Lesson Video: Two-Step Problems with Bar Models: Numbers up to 100 Mathematics

Video Transcript

Two-Step Problems with Bar Models: Numbers up to 100

In this video, we’re going to learn how to solve two-step addition and subtraction problems by using bar models to help us.

This is what we call a two-step problem. But why is it called a two-step problem? Let’s start by reading it carefully. At the school Sports Day, there are 14 teachers and 63 children. The number of parents who attend is 25 less than the total of teachers and children. How many parents attend the Sports Day?

Perhaps, you still don’t know why it’s called a two-step problem. Let’s think about what we have to do to find the answer. The question asked us to find out how many parents go along to Sports Day. And the question actually tells us how many parents there are. The number of parents who attend is 25 less than the total of teachers and children. We could look at this sentence and say to ourselves, “Oh! We need to subtract to find the answer. We need to find 25 less than something.” So, we need to take away 25. But 25 less than what? We need to take away 25 from the total of teachers and children. Do we know what the total of teachers and children is? Well, we don’t, do we? But we do know that there are 14 teachers and 63 children.

The first thing we’re gonna have to do is to add these two numbers together. Then, we can take away 25. We need to add then subtract to find the answer. And this is why we call it a two-step problem. We need to do two things or take two steps to find the answer. You know with problems like this, they’re written all in words, sometimes it can be quite tricky to know what it is we have to do. And this is why drawing bar models can be really useful. They don’t tell us what the answer is, but they do tell us how to get there. Let’s sketch some bar models to help us understand what we need to do to solve this problem.

The first piece of information we’re told is that at the school Sports Day, there are 14 teachers. So, let’s start off by drawing a bar that represents 14 teachers. And it might be a good idea to label it with the number 14 so we remember exactly what it represents. We’re then told that there are 63 children. So we can draw another bar, a much longer bar, to represent the number of children. And we better label this with the number 63 so we don’t forget. The next thing we’re told is that the number of parents who attend is 25 less than the total of teachers and children.

So, the first thing we’re going to have to do is to add together 14 and 63 to find out what the total of teachers and children is. This is represented by the whole bar by adding the two parts together. Now, if we looked at this bar model just to begin with, we’d say to ourselves, “I can see what I need to do. I need to add together 14 and 63. That’s how I find out what the question mark’s worth.” By sketching the bar model, it hasn’t told us the answer, but it has told us what we need to do. We need to add.

As we’ve said already though, there are two steps to our problem, so we’re going to need to draw two bar models. First, we need to draw a bar that represents the total of teachers and children. We don’t know exactly how long this is because we haven’t added the first two numbers together, but we’ve drawn the bar exactly the same length as the first bar model. Now, we’re told the number of parents who attend is 25 less than this amount. How could we show 25 less? We could label a part that’s worth 25 in a different color or shade it and then the part that we want to find, which is 25 less than the whole amount.

Again, we don’t know what this is. We haven’t done the maths yet. But by sketching our second bar model, we now know the second thing we need to do. We’ve used bar models to understand the two steps that we need to do to solve the problem. We’re going to look at some problems now where we work out the answers. We won’t work out the answer to this particular problem, but if we wanted to, we know how we could. First, we’d add; then, we’d subtract. Let’s practice what we’ve learned now. We’re gonna use some bar models to help solve some two-step problems.

In a garden, there are 53 roses. There are 19 fewer daffodils than roses. How many daffodils are there? How many flowers are in the garden?

What we have here is what we call a two-step problem. It’s not because we’re being asked two questions. It’s because to answer the final question, we have to do two things. We have to answer the first question to get to the second question. It’s like taking two steps up to your front door. We have to stand on the first step to get to the second step. To help us understand what we need to do to solve this problem, we’re shown some bar models.

Now, bar models don’t give us the answer, but they do help us understand a problem, understand what we need to do. This problem is set in a garden. And to begin with, we’re told that there are 53 roses. Can you see those roses represented on our first bar model? It’s this blue bar here, isn’t it? We can see that it’s labeled 53. The next thing we’re told is the number of daffodils in the garden. Now, we’re not told exactly how many daffodils there are, but we are given a clue. There are 19 fewer daffodils than roses. And we can see that this has been drawn on our bar model too. We can see an orange bar has been drawn to represent daffodils, but it’s shorter than the blue bar. And we can see the label 19 fewer.

