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.
