Video: Counting the Rows, Columns, and Squares when Partitioning Rectangles

These rectangles have been partitioned into equal squares. The blue rectangle has _ rows. There are _ squares in each row of the blue rectangle. The orange rectangle has _ columns. There are _ squares in each column of the orange rectangle. Both rectangles have _ squares.

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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.

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