Video Transcript
Word Problems: Multiplication and
Division
In this video, we’re going to learn
how to solve one- or two-step problems, where one of the steps involves multiplying
or dividing. Now, when we’re given a problem
written in words just like the one on this title screen, it’s not always clear what
we need to do to find the answer. It’s often helpful to read through
the words several times to try to understand what it’s all about and to ask
ourselves some questions. Let’s go through an example.
A farmer counts 36 sheep’s legs in
a field. How many sheep are there?
Now, the first thing we should do
when we’re given a word problem like this is to read it through a couple of times to
understand what it means. In this case, we’ve got a farmer in
a field. And they haven’t counted the number
of sheep in the field; they’ve counted the number of sheep’s legs. I don’t know why they have done
this, but this is what they’ve done.
Now, probably the first question we
can ask ourselves is “what do we need to find out?” And often we can see this in the
very last part of the problem where there’s a question. In this problem, we need to find
out how many sheep there are. And we’re going to need to look for
clues in the question to help us find out how many sheep there are. And that’s why perhaps the second
thing we need to ask ourselves is “what have we been told in the question that will
help us?”
Well, there’s only one number in
our question, but there are actually two clues. The first clue is the number of
sheep’s legs that the farmer counts. There are 36 of them
altogether. But you know, there’s another
number that we need to use to help us solve this problem, and the clue is in the
name of the animal. These are not farmer’s legs we’re
counting or spider’s legs; these are sheep’s legs. And we know that sheep have four
legs. So, we know both the number of legs
there are altogether. There’s 36 and also the number of
legs that each sheep has, which is four.
Now what are we going to do with
the numbers 36 and four to solve the problem? In word problems like this, there
aren’t any symbols telling us to add, subtract, multiply, or divide. And in this particular problem, we
can’t even see any words to help us. What are we gonna do to solve the
problem? This is where we can ask ourselves
a third question. Can we model the problem to help
work out what to do? And by “model the problem,” we mean
use things like maths equipment, place value blocks, or counters; maybe sketch a
diagram. In this problem, we’re going to use
a bar model. They’re always helpful.
First, we’ll draw a bar to
represent the total number of sheep’s legs that the farmer counts, which we said was
36. Then, we can draw smaller bars to
represent each sheep that he counts. So, there are four legs on the
first sheep, four legs on the second sheep, and so on. Now, we don’t know how many sheep
there are because that’s the whole point of the problem, isn’t it? But at least, this partly drawn bar
model shows exactly what we need to do to solve the problem. We need to find out how many fours
there are in 36. In other words, this is a division
problem.
And now we can write the problem as
an equation. 36 divided by four equals what? And so now all we need to do is to
solve the problem. And of course, we’ve got a choice
now. How are we going to divide 36 by
four? One way to find out how many fours
there are in 36 is to skip count in fours. Perhaps, we could complete our bar
model as we do this. Four, eight, 12, 16, 20, 24, 28,
32, 36. So, that’s nine lots of four that
we counted. 36 divided by four equals nine. So, now, we can answer the problem;
there are nine sheep.
Now, we used five questions to help
us solve this word problem. You don’t have to use these
questions at all. You don’t even have to have five of
them. But the important thing is that
when you see a word problem, you do ask yourself some questions. Let’s try one more example. This time, we’re going to go a lot
quicker. As you’ll see, this is quite
similar to the last one, but there are differences.
A farmer counts seven sheep in a
field. How many sheep’s legs can he
see?
So, firstly, what do we need to
find out? We need to find the number of
sheep’s legs that the farmer can see. And what have we been told in the
problem that can help us? Well, we know that there are seven
sheep in the field. And of course, we know that each
sheep has four legs. And so once again, to help us find
out whether we need to add, subtract, or multiply, or divide, we could model the
problem. This time we could use counters:
seven groups, one for each sheep, and then four counters in each group, one for each
sheep’s leg.
We can see that to find the total
number of counters, we need to find seven lots of four or seven multiplied by
four. This time, it’s a multiplication
question. Seven times four equals what? Perhaps, we could use some facts we
already know to help us. We know that five fours are 20, and
two fours are eight. And by splitting our seven fours up
like this, we know the answer. 20 plus eight equals 28. And so, the farmer can see 28
legs.
Now these have just been some silly
problems about sheep’s legs. But hopefully you can see that by
asking ourselves several questions, we can find out what we need to do to solve a
problem. let’s try putting into practice what we’ve learned now. We’ll try solving some word
problems where we need to use either multiplication or division to find the
answer.
If there are three pieces of cheese
in a box, how many pieces are there in seven boxes?
Nowhere in this word problem does
it tell us what we need to do to find the answer. So how do we know what we need to
do? Well, first of all, we could look
at the problem and ask ourselves what we need to find out. And that’s the number of pieces of
cheese there are in seven boxes. And the problem tells us one more
piece of information that will help us find the answer. And that’s that each box contains
three pieces of cheese. To help us understand how to use
this information we’ve been given, we could sketch a bar model.
There are three pieces of cheese in
a box so we could draw a small bar and label it three. And so, to show how many pieces
there are in seven boxes, we can draw seven small bars and label them all with the
number three. And we can see now what we need to
do to find the answer. We need to find seven lots of
three. This is a multiplication problem,
isn’t it? And to solve it, we’re going to
have to find the answer to seven times three. Let’s remind ourselves of our three
times table facts.
One times three is three, two
threes are six, three times three is nine, four threes are 12, five times three is
15, six threes are 18, and seven threes are 21. And so, we know that if there are
three pieces of cheese in a box, the number of pieces that there will be in seven
boxes will be the answer to seven times three. The answer is 21 pieces.
