Area of Irregular Shapes

The other day, one of the teachers showed me a worksheet designed to have his students calculate area for an irregular shape and asked what the best way to teach students how to find area for this type of shape.

He teaches math to 5th and 6th graders and wants to make sure they are prepared when they get into high school.  I know from past experience that most students have trouble visualizing splitting the shape into two regular shapes.

I told him to copy the shapes onto graph paper so students can cut the shape into two regular pieces. There are at least three way students could cut this into smaller pieces.

1. Cut the top 2 x 3 area off so students are left with a 5 x 2 area.
2.  Cut the right 2 x 3 area off so students are left with a 2 x 5 area.
3.  Cut both the top 2x3 area and the right 2 x 3 area which leaves a 3 x 3 area.

No matter which way the student divides the shape, the area is the same. This is a good discovery because my students too often focus on "the correct way" to calculate area.

The second step would be to have students take the units and draw in the lines themselves to calculate the area by mathematically using a worksheet where they fill in the values as a guided practice.  This is the step to introduce the idea of subtracting distances to find the measurements of the smaller shapes.

The third step is having students calculate the shapes without drawing in the lines. By this point, students have developed the ability to see the smaller shapes. This process helps students develop the ability to picture the divisions possible in the irregular shape. 

Unfortunately, we assume that by the time students reach high school they know how to do this.  We forget that many students get teachers who are still into assigning worksheet after worksheet and do not differentiate or scaffold instruction.  So students are often missing pieces in their foundational knowledge.