Partitioning Rectangles into Rows and Columns

Partitioning a rectangle means dividing it into equal-sized squares. This helps us understand how space works inside a shape and is the first step to learning about area!

What are Rows and Columns?

Before we divide a rectangle, we need to know the difference between rows and columns:

• Rows go side to side (left to right). Think of rows of seats in a movie theater.
• Columns go up and down (top to bottom). Think of tall columns holding up a building.

How to Partition a Rectangle

Let's say we want to partition a rectangle into 3 rows and 4 columns.

1. Draw the rows: To make 3 equal rows, draw 2 straight lines going from left to right.
2. Draw the columns: To make 4 equal columns, draw 3 straight lines going from top to bottom.

Now, your rectangle is filled with a grid of equal-sized squares!

Counting the Squares

Once the rectangle is partitioned, how many squares are there in total?

You can count them one by one, but there is a faster way! We can use repeated addition by looking at the rows or columns.

Example 1: 3 rows and 4 columns

• There are $4$ squares in each row.
• Since there are $3$ rows, we can add the squares in each row together: $4 + 4 + 4 = 12$
• There are $12$ squares in total.

Example 2: 5 rows and 2 columns

• There are $2$ squares in each row.
• Since there are $5$ rows, we can add: $2 + 2 + 2 + 2 + 2 = 10$
• The rectangle is divided into $10$ equal parts.

Partitioning rectangles shows us how arrays work and makes counting shapes much faster!