I do not play many games with high school students although I am sure they
would work.
Whenever clean-up threatens to loom large, I do a couple of things:
1. I lay out tools on a sheet of paper taped to a table. I trace around
the objects with a marker so students know where to find things and where
to return them. This really does not take a huge amount of time and it
really keeps tools in place. When it is almost time to leave I can tell at
a glance what is missing. I'll say, "A brayer missing; you're not going
anywhere until it comes back." At this point someone usually has it in hand
and holds it up so that the class is not "held up." After a few days, I do
not even have to check, the stuff is just there.
I find when I do this, it shows that I am serious about taking care of
the materials and this concern just transfers to the kids.
2. During the clay or other messy units, I just print a roster from my
grade book. I assign monitoring and wiping up the clay room to one student
and cleaning up the sinks to another. They do not protest the cleaning up
as long as everyone gets his/her fair turn.
Occasionally I'll even have a student spontaneously clean the paint
trays or sinks without my request. I will then compliment or even hug the
student (small family-type school and I'm a "seasoned," read old, teacher
so we can still get away with this) and fill-in one of their cleaning turns
on the roster.