I teach Newton’s laws knowing they are strictly false. What exactly am I teaching?

This term I'm teaching mechanics to a senior secondary class in Lagos. F = ma, the laws of motion, gravitation. I teach it with full confidence, and I also know that relativity and quantum theory say it is not strictly true of anything.

The usual answer is that Newton is a limiting case: at speeds much lower than light and in weak gravity, Einstein's equations reduce to Newton's. But Kuhn, in The Structure of Scientific Revolutions, argues that this is misleading. What you derive from relativity in the limit looks like Newton's laws, but the words in it (mass, space, time) no longer mean what Newton meant. On his view the two theories are not one true and one approximately true; they are different pictures.

Nancy Cartwright goes further in another direction: even our best fundamental laws, taken literally, are false of real things, which never meet the ideal conditions the laws describe.

So when a student writes F = ma in her exercise book, has she learned something true, something false, or something useful? Does "approximately true" even make sense, or is it just a polite way of saying "false but handy"?