Video Transcript
Scarlett, the gardener, charges
customers by how many individual square pieces of grass she lays when she creates a
new backyard design. Order these yards from least to
most expensive.
The first sentence in this question
tells us about Scarlett, a gardener. She clearly designs the backyards
for different people. And she makes these designs by
laying out individual square pieces of grass to make different shapes. This first sentence tells us that
Scarlett charges customers according to how many individual square pieces of grass
she uses. The more pieces of grass, the more
expensive the backyard.
Now, even though we’re told to
order the yards from least to most expensive, this question isn’t about money at
all. It’s about us understanding which
of the shapes we can see contains the most squares. We know that the space inside a
shape, and in this question we’re talking about the space inside Scarlett’s designs,
is called its area. So really, this question is asking
us to put the shapes A, B, C, and D in order of area from smallest to largest
area. Now, if you were to look at these
four designs, do you think you could spot which one has the smallest area?
Shape A looks like it might be the
thinnest, and shape B is definitely the smallest in terms of height. But neither of these two facts help
us because what we need to think about is the space inside each shape. And the only way we’re going to
find this is by counting the squares that Scarlett’s going to need to use.
Now, we can’t see any squares
inside each of these shapes. But because they’ve been drawn on
squared paper, we know where the squares belong. In fact, we could draw them on
using a pencil. That’s a lot clearer. Now let’s count them. Design A has an area of 10 square
units. Let’s label that so we don’t forget
it. Design B is made up of 11 square
pieces of grass, so we can say the area of this shape is 11 square units. The person who pays Scarlett for
design C is going to need to pay her for 12 square pieces of grass. So shape C has an area of 12 square
units, and we can see that yard C has an area of nine square units.
Each of the areas is different and
so we can put them in order really quickly. The yard that needs the smallest
number of square pieces of grass is yard D, with nine square units. Then we have yard A with 10, yard B
with 11, and the largest yard, so the one that’s going to cost most money, is yard
C. In this question, we were asked to
order the yards from least to most expensive. But we realized this question was
really asking us to order them from smallest to largest area. In order, the designs are D, A, B,
and C.
