Another lesson repeat was these clay fish by first graders. I've seen them on a few sites where they made them with pinch pots. For ours, we used a clay slab or pancake wrapped around newspaper.
The students added texture to the fish and painted the clay with watercolor after firing.
Kindergarteners tend to flatten their clay no matter what you are making with them. I just go for the flattening instinct and have students make clay masks. This student didn't add a lot of clay, but kept nice details through drawing and, again, painting with watercolor.