Morality in the Classroom

People tend to be resistant to teaching morality in schools. People think it involves teaching controversial topics such as religion, sexuality, politics, abortion, etc. However, we do teach morality in schools, and I don't see how we could avoid it. With children, we teach "right" from "wrong" probably as much as we teach academic things. Children need to learn how to behave in socially acceptable ways in order to grow and be able to function in the world. Even with older students, we still teach them right from wrong. For example, colleges take plagiarism extremely seriously, because it is wrong to steal people's intellectual property. Some things, we accept as clearly right or wrong. Others, such as the controversial topics I mentioned above, are less clear, so we avoid talking about them. However, we apparently do teach morality to students.

Question: Where do we draw the line between morality that should be taught in schools and morality that is too controversial?