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.
