The one we have in mind is the ordinary use where it means "maybe": "It may rain tomorrow."
As you may have noticed, this is actually very rare in KS3 writing. For that matter, it's very rare where most KS3 writing comes from - casual conversation. According to a recent count, in conversation it's even rarer than "shall", which makes it a rare bird indeed.
But unlike "shall", it's extremely common in academic writing, so it's a real give-away for prowess in more formal modes. KS3 writers would do well to sprinkle "may" fairly liberally in their writing of, say, literature essays.
You may think this is terrible pedagogy. Surely literacy is about something more important than sprinkling obscure words? Yes, absolutely right; but "may" is a really useful word, and should be near the top of every writer's toolkit.
The point is that it expresses uncertainty, and there's a lot that we're uncertain of (especially at KS3). KS3 writing is often full of "I think...", which is a crude way of showing uncertainty:
"I think Shakespeare wants to make fun of Malvolio."
It would at least relieve the tedium of marking to see the odd "may" in such cases:
"Shakespeare may want to make fun of Malvolio."
"May" even has the advantage in terms of length.
Better still, "may" forces us to distinguish two kinds of uncertainty which are both lumped together by "I think". We only use "may" when we're uncertain about whether something is factually correct - it may rain, that may be true, there may be life on Mars, and so on.
But we also use "I think" for another kind of uncertainty, where we're making a personal judgement, as in "I think your tie is very smart." This is most definitely not a case for "may": "Your tie may be very smart."
This important distinction is a fundamental thinking skill, but it may not be clear to KS3 writers. So long as they can get away with "I think" in both cases, they need not face the choice and can continue in a blur of vagueness.
So we stick to our pedagogical guns: heap praise on every "may" and blame on every "I think".
If you encourage them to use "may" for factual uncertainty, then at least they may be more certain about what kind of uncertainty they're suffering from.
Richard Hudson is professor of linguistics at University College, London
Geoff Barton is headteacher of King Edward VI School, Bury St Edmunds, Suffolk