I had the kids cut and draw into scratch-foam (they can use a pencil since the scratch foam is so soft, just about anything hard will make a permanent impression) and then glue their designs onto pieces of stiff foam core. The next day (after the glue was dry) I showed them different ways to ink up their plates. We used water-based block printing inks (super easy cleanup and non-toxic) and they tried rolling the ink on in both solid colors and gradations, and also tried making up a palette of different colored inks and painting it on (thus adding the texture of brushstrokes.)
I've done this and a variation of this project with kids many times and it is always a big hit. It is quick, easy, and a great introduction to relief printmaking.