Using Color Tiles to Measure Area of Irregular Shapes

by C. Elkins

I have heard from a few 4th 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:
  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!

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