Problems are in textbooks.
They have answers usually found in the back of the book, what we make in design are decisions. We do a disservice to students by calling these things design problems. We understand that decision making is problem-solving in a colloquial sense, but it means something different in academics. Our curriculums seem to be deficient in statistics and probability. if you're serious about introducing design at K-12 levels, time is a big issue. Maybe it can be make more efficient in some way.