ABSTRACT
I had a student who basically understood the difference between area and perimeter. I drew this rectangle on a grid. To figure the area, she counted down like this (Figure 11.1a), then she counted across like this (11.1b). Then she multiplied three times four and got twelve. So, I asked her what the perimeter was. She said it was "the squares around the outside." She counted like this (11.1c). She understood the perimeter, she just counted wrong. She was always off by four.
