Well, the student is confusing area with perimeter. The left-hand figure is more interesting in that the student seems to have been so concerned with getting 16 grid squares filled in that they forgot that the larger figure should be a square. Or in some way they didn’t understand that part of the directions.

It would be interesting to see what they would have come up with if the grid on the right was only 9 squares wide. Two full rows plus two more grid squares on the next row?

Alan Dendy

This is the product of a process. There is a lot of missing information if we only look at the end result. I wonder what we would find out about his/her thinking if we included observation and conversation to our analysis toolkit.

The rectangle on the right is totally familiar to me. Students leave off the sides. I am not convinced that they are confusing area with perimeter, because when I sit with them and make them count each line segment, it’s clear that they are surprised that the verticals count.

Point taken, crazedmummy. I can imagine that with the rectangle, and the experience you described backs you up.

But I’m not sure I can see how the student could be thinking that the outside of the shaded figure on the left is made up of 16 line segments, whereas it is clearly made up of 16 full squares.