Maths and Halloween do mix!
Spatial ability develops in tandem with hands-on experiences. Experiences where the hands-on activity, in this case painting and folding, will lead to changes.
I tried using the name of a person, written quickly along a fold line in wettish white paint and with feathering to each letter. My first trial we with the name Pete.
Quickly folding before the paint dries gives a partially predictable resulting symmetry.
I discovered that a couple of google-eyes added that extra pizzazz!
If I was in your classroom, I would insist that the symmetry is maintained with any additions that students make .... after all, that's the mathematical idea that we're trying to promote with this activity.
Bet you can guess the name that this one started out as!