### Video Transcript

Two-Step Problems with Bar Models:
Numbers up to 10,000

In this video, we’re going to learn
how to solve two-step addition and subtraction problems. And we’re going to do this by
modeling the problems using both bar models and also by writing equations. Here’s an example of a two-step
problem. Let’s read it carefully to find out
why we might describe it as a two-step problem.

Dalia posts a gift to her friend in
the United Kingdom. The parcel travels 5,619 kilometers
from Cairo to London in the back of a delivery lorry. It is then flown another 662
kilometers from London to Glasgow. Finally, a mail van takes it 18
kilometers to her friend’s house. How far has the parcel traveled
altogether?

Perhaps you’re still not sure why
it’s called a two-step problem. Let’s go through what we need to do
to find the answer. If we skip to the final question,
we can see that what we need to do is to find how far the parcel’s traveled
altogether. And this word “altogether” is a key
word. It shows us we’re going to need to
add to find the answer.

Now, there are three important
numbers in this question. And they stand for the three parts
to the journey that this parcel makes. The longest distance is this 5,619
kilometers it takes to drive from Cairo to London. Then there’s a flight from London
up to Glasgow, which is another 662 kilometers. And then we’ve got that local mail
van, which carries it the last 18 kilometers to her friend’s house. So to find out how far the parcel’s
traveled altogether, we’re going to need to find the total of these three
distances.

Now, one way we could show what we
need to do is by using a bar model. The whole amount is unknown at the
moment. This is the amount we need to
find. But we do know three parts that
make up the whole amount: 5,619, 662, and 18. Now, although we can use different
methods to find the answer here, we’re still going to have to add these three
numbers together. And we’re going to have to do it in
two steps.

Now, we know that two and eight are
a pair that make 10. So we could start by adding
together 662 and 18. And then once we’ve done that, we
could add the total to 5,619 to find the overall distance. So in this question, there are two
things we need to do to find the answer. There are two steps. In this question, both of the steps
are addition. But we’re also gonna be working
with subtraction in this video. And sometimes a problem might need
us to subtract first and then add or add then subtract. That’s why using a bar model and
also writing out what we need to do in equation form is really helpful to us.

We can then see what it is we need
to do to get to the final answer. Now, as this was just an example,
we won’t work out the answer to this particular problem. But at least we know how we could
if we wanted to. Now, probably the best way to learn
how to solve two-step problems like this is just to practice doing them. So let’s go through some practice
problems now. Each one is going to have two
steps. And to find out what we need to do
to get to the answer, we’re going to try sketching some bar models and also write
equations to help.

Noah, Mason, and Benjamin decided
to buy a new laptop for their father. The laptop costs 1,750 dollars. Noah decided to pay 650
dollars. Mason decided to pay 500
dollars. How much should Benjamin pay so
that they can buy the laptop?

Here we’ve got what we call a word
problem. It’s the sort of problem where we
can’t see any symbols to tell us whether we need to add, subtract, multiply, or
divide to help us solve it. Instead, we need to think carefully
about the story behind the words, what do they describe. And there are a couple of things we
can do to help ourselves here. A really useful tool for working
out what we need to do to solve a problem is to draw a bar model. And in this question, we’ve been
given a bar model already. Let’s re-read the question again
right from the start, and we’ll look at how the bar model models it.

Our story begins with three
brothers. We’ve got Noah, Mason, and
Benjamin. And we’re told that they want to
buy a new laptop for their father. The first really important piece of
information we’re given is the cost of that laptop. It costs 1,750 dollars. Can you see this on the bar
model? It’s written at the top here. And the way that our bar model’s
been labeled, we can see that this represents the total amount. The whole length of the bar model
represents 1,750 dollars. But how are our three brothers
going to pay for this present for their father?

We’re told that Noah decided to pay
650 dollars. And we can see this labeled in the
first part of our bar model. Next, we’re told that Mason decided
to pay 500 dollars. And the second part of our bar
model is labeled to show this amount. We’re finally asked how much should
Benjamin pay. And we can see that this relates to
the third part of our bar model. It’s the part that hasn’t been
labeled, and it’s the part we need to find out.

So we’ve seen that the whole length
of the bar model represents the whole cost of the laptop. And then its three parts represent
the three parts of this whole amount that Noah, Mason, and Benjamin are going to
pay. So what do we need to do to find
the answer? As we’ve said already, there aren’t
any symbols in the problem to tell us. But thankfully, we can use our bar
model to help us. To find the amount that Benjamin
needs to pay, we simply need to start with the whole amount and then subtract the
two amounts that his brothers have already paid. Then we’ll know what’s left.

Now, there are two ways we could do
this. One way to find the answer might be
to start with the whole amount and subtract Noah’s payment and then whatever we’re
left with to subtract Mason’s payment from it. Then we’d be left with the amount
that Benjamin needs to pay. Or we could start with an
addition. We could find out how much Noah and
Mason have paid already. Then we’d need to subtract this
from the whole amount. Now, it doesn’t matter which one of
these two methods we use. Both of them are going to bring us
to the right answer. Let’s use the first one, and then
maybe we’ll show the second one just as a check.

So to begin with, we could subtract
650 from 1,750. This is the sort of calculation we
could do in our heads because 650 is 100 less than 750. So we’ll be left with 1,100. And then if we take 1,100 and
subtract the amount that Mason decides to pay, again, we could do this in our heads,
1,100 subtract 500. We know that if we had 1,000 and we
subtracted 500, we’d have an answer of 500. So if we start off with 100 more
than 1,000, but we still take away 500, our answer is going to be 100 more than
500. It looks like Benjamin’s going to
need to pay 600 dollars, doesn’t it?

