Partitioning rectangles

So, I have a rectangle drawn right over here, and my goal is to split this rectangle up into smaller equal squares. The way that I'm going to do that is by first dividing this rectangle into two rows—two equal rows—and then I'm going to divide this rectangle into five equal columns.

Now, I know some of you are saying, "What is a row and what is a column?" So, a row—at least, my brain thinks about it as a part of the rectangle that is going from left to right. One way to think about it is, if I had a bunch of, let's say, these are apples here, and if I wanted to think about dividing these apples into rows, I would say that this is the first row, this is the second row, and that this is the third row.

If I were to think in terms of columns, I tend to think of columns as going up and down. So, the columns—in this case—this would be one column, this would be another column, this would be a third column, and this would be a fourth column.

Now that we understand what rows and columns are, let's first think about—maybe pause this video and think about—how would you divide this rectangle into two rows? Well, the way that I would tackle it is I would draw a line that goes from left to right, and there you have it! I now have the rectangle split into one row and now a second row.

Now, pause the video and you could draw this if you have a pencil and paper with you, or you could just think about what I should do. How would I now divide this rectangle into five columns? Well, what I could do is make a bunch of lines that go from top to bottom. So that's one column there, this is a second column, this is a third column, this is a fourth column, and a fifth column.

So there you have it! I have two rows—one row, two rows—and I have five columns—one, two, three, four, five. Now, what's interesting is when I split the rectangle in this way into two rows and five columns, how many equal-sized squares did I create? Well, I've created one, two, three, four, five, six, seven, eight, nine, ten equal squares.

And that makes sense because each row has five. I have one, two, three, four, five; one, two, three, four, five—and five plus five is equal to ten. Another way to think about it is each column has two: one, two; one, two; one, two; one, two; one, two—and two plus two is four, plus two is six, plus two is eight, plus two is ten.

So that's what splitting the rectangle into two rows and five columns gets me: it splits it into ten sections.