# Question Video: Recognizing That Area Is Found by Covering a Plane Figure in Unit Squares without Gaps Mathematics • 3rd Grade

Natalie thinks that the shape has an area of 15 square units. Is she correct? [A] Yes, because there are 15 tiles. [B] Yes, because the tiles do not overlap. [C] Yes, because the square units cover the whole area. [D] No, because the square units do not cover the whole area.

03:18

### Video Transcript

Natalie thinks that this shape has an area of 15 square units. Is she correct? Yes, because there are 15 tiles. Yes, because the tiles do not overlap. Yes, because the square units cover the whole area. Or no, because the square units do not cover the whole area.

The shape that’s mentioned in this first sentence is this rectangle that we’re shown here. And we’re told that Natalie thinks that this rectangle has an area of 15 square units. Now where do you think she gets this idea from? Well, we know that the area of a flat shape is a measure of the space inside it. And in the space inside Natalie’s rectangle, she’s placed some blue square units. Maybe these are pieces of colored card or something like that. And if we count them, there are 15 of them. This is where Natalie gets the idea of 15 square units from.

So is Natalie correct? Does this shape have an area of 15 square units? This is not just a straightforward yes–no question. We’re given four possible answers, but as well as saying yes or no, each one contains a reason. This question is really asking us, is Natalie correct and why? Let’s go through our four possible answers. Now we know from having counted them that part of our first possible answer is correct. There are actually 15 tiles. This bit’s true. Maybe our first answer is the right one. Let’s have a look at the second. Our second answer also suggests that Natalie might be right, but this time for a different reason. This time, it’s because the tiles do not overlap.

We know that whenever we measure area, it’s important that the units that we use are in their own space. They don’t overlap at all. So it’s definitely important that Natalie hasn’t overlapped any of her square units. But you know, Natalie has made one mistake. To measure the area or the space inside a shape, we need to make sure that all of that space is covered. Our next two possible answers tell us that the square units cover the whole area, but then the square units do not cover the whole area. Which one of these is true? Well, we don’t have to look very hard, do we?

There’s a lot of white space in this rectangle. Natalie’s square units aren’t touching each other at all. They haven’t covered the whole area. So although there are 15 tiles and the tiles that Natalie’s used do not overlap, and these are both very good things, Natalie hasn’t pushed them all up really close to each other so that they cover the whole area. This is the mistake that she’s made. So when Natalie says that the shape has an area of 15 square units, is she correct? No, because the square units do not cover the whole area.