Video: Using Bar Models to Represent Multiplicative Comparison

Rosie has 48 badges. She has 3 times as many badges as Max. Which of the following models represents this situation?

05:03

Video Transcript

Rosie has 48 badges. She has three times as many badges as Max. Which of the following models represents this situation?

When it comes to helping us understand a maths problem, bar models are brilliant. They really help to illustrate what a problem is asking us. And in this particular question, we’re given a situation and then given five possible bar models. We need to decide which one represents the situation. So let’s have a think about what the question is asking us. The first thing we’re told is that Rosie has 48 badges. Now, if we look carefully at each of the bar models, we can see that the bar that represents Rosie, this must be the bar that represents the number of badges that Rosie has, is labeled 48 on all of them. So all of them show that Rosie has 48 badges. The second piece of information we’re told is that Rosie has three times as many badges as Max.

Now, only one of our bar models shows this correctly. But every single one of them shows the number three in some way. In the first example, Max has three bars, the same length as Rosie’s. In the second example, there’s a bar labeled three. In the third example, the difference between Rosie’s bar and Max’s bar is three. In the fourth example, Rosie has three bars compared to Max’s one. And in the final example, Rosie’s bar has three more sections than Max. So the number three is represented in lots of different ways in these models. But only one of them represents the situation in the problem. Perhaps the best way to identify which of the models is correct is to look at each one and to ask ourselves, what does it show us. If we try to describe the model using words, perhaps we’ll be able to see which one is describing the situation.

Let’s begin by looking at the first bar model. Here we can see that Rosie has 48 badges. But Max has more badges than Rosie. In fact, he has three times as many badges as Rosie, because we can see that his bar is made up of three equal sections. Each one of them is 48 long. So for this bar model to be correct, the second sentence in our problem should actually read. Max has three times as many badges as Rosie, not the other way around. This model is not correct. Let’s put a little cross to remind ourselves that this isn’t right.

We should be able to see very quickly that the second example isn’t right either. Can you see that the bar that represents the number of badges that Max has is longer than Rosie’s bar? Just like the first example, in this model, Max has the most badges. So we know straight away that this one isn’t correct either. In fact, if this model was true, then the question would read. Rosie has 48 badges. Max has three more. But that’s not what the question says. So this model is also not correct.

Our third model looks more promising. Rosie has more badges than Max this time. How many more badges than Max does she have? She has three more badges than Max, but not three times as many badges as Max, just three badges. For this model to be true, the second sentence would have to read. Rosie has three more badges than Max. And it doesn’t say that. So once again, this model does not represent the situation. In our fourth example, Rosie’s bar is labeled 48 as all the others are. And we can see that her bar has been split into three equal parts. One of those parts is the same as the number of badges that Max has. Rosie has three times as many badges as Max. This is what our question tells us. So this model represents the situation in the question.

So although we think we found the correct answer, let’s just look at the final model and see why this one is not right. This one is very similar to the model we just looked at. But this time, Rosie has four times as many badges as Max. So we know this particular model is not right. If Rosie has 48 badges and she has three times as many badges as Max, then the model we’re looking for is one where Rosie’s bar is labeled 48. And it’s three times as long as Max’s. The correct answer is this bar model here.

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