If one is going to do grid drawings, for whatever motive- DISTORT the grid.
Do your regular grid on a photo they have taken of themselves. Portraits
work best. Cut the photo up into squares. Number the backs of the squares.
Then have the students draw a large distorted grid(like a warp in space)
,number appropriately and then they can try to solve the visual problems
of translating the material in a square into a larger distorted shape.It is
a good exercise in spatial relationships and gives permission to the
student to "play". I consider this a quick fix lesson but they sometimes
have their place in the art class room too.