Reasoning with tape diagrams to connect situations and equations

0:00- [Instructor] We're asked which situation could the tape diagram represent? So pause the video, have a go at this before we do this together. All right, now let's do this together, and let's see, this tape diagram, before I even look at the scenarios, I have four of these Xs in green.

0:14So these over here, that is 4X. I could just write X plus X plus X plus X, but that's 4X. So I have 4X plus five, and in total, that's equal to 29. So I could write 4X plus five, I'll try to do that in a similar color, plus five is equal to 29, equal to 29. So let's see which of these scenarios could be described the same way.

0:39A librarian organizes four shelves, four shelves. Each shelf already has five books, okay? And she adds an equal number of new books to each shelf. So maybe that equal number of new books, that's the unknown that is X. There are 29 total books, so 29 books total.

1:03So let's see, on each shelf in this scenario, it has five, and then we add X. So this is per shelf, you have five plus X, that's per shelf. And then we have four of these shelves. This 4X isn't referring to these four shelves, that was what I did before. These four shelves, I would multiply how many I have in each shelf, which is five plus X times four, and then they told us that I have 29 books in total.

1:3129 books in total. Now, are these equivalent equations? If we were to distribute this four, we would get four times five is 20, four times X is 4X, we would get that equaling 29. 20 plus 4X equals 29, or 4X plus 20. Well, this is 4X plus five. So this one doesn't make sense to me, so I'll rule that one out.

1:57It's a very different expression. A coach has 29 tennis balls. I'll color code it again. Whoops, let me do the pink because 29, I'm trying to do it in pink. Has 29 tennis balls. She places five balls in each of four baskets, in each of four baskets, and keeps the rest in a cart.

2:19So let's call this the unknown, this is X. So I would write this as an equation. So the total is 29. That is going to be equal five balls in each of four baskets. That's going to be five times four. So it's going to be five times four, and then the rest are kept in a cart, so plus X.

2:43So this would be 20 plus X, which is very different than what we have here. This would be analogous to if this wasn't an X, if this was a five, this was a five, this was a five, and then this was an X, then this would be four times five plus X is equal to 29, but that's not the scenario, so let's rule that one out.

3:00Hopefully this is the answer. A fish tank already contains five fish. So already contains, let me underline that, already contains five fish. A pet store owner adds four equal size groups of fish. So adds four equal size groups of fish. So we started with five, and then if we say that each group of those equal size groups has X, then this would be plus, let me do that in color.

3:31Actually, let me do it in the green because that's what I was doing before. So this part right over here would be plus 4X. So we started with five, we're adding 4X, four equal size groups of fish. Each group of fish has X. There are now 29 fish in the tank. So in total, this is going to be 29, and that's exactly what we wrote up here, it's just we changed the order of addition, which, of course, you can do.

3:54Five plus 4X is the same thing as 4X plus five, so I definitely like that choice.