The "show your work" thing is a constant bugaboo around here. It's difficult for kids who don't actually do any work to get the answers to learn to show the parts that the teacher is looking for. I have been fighting this battle for years.
It's necessary to explain (repeatedly) that if he doesn't show how he got the answer, the teacher doesn't know whether he knows how to do it or he looked in the back of the book or on his neighbor's paper or online. And also that if he doesn't show the teacher that he can do the work, he won't get to do anything more interesting and will have to keep doing the same boring thing over and over. It's much more motivating when phrased in terms of self-interest rather than conformity.
It's definitely hard enough to fight the battle with the kid to get him to learn to show something useful in the way of work, so I don't recommend adding a (losing) battle with the teacher to try and convince her that he shouldn't have to show his work. Even if "show your work" is useless when the question is "9x5=?", it will eventually become a necessary thing to do in order to keep track of his place in algebra or geometry.
But rest assured, it's a perfectly normal problem that you have.
And err...what's wrong with the Rats of NIMH? That was a good book.
