already that the answer is going to be 90. Looks like this is the correct
problem, doesn’t it? Let’s just check the last one.

Our final problem is very similar
to the one before it. Can you see there’s only one
difference? Instead of Noah being 18 years old,
he’s now 90 years old. So we can draw a very similar bar
model to represent this problem. We can start off drawing a bar to
represent Noah’s age. And as we say, instead of 18, it’s
now 90. And again, we can show Sophia’s age
by drawing five times this bar, each one labeled 90. Can you see that this problem
doesn’t really make a lot of sense, does it? To find Sophia’s age in this
problem, we’d have to multiply five by 90. The answer is going to be over
400. And this isn’t very realistic at
all. It’s also not the same as the
equation we were looking for.

We found the problem that can be
solved by the equation five times 18 equals 90. And the way we did it was by
sketching a bar model for each of the problems and thinking about how we might find
the answer. The correct problem is the one that
reads, “Noah is 18 years old. Sophia is five times as old as
Noah. How old is Sophia?”

Select the problem that can be
solved by the addition equation 26 plus 12 equals 38. In the morning, 26 boats set sail
from a harbor. In the afternoon, 12 more boats set
sail. How many boats are out sailing by
the afternoon? Or in the morning, 26 boats set
sail from a harbor. In the afternoon, 12 times as many
boats set sail than in the morning. How many boats set sail in the
afternoon?

Sometimes, when we’re solving a
word problem, we can see a lot of words on the page. Well, in this problem, we’ve got
enough words for about three problems. Our two possible answers are word
problems. And then the original question
itself is a word problem, too. So there are lots of words
here. We need to go through the whole
problem really carefully. To begin with, we’re told to select
or to choose the problem that can be solved by an addition equation. We know that sometimes we solve
problems by adding, subtracting, maybe multiplying, dividing, sometimes by doing
more than one thing.

But the problem we’re looking for
is the problem that can be solved by using a particular addition equation. And we’re told what it is. 26 plus 12 equals 38. And we’re given two word problems
as possible answers. If we were to try to work out the
answer to these problems, we’d only be able to solve one of them by working out 26
plus 12 equals 38. But which one? Now, there are no pictures or
diagrams to help us understand these problems. So in cases like this, sometimes a
bar model can be really helpful. Let’s look at the first problem to
begin with.

We’re told that in the morning 26
boats set sail from a harbor. So we could start off by drawing a
bar and labeling it 26. These are the boats that go out in
the morning, but we’re then told something else happens in the afternoon: 12 more
boats set sail. So we can draw a little bit extra
to our bar and we’ll label it 12 for the 12 more boats. Then finally, we’re asked how many
boats are out sailing by the afternoon. We could draw one long bar that
sums up this amount. We know that the answer is going to
be the 26 boats that set sail in the morning and then the 12 more, in other words,
26 plus 12.

This problem can be solved by using
addition. And when we look at the addition
equation in our first sentence, it looks like we found the right answer already. But it’s very important that we
check all possible answers. So let’s look at our final word
problem. This problem starts off in a
similar way: In the morning, 26 boats set sail from a harbor. But can you see where the
difference lies? In the afternoon, 12 times as many
boats set sail than in the morning. We’re going to need a little bit
more space for this bar model, aren’t we? If we draw a bar to represent the
number of boats that set sail in the morning, which is 26 again, then to show the
number of boats that set sail in the afternoon, we’re going to have to make this 12
times as long.

To answer this problem, we’d need
to find 12 lots of 26 or 12 times 26. This is a multiplication
problem. In both of the problems, we
compared the number of boats that set sail from a harbor in the morning to in the
afternoon; but they’re both solved in very different ways. We used bar models to work out
which operation to use. The problem that can be solved by
the addition equation 26 plus 12 equals 38 is the one that reads, “In the morning,
26 boats set sail from a harbor. In the afternoon, 12 more boats set
sail. How many boats are out sailing by
the afternoon?”

Jacob started training to join the
basketball team. In the first week, he scored a
total of 23 baskets. In the second week, he scored 12
more baskets than in the first week. Should I add or multiply to find
the number of baskets he scored in the second week? Why? Because “a total of” tells us to
use addition. Because “12 more” tells us to use
multiplication. Because “a total of” tells us to
use multiplication. Because “12 more” tells us to use
addition. Or because 12 more tells us to use
subtraction.

Questions like this are really
interesting because they’re not asking us to find the answer; they’re asking us how
we would find the answer. So we don’t have to work any
answers out to our calculation here. We just need to work out what the
calculation is. To begin with, let’s read that word
problem once again. And as we do, we could sketch a bar
model to help us understand what we need to do. So, firstly, we’re told that Jacob
started training to join the basketball team. In the first week, he scored a
total of 23 baskets. So we could draw a bar to represent
week one. And we’ll label it 23 to represent
all those baskets he scored in week one.

But it seems that Jacob’s training
pays off, doesn’t it, because we’re told that in week two, he scored 12 more baskets
than in the first week. How could we show the idea of 12
more than 23 on our bar model? Well, we could draw an extra bar
labeled 12. Those are the 12 more that he
scored. And then we could draw a new bar
that covers all of this length. And this is the number of baskets
that Jacob scores in the second week. Now, as we’ve said already, we’re
not asked to find out how many baskets Jacob scores in the second week. We’re just asked how we would do
this. Should we add or multiply? Well, we can see by looking at our
bar model, can’t we, that the length of the second bar is worth 23 plus 12 more. We’re going to need to add to find
the answer, aren’t we?

And then comes a really important
question: Why? How do we know that we need to add
and not multiply? What is it about the problem that
we were given that shows us that we need to add to find the answer. We’re given five possible
explanations here. Now perhaps the first time we read
through these, it might have sounded a little complicated, but we can get rid of
some of these answers straight away because we’ve already decided we need to add to
find the answer. We don’t need to use
multiplication, so we can cross through this sentence. And we know this sentence is wrong,
too. And we definitely don’t need to use
subtraction, do we? So we’re only left with two
possible answers.

And the only difference between
these answers are two little phrases. Did we see the words “a total of”
in the question and thought to ourselves, oh, we need to use addition? Or did we see the phrase “12 more”
and that’s what told us we needed to use addition? Well, firstly, we know that finding
the total of something does mean that we need to use addition. But when we go back to the question
and look at how those words are used, we’re just told in the first week he scored a
total of 23 baskets. In other words, this was the amount
he scored in week one. It’s got nothing to do with us
finding the answer to the question, has it? It’s just saying that was the whole
amount.

Now, if we find the phrase “12
more,” we can see that this is all about comparing the two weeks together, isn’t
it? In week two, he scored 12 more than
in the first week. This is where we find our answer,
and this is how we know we need to use addition. In this question, we didn’t solve a
word problem. We just thought about how we would
solve it. To begin with, we used a bar model
to work out that we needed to add to find the number of baskets that Jacob scored in
the second week. And we know we need to add because
“12 more” tells us to use addition.

So what have we learned in this
video? We have learned how to solve
comparison problems by using addition or multiplication. We’ve also used bar models to help
us choose which operation to use.