### Video Transcript

Comparing Lengths Indirectly

In this video, we’re going to learn
how to compare the lengths of two objects by comparing their lengths to a third
object, either by looking at them or measuring with square units. Here are two plants, one in a red
pot and one in a blue pot. Now, let’s imagine that these
plants are in different parts of our garden. They’re not right next to each
other, so it’s difficult to tell which one is taller than the other. We can’t compare the height of the
two plants directly just by looking. But there is a way that we can
still tell whether one plant is taller than the other. Here’s a third plant. Now, if we compare the height of
both of the other plants with this new plant, we could be able to tell which is
taller.

First, let’s compare the plant in
the red pot with the plant in the orange pot. We can see that the plant in the
red pot is taller. Now, we can do the same thing with
the plant in the blue pot. If we compare the plant in the blue
pot with our third object, which is the cactus in the orange pot, we can see that
it’s shorter than the cactus. One of our plants is taller than
the cactus and the other plant is shorter. Because we’ve compared both the
first and the second plant with the same third object, we know enough to be able to
compare the first two plants with each other. We didn’t need to put them side by
side, but we can still tell that the plant in the red pot is taller than the plant
in the blue pot.

And you know, the third thing that
we compare our objects to doesn’t even have to be another object. These two carrots aren’t next to
each other, so they’re difficult to compare the length of directly. But instead of using another
object, we could use square units. Here’s a chain of six squares. We’ll call our first carrot, carrot
A. Let’s compare the length of carrot
A with our square units. The length of carrot A is shorter
than the six units. Let’s do the same with carrot
B. Carrot B is ever so slightly longer
than our six square units.

Because we’ve compared both carrots
with the same object, we can now say which of the two carrots is longer than the
other. Carrot B is longer than carrot
A. And we didn’t even need to put them
next to each other to tell this. Let’s have a go at answering some
questions now where we have to compare the lengths or the heights of two
objects. And we’re going to work out the
answer by comparing their lengths or heights with a third object.

The blue pencil is longer than the
orange pencil. The orange pencil is longer than
the green pencil. Which pencil is longest?

In this question, we’re given two
statements where pencils are compared with each other. There are three different pencils
altogether. There’s a blue one, an orange one,
and a green one. And we’re asked, which of these
pencils is the longest? So we need to compare these three
pencils together. But none of the sentences and none
of the pictures show all three pencils at the same time. They only compare two pencils at a
time. So we need to use the facts that
we’re given to try to work out which pencil is longest.

Our first fact, and the picture
underneath it, tells us that the blue pencil is longer than the orange pencil. To help us show this fact, perhaps,
we could draw a line like this. We could put things that are
shorter towards the left of the line and things that are longer towards the right of
the line. To show that the blue pencil is
longer than the orange pencil, we could put a blue and an orange counter on our
line. Because the blue pencil is longer,
we’ve put the blue counter on the right of the orange one. In our second sentence, the blue
pencil isn’t mentioned at all.

This time, the green pencil is
compared with the orange pencil. And we’re told that the orange
pencil is longer than the green pencil. In other words, the green pencil is
shorter than the orange pencil. And we can see that from the
picture. Because the green pencil is
shorter, we’re going to have to put a green counter to the left of the orange
counter on our line. If we look at our line, we can see
that the blue pencil is the longest. The blue pencil is longer than the
orange pencil, which is longer than the green pencil. The longest pencil is blue.

Matthew is taller than Daniel and
shorter than Benjamin. Who is the shortest?

In this question, we need to
compare the heights of three different boys. There’s Matthew, Daniel, and
Benjamin. The question asks us, who is the
shortest? But we aren’t given any pictures or
measurements to help us. How can we compare these three
children’s heights? Well, we’re given one sentence to
help us here. And in this sentence, we’re given
two facts. We know what two children’s heights
are compared with Matthew. And we can use this to help us find
the answer. To help us solve the problem, let’s
draw a line. And we’ll go from left to right,
shorter to taller.

So the first part of our sentence
compares Matthew with Daniel. And we’re told Matthew is taller
than Daniel. There we go. So we’ve written the letters M and
D on our line. Because we know Matthew is taller
than Daniel, we’ve written the M to the right of the letter D. The second fact that we’re told is
also to do with Matthew. But this time we’re comparing
Benjamin’s height with Matthew. So Matthew is taller than
Daniel. But he’s shorter than Benjamin.

Now, if Matthew is shorter than
Benjamin, we’re going to have to write the letter B for Benjamin somewhere here. Benjamin is taller than
Matthew. And because Matthew is taller than
Daniel, Benjamin is the tallest. But our question asks us, who is
the shortest? We can use the diagram we’ve drawn
to help us. The shortest out of the three boys
is Daniel.

Complete the following statements
with taller or shorter. The rabbit is what than the eight
blocks. The carrot is what than the eight
blocks. The rabbit is what than the
carrot.

This is a comparing problem where
we’re comparing the heights of different objects. And in the final sentence, we have
to either say that the rabbit is taller than the carrot or the rabbit is shorter
than the carrot. But unfortunately, we haven’t got
the rabbit and the carrot side by side in one of the pictures. To find the answer, we have to
compare both objects, the rabbit and the carrot, with a third object. And the third object, as we can see
from the picture, is eight blocks. And these eight blocks are in the
tower.

Let’s start by comparing the rabbit
with the eight blocks. Is the rabbit taller or shorter
than the eight blocks? We can see that the top of her ear
comes above the tower, doesn’t it? The rabbit is taller than the eight
blocks. Now, let’s compare the carrot with
the same eight blocks. And if we compare the height of the
carrot with the height of the blocks, we can see it doesn’t reach all the way to the
top, does it? We have to use the word shorter to
complete this sentence. The carrot is shorter than the
eight blocks.

So if the rabbit is taller than the
eight blocks and the carrot is shorter than the eight blocks, we now know which is
taller out of the rabbit and the carrot. The rabbit is taller than the
carrot. The rabbit is taller than the eight
blocks. The carrot is shorter than the
eight blocks. And that’s how we know the rabbit
is taller than the carrot. The missing words are taller,
shorter, and taller.

Now, what have we learned in this
video? We’ve learned that we don’t always
need to see two objects next to each other or measure them to know which is longer
or shorter. Instead, we can compare the lengths
or heights of two objects by comparing each one to a third object.