Let’s see whether that second
method of ours would’ve found us the same answer. First, we’d need to add 650 and
500. This gives us a total of 1,150. This is the amount that those two
brothers have paid altogether. And then if we subtract this from
the whole amount, 1,750 take away 1,150, we’re left with 600.

We’ve used a bar model here to help
us solve this two-step problem. And we’ve also talked about how we
could solve it in two different ways. If a laptop costs 1,750 dollars,
Noah pays 650 dollars of that, and Mason pays 500 dollars, then we know the amount
that Benjamin needs to pay is 600 dollars.

Ethan and Anthony are competing in
a video game. Ethan scores 3,700 points. Anthony scores 300 points less than
Ethan. How many points does Anthony
score? How many points do they score
altogether?

This problem describes Ethan and
Anthony, who are playing a video game. The first piece of information
we’re given is Ethan’s score. We’re told that he has 3,700
points. And then we’re told Anthony’s
score, or rather we’re told something about Anthony’s score. We’re told that Anthony scores 300
points less than Ethan.

Now, we’re given a bar model, and
this helps us to see the relationship between these two boys’ scores. The bar that represents Ethan’s
score is labeled 3,700. And although the bar representing
Anthony’s score isn’t filled in yet — we don’t know it — we can see that it’s 300
less than Ethan’s. And we’ve got two questions to
answer. And the first one asks us, how many
points does Antony score?

Now, as we’ve said already, his
score is 300 less than 3,700. We’re going to need to subtract to
find the answer. But it’s the sort of calculation we
could do quickly in our heads. We know that 700 take away 300
would leave us with 400. So 3,700 take away 300 is going to
leave us with 3,400.

In the final part of our problem,
we’re asked, “How many points do they score altogether?” What’s their overall total? Now, if we’d have been asked this
right at the start, we might have said to ourselves, well, we can’t find the overall
score. Because to do that, we’d need to
know what Anthony’s score was, and we don’t know that. In other words, we’d have
recognized this as being a two-step problem. First, we’d have needed to find out
Anthony’s score, and then we’d be able to add the two together. But because we’ve already
calculated Anthony’s score, we’ve done the first part of this two-step problem. We just now need to add the two
boys’ scores together.

If we were to sketch another bar
model just to show what we need to do here, it might look like this. We need to add together 3,700 and
3,400. Both our numbers have a three in
the thousands place. And so the total of our thousands
is 6,000. Then we just need to add the
hundreds. Now, we know that 700 plus 300
would be the same as 1,000. So 700 plus 400 will be 100 more
than this. It’s going to equal 1,100. And if we add together our 6,000
with this 1,100, we can see that the boys’ total score is 7,100.

We’ve solved the two parts of this
problem by using bar models to help us. They showed us we needed to
subtract to find the first part and then add for the second. The number of points that Anthony
scores is 3,400 points, and the number of points they score altogether is 7,100
points.

In a library, there are a total of
3,152 science books, English novels, and mathematics books. The number of science books is
1,023, and the number of English novels is 1,210. How many mathematics books are
there in the library?

In this problem, we need to find
the number of maths books that there are in a library. And we’re given some information to
help us. Firstly, we’re told the overall
total of science, English, and the maths books altogether. And this is 3,152. You know, if we were to represent
this problem using a bar model, we’d start off by drawing a bar and labeling it with
this number. This is the whole amount.

Now, we know there are three parts
to this whole amount. There’s a number of science books,
English novels, and mathematics books. Now, we don’t know the number of
maths books. This is the part we need to
find. So we can label this with a
question mark. But we can split the rest of the
bar into two parts because there are two pieces of information that we do know. We’re told that the number of
science books is 1,023 and the number of English novels is 1,210. So how are we going to find the
value of this missing part?

Well, it’s a good job we sketched a
bar model ’cause it gives us a good idea of what to do. Our problem is going to involve
subtraction because we need to find the difference between the total amount, which
is 3,152, and the total of science and English books. But we don’t know an amount for
that yet. We just know these amounts
separately. So to solve this problem, there are
actually two ways we could do it. The first method we could use is to
add together 1,023 and 1,210. This will give us the total amount
of science and English books. And then whatever this amount is,
we could take it away from the whole amount to find the number of maths books.

Another way of finding the same
answer would be to start with the whole amount and then just take away the two
amounts of books that we already know, so 1,210, and then from whatever’s left take
away 1,023. Let’s quickly show how these two
methods will give us the same answer.

1,023 plus 1,210 gives us a total
of 2,233. Remember, this is the total number
of science and English books. Now, we can take this number and
subtract it from the total amount. We’ll have to do a bit of
regrouping to get there, but the answer’s 919. Now, if we check this just by
showing the second method, we could start with the whole amount and subtract just
the number of English novels. This gives us the answer 1,942. Now we’d need to do our second
subtraction and take away the number of science books, 919.

We used a bar model to help us work
out what we needed to do to solve this problem. And there were two ways. Both of them would’ve found us the
correct answer, didn’t matter which one we chose. The number of mathematics books
that there are in this library is 919.

So what have we learned in this
video? We’ve learned how to solve two-step
problems involving addition and subtraction. We’ve done this by modeling them
using bar models and by writing equations.