I was helping a home-schooled student with her homework when we came upon several images of figures that we were supposed to find the perimeter of. In several of the figures, some of the lengths were not given; yet, with some thought, the perimeter could still be figured out. For example, the perimeter of the above figure is 28. She could not "see" this.
Her arithmetic skill are admirable. She is neat, organized, and is capable of looking over her work and finding where she made her mistake. Yet, drawing the square and showing what equalled what, did not impress her. I longed for a box of toothpicks. I got the feeling that she was getting area and perimeter confused in some way but I ran out of time before we could resolve her problem.
Does anyone have any ideas what conceptual problems she wasn't resolving?