I grew up moving all around, as did my DH, so when the kids wanted to mark heights in early grade school, we got a piece of 6 foot plus more bit of wood and used that, kind of a double heighted and thick extra wide yard stick. Not so wide to have silly pictures drawn on it, but easily portable from house to house! funny though, we are still in the same house...
There was a movie/tv show that had an opening scene of the family door where all the heights were marked, and then they moved, but the door was delivered later to the new house?
I am totally going to let my grandkids draw on the walls!!!