Lesson Video: Word Problems: Multiplication and Division | Nagwa Lesson Video: Word Problems: Multiplication and Division | Nagwa

Lesson Video: Word Problems: Multiplication and Division Mathematics • Third Year of Primary School

In this video, we will learn how to solve one- and two-step problems where one of the steps involves multiplying or dividing numbers within the times tables up to 10 × 10.

16:50

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.

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