Now, later on, we’re going to be asked how many flowers are in the garden? So, we’re going to need to add together the number of roses and the number of daffodils. But at the moment, we don’t know how many daffodils there are. So, before we do any adding, we need to complete the first step, and that is to subtract. To find 19 fewer than 53, we need to find the answer to 53 take away 19. Let’s sketch a blank number line to help us. We’ll start with the number 53.

Now, we know that 19 can be split into 10 and nine. So, to begin with, let’s make a jump of 10 backwards. 53 take away 10 is 43. Now, we just need to take away nine. The number 43 doesn’t have nine ones for us to take away. So, let’s take away nine in two different parts. First, we’ll take away three because taking three away from 43 is very quick to do, and then we’ll take away what’s left. Three and six make nine. So, we’ll have to take away another six. First of all, a jump of three, 43 take away three is 40. Now, we need to take away the other six. 40 take away six is 34. The number of daffodils is 34. We could even label our bar model with this number.

And now that we’ve completed our first step, we can solve the whole problem. We’re asked how many flowers are in the garden. And the bar model underneath shows us that the total number of flowers is the same as the number of roses, which is labeled 53, as well as the number of daffodils. In the first step, we worked out how many daffodils there are. And so, we now know how to find the total number of flowers. We just need to add together 53 and 34. We know that 53 is five 10s and three ones and 34 is three 10s and four ones. Five 10s plus another three 10s equals eight 10s. And three ones plus another four ones makes a total of seven ones. And eight 10s and seven ones equals 87.

To find the total number of flowers in the garden, which was the last thing we were being asked to do, we had to complete two steps. We knew that there were 19 fewer daffodils than roses, so we first had to calculate the number of daffodils. 53 take away 19 equals 34 daffodils. Our second step then was to add the number of daffodils to the number of roses. 53 and 34 make 87 altogether. So, the number of flowers in the garden is 87.

Anthony and Liam were seeing who could run farther in 10 seconds. Anthony only ran 18 meters because he tripped over. Liam ran 62 meters farther than Anthony. How many meters did Liam run? How many meters did the boys run in total?

This is what we call a two-step problem. And you know, it’s not because we’re being asked two questions. To understand why this is a two-step problem, let’s look at the final question. We’re being asked how many meters that boys ran in total. You know, we could draw a bar model to represent this. To find the total number of meters that the boys ran, we need to add together the distance that Anthony ran, which we know is 18 meters, to the distance that Liam ran.

But if we read the question carefully, we’re not told exactly how far that Liam ran; we’re just given a clue. We’re told that he ran 62 meters farther than Anthony. So, for us to be able to find out the total number of meters that the boys ran, we’re first gonna have to work out how far Liam ran. And this is why it’s a two-step problem. There are two things we need to do to get to the final answer. And that’s why our two-step problem has been split into two questions. The first question asked us to find out how many meters Liam ran. And we can draw a bar model to help with this too.

We know that because he tripped over, Anthony only ran 18 meters. And we also know that Liam ran 62 meters farther. Can you see now how to calculate how far Liam ran? Sketching a bar model helps us to understand what we need to do. We need to add together 18 and 62. We know that 18 is the same as one 10 and eight ones. And 62 is the same as six 10s and two ones. If we add one 10 and six 10s together, we get a total of seven 10s. But these aren’t the only 10s we have because if we add eight ones and two ones together they make 10. So, instead of seven 10s, we have eight 10s. And we know eight 10s are worth 80. The number of meters that Liam ran is 80.

And now that we’ve worked out the answer to the first step of our problem, we can use it to help solve the second step. We could even label our bar model with the number of meters that Liam ran. Let’s put 80 in there. Again, our bar model doesn’t tell us the answer, but it does show us how to work it out. To find the total number of meters that the boys ran, we need to add together 18 and 80. As we said already, 18 is the same as one 10 and eight ones and 80 is the same as eight 10s. So, it has zero ones. One 10 plus eight 10s equals nine 10s. And then, if we add eight and zero together, we get a total of eight. The total distance the boys ran is 98 meters.

To find the total distance the boys ran, we needed to complete two steps and we used bar models to help us. The number of meters that Liam ran is 80, and the number of meters that the boys ran in total is 98.

What have we learned in this video? We’ve learned how to solve two-step addition and subtraction problems, using bar models to help us identify the two steps.