Learn English – Phrases similar to “what would you do?”

In my district, we had two breaks in elementary school: a fifteen-minute recess and a 45-minute lunch break. The students go outside and play during both breaks. Teachers look after the kids during recess; at lunch, that's done by a rotation of parent supervisors.

In high school, there were four classes a day, in different classrooms. Students got a five-minute break to move between their first and second classes. Between the second and third classes, there was a fifteen-minute long break. Lunch break was an hour between third and fourth classes. In all cases, students didn't have to go outside, so a rotation of teachers roamed the halls making sure nothing bad happened.

My teachers usually referred to this as supervision or being on duty, as in

"I can't meet then. I have supervision tomorrow."

"I'm on duty (at recess / after third period / etc.)"

"Who else is on duty today?"

I come from a family of teachers, so I can confirm that these are still common usage in my district. However, I'd imagine that usage differs from place to place, especially if a specific phrase like lunchtime supervision or recess duty is used in your collective bargaining agreement. Any combination of

playground / lunch / recess / break / ...

supervision / monitoring / duty

will give you an understandable term for this situation which I guarantee is widely used somewhere; the examples playground duty, playground monitoring, and lunch monitoring, are all cited in other answers. (Note that none of these take the article a; you'd say "I have playground duty" instead of "I have a playground duty.") So

"I have break duty after my 4th lesson on second floor"

sounds good to me!

Your best answer for what you should call it, though comes from Mitch's comment: use whatever phrase is most commonly used by the teachers around you!

This is, I think, an instance of ‘baby-talk’ (what linguists call child-directed speech), which is a special dialect adopted by adults in speaking to small children. Although medica is undoubtedly correct in asserting that children employ such terms as “pretty please”, “boo-boo”, “yucky” with each other, I believe they learn them in the first instance from adults.

Some elements of baby-talk—simplified syntax, a deliberately narrowed lexicon, morphological adjustments to mark word and phrase boundaries more clearly—are believed to be of value in providing a child more intelligible models for imitation. But there is a large range of ‘styles’ within this dialect, and many people adopt distinctive (mis)pronunciations and words and phrases which they suppose are characteristic of child speech, as if the child's progressive acquisition of language were not an awe-inspiring and heroic achievement but a species of imbecility to be catered to. At one time it was common in novels to represent the speech of children as baby talk—very like the demeaning representations of African-American or rural or foreign speech which once passed for humor on the stage and in literature.

Baby-talk is also used to pets, and with markedly ironic intent in ordinary speech between adults. And some children, having found that baby talk is regarded as ‘cute’ and endearing, carry some of it terms into adolescence and even adulthood. My impression is that this is less common than it was fifty years ago; I hope I am right.