"The paper plate is cheap" is, I think, correct. UK English talk of "paper plates" and "paper bowl" sounds odd and unusual.
It's like a "paper cup" you might use in the bathroom or with a water bubbler. Kind of like a styrofoam bowl, used for snacks or holding small items. I could definitely see a teacher getting good use of them in a classroom, especially in younger grades.
Paper bowls are made out of a waxed stiff paper and are used as disposable bowls. They are often used for ice cream, soup, or craft projects in American schools.