Area model division - Definition with Examples

What is Area Model Division?

The area of a shape is the space occupied by the shape. 

If a rectangle has a length equal to 32 units and a width equal to 23 units, then we can find its area by calculating the product 32 ⨉ 23. In other words, when we consider the product 32 ⨉ 23, geometrically, it can be interpreted as the area of a rectangle of length 32 units and width 23 units.

Similarly, we can geometrically interpret a division problem, say, 555 ÷ 15, as the missing dimension of a rectangle of area 555 square units and one side length 15 units.

• We can divide this rectangle into several small rectangles. Then, we can calculate the length of each small rectangle and add them together to find the length of the large rectangle.

• First, consider a small rectangle of width 15 units and length 20 units. The area of this rectangle is 300 square units. So the area of the rest of the rectangle is 555 – 300 = 255 square units.

      

Now, we have an area of 255 square units left. Since 15 ⨉ 10 = 150, another rectangle of width 15 units and length 10 units can be created.

We are now left with an area of 255 – 150 = 105 square units. As 15 ⨉ 7 = 105, the shaded rectangle has a width of 15 units and a length of 7 units. 

Thus, the length of the large rectangle is 20 + 10 + 7 = 37 units. Therefore, 555 ÷ 15 = 37.

Example: Catherine has 540 saplings to plant on her farm. If she plants 30 saplings in a row, how many such rows would there be?

The number of rows is given by the quotient 540 ÷ 30. Now, in the area model for division, we need to find the missing dimension of the rectangle that has an area of 540 square units and a length of 30 units.

Step 1:

Step 2:  

Thus, 540 ÷ 30 = 18. Therefore, there will be 18 rows of saplings on the farm.