There are 30 students in a
classroom. They sit in five rows. Noah writes this equation to find
out how many children are in each row. 30 what five equals what. Which symbol is missing from his
equation? How many children are in each
row?
In this question, we’re told about
a problem that Noah is trying to solve. He wants to find out how many
children are in each row in his classroom. Now, we’re told some facts about
Noah’s classroom. Did you spot them? We’re told that there are 30
students in the classroom altogether, and we’re also told that they sit in five
rows. Now to help him find how many
children are in each row, Noah writes an equation. Can you see? It contains the numbers 30 and
five, but there’s also a missing symbol.
To find the answer, does Noah need
to add 30 and five, take away five from 30, multiply 30 by five, or divide 30 by
five? Which symbol is missing from his
equation? Let’s draw a model to help us
understand what we need to do to solve the problem. We know there are 30 students
altogether, so we could draw a bar to represent this. And then we could split the bar
into five equal groups, just like the five equal rows that the children are sitting
in.
So to find out how many children
there are in one row, Noah is going to need to split 30 into five equal parts. He’s going to need to divide
it. This is a division problem. And so, the symbol that’s missing
from Noah’s equation is the division symbol.
How many children are in each
row? Now that we know it’s a division
problem, we can find this answer. What is 30 divided by five? We could use our knowledge of times
tables facts here to help us. Can you think of a five times
tables fact that shows us how any fives there are in 30? Six times five equals 30, and so 30
divided by five equals six. If there are 30 students in a
classroom and they sit in five rows, we can find out how many children are in each
row by solving 30 divided by five. The symbol that’s missing from
Noah’s equation is the division symbol, and the number of children that are in each
row is six.
A boy has seven boxes of fish and a
girl has one box of fish. Each box has 10 fish. How many fish do they have
together?
When we look at a word problem like
this, we can’t see a symbol to tell us what to do. You know there’s something else we
can’t see, too. We can’t see how many steps we need
to do to solve the problem. Sometimes, we need to do more than
one thing. First of all, let’s look at what
this problem is asking us to find out. Well, we’re told about a boy and a
girl who both have boxes of fish. And we need to find out how many
fish they have together. In other words, what’s the
total?
Now, what have we been told in the
question that’s going to help us to solve the problem? Well, we know that the boy has
seven boxes of fish and the girl has one box of fish. And we’re also told how many fish
there are in each box. And that’s 10. Let’s model the problem to work out
what it is we need to do to solve it. Here are the boy’s seven boxes of
fish and let’s include the girl’s box of fish as well. So, the number of boxes of fish
that they have is seven plus another one. But we’re also told that each box
contains 10 fish. So, we’re going to need to find a
few lots of 10, aren’t we?
This is going to involve
multiplication. So, we can see by looking at this
model what we need to do to find the total amount. There are going to be two steps to
our problem. First of all, we need to add
together seven and one more, which, of course, is eight. So, we can start by saying that
there are eight boxes of fish altogether. And because there are 10 fish in
each box, we need to find the answer to eight lots of 10, eight multiplied by
10. Now, of course, we know this is
80.
Although we had to multiply in this
problem, we also had to add to begin with. It was a two-step problem. There were two things we needed to
do. We found the total number of boxes
by adding seven and another one. And then, we multiplied this answer
by 10 to find out the total number of fish. Together, the children have 80
fish.
A teacher has three packs of
pencils. Each pack contains eight
pencils. She opens all the packs and shares
the pencils between six tables. How many pencils will each table
have?
The first thing we can do with this
problem is to look at what it’s asking us. It’s talking about a teacher
sharing out pencils between some tables. And we need to find out how many
pencils each table has. Now, let’s read through the problem
again really carefully. And this time, we’re going to
underline all the pieces of information we can use to help us.
We’re told that the teacher has
three packs of pencils. And also, we’re told how many
pencils there are inside each pack, and that’s eight. But then, we’re told that the
teacher opens up all the packs. Can you imagine her doing this? Those three packets of pencils are
all going to be merged into one, aren’t they? One big pile. And then we’re told that she shares
the pencils between six tables.
Now there’s more than one thing we
need to do in this problem to find the answer. Firstly, we need to find out how
many pencils there are altogether. We could sketch this bar model to
help us. Each of these small bars represents
a pack of pencils. And because we know that there are
eight pencils in each pack, we can write the number eight inside each bar. So, can you see what we need to do
to find the total number of pencils? We need to find three lots of
eight, three times eight. So, part one of our problem is
going to involve multiplication.
But there’s a second part to our
problem because we’re told that their teacher shares the pencils between six
tables. So, we can take our bar and show
how it can be split into six equal parts. And to find the number of pencils
at each table is going to have, we need to divide our total by six. So, the second part of our problem
is going to involve division. Now that we know what we need to do
to find the answer, let’s work it out. And we’re going to write equations
to help us.
Firstly, we said to find the total
number of pencils we need to find three times eight. One times eight is eight, two times
eight is 16, three times eight 24. So, the pile of pencils that the
teacher has when she tips them all out is 24. But then, as we’ve said, she needs
to share these into six equal groups. What is 24 divided by six? Well, if we count in sixes, six,
12, 18, 24, we can see that there are four sixes in 24. Or if you think about it in another
way, there are six fours in 24. And so, if we split 24 into six
equal groups, there’ll be four in each group.
In this two-step problem, we’ve
used both multiplication and division to find the answer. Each table will have four
pencils.
What have we learned in this
video? We’ve learned how to solve one- or
two-step problems where we need to use multiplication or division. We’ve also thought carefully about
the sorts of questions we need to ask to solve a problem.
