by C. Elkins

I have heard from a few 4^th grade teachers that a new standard is difficult for their students to grasp. It is 4.GM.2.2: Find the area of polygons that can be decomposed into rectangles.

I have a couple of suggestions which help students with a concrete-pictorial-abstract progression approach to this problem (which is more developmentally appropriate).

1. I have attached an activity which involves the use of 1” color tiles to partition off irregular shapes and then determine the area of each smaller rectangle. It’s free and in 2 parts:
   • Directions and example pictures: Using Color Tiles directions
   • Forms for students to use (labeled A-E), plus extra blank 1” grid and cm paper:  Using color files forms
2. I located an excellent reference which shows pictorially how to do this step-by-step. It also includes good information about perimeter. It is:  Area and Perimeter

Some troubleshooting tips: 

• To notice how an irregular shape can be partitioned (decomposed) into smaller rectangles, use colored markers to outline these “hidden” shapes.
• Remember, there can be more than 1 way to partition an irregular shape into smaller rectangles.
• I have noticed some kids try to multiply all of the numbers shown. Remind students they only need 2 measurements (length and width). These are 2 adjoining sides (not opposite sides).
• Students often aren’t sure how to determine the length or width of a missing dimension. Remind them that opposite sides of a rectangle are equal length. Sometimes subtraction may be needed to compute the missing part.
• Have students compute the area of each smaller rectangle and write the sub-total inside each one.
• Then find the total by adding the area of each smaller rectangle together.
• Area can sometimes be calculated by imagining the whole shape is one large rectangle, and then subtracting the area of the small insets.
• When provided irregular shapes without gridlines, have students redraw the shape on grid paper, or use cm or inch tiles to reconstruct and check.
• Try actual applications such as computing classroom floor space.

Your ideas are also welcomed on this blog!