Video Transcript
These rectangles have been
partitioned into equal squares. The blue rectangle has what
rows. There are what squares in each row
of the blue rectangle. The orange rectangle has what
columns. There are what squares in each
column of the orange rectangle. Both rectangles have what
squares.
We’ve got several sentences here
that describe the two rectangles that we can see in the diagram. And each of the sentences has a
missing number. Our question is all about the rows
and the columns that we get when we partition rectangles into equal squares and also
how we can use these rows and columns to find the total number of squares that the
rectangle has been divided into.
To begin with, we’re told that the
rectangles have bean partitioned or split up into equal squares. We’ve got this long blue rectangle
here. And if we quickly look at all the
squares that it’s been split into, we can see that they’re all equal; they’re all
the same size. And then, we’ve got this orange
rectangle on the right here. Again, we can see that it’s been
split into equal squares. This is an interesting rectangle
because its length and width are the same size. It’s a special kind of
rectangle. Of course, we call it a square.
Our first sentence describes the
blue rectangle. The blue rectangle has what
rows. We know that a row of squares is a
number of squares that are in a line going across the shape. We can see one, two rows of
squares. The blue rectangle has two
rows. We then need to think about the
number of squares that there are in each row of the blue rectangle. Let’s count them: one, two, three,
four, five, six, seven. There are eight equal squares in a
row. And, of course, we know that both
rows are the same length. And so, we can complete the second
sentence. There are eight squares in each row
of the blue rectangle.
In the next part of the problem, we
need to think about the orange rectangle. The next sentence says, “The orange
rectangle has what columns.” We know that a column is a line of
squares that goes up and down. How many columns can we see in the
orange rectangle? One, two, three. There are four columns in the
orange rectangle. The orange rectangle has four
columns in the next sentence. We need to think about the number
of squares that there are in each column of the rectangle.
Let’s look at the first column on
the left-hand side. We’ll count the squares. There are one, two, three, four
squares in this column and there are four squares in all the columns. So the orange rectangle has four
columns, and there are four squares in each column. There’s the same amount of squares
in the column as there are columns. And we know this is the case
because as we’ve said already, this is a special kind of rectangle. It’s a square, isn’t it?
In the final sentence, we need to
write the number of squares altogether in both rectangles. Did you know that both rectangles
have the same number of squares? So we’re only looking for one
number here. Now, how are we going to find the
number of squares in each rectangle? Are we just going to count them
one, two, three, four, and so on? Or perhaps we can use our knowledge
of rows and columns to help. Let’s go back over the sentences
that we’ve completed.
The blue rectangle has two rows,
and there are eight squares in each row. So we can think of this as being
like two groups of eight. Eight plus eight equals 16. The blue rectangle contains 16
equal squares. When we looked at the orange
rectangle, we were looking at the columns, weren’t we? And we said that it has four
columns and also that there are four squares in each column. So in other words, we have four
groups of four squares. We can find the total number of
squares then by finding four lots of four.
Let’s count in four four times:
four, eight, 12, 16. Two lots of eight is 16 and four
lots of four equals 16 too. The blue rectangle has two
rows. There are eight squares in each row
of the blue rectangle. The orange rectangle has four
columns. There are four squares in each
column of the orange rectangle. Both rectangles have 16
squares.
