Making egg carton prints is a really easy and cheap activity for a rainy day.
It really is as simple as
Cut. Dip. Print!
Keep your egg cartons and then you can chop them into smaller pieces.
Make a mixture of acrylic paint and water that is the right consistency to stick and to not be too thick and then simply dip the egg cartons in the mixture and then print onto watercolour paper.
It may take a few efforts to get a distinct image but this overlaying is part of the fun.