What is a word (verb) for asking a question where you know the answer, and you're trying to get someone else to say it?

For example:

"And Columbus sailed the ocean blue in...?" the teacher _____ed, scanning the room for someone to call on."

"angling or fishing for the right answer" seems to fit.

"And Columbus sailed the ocean blue in...?" the teacher scanned the room fishing/angling for the right answer."

• fish for - "To seek something in a sly or indirect way: fish for compliments." - TFD

• angle for - "to try to get or achieve something in an indirect way" TFD

The teacher asked a leading question : "And Columbus sailed the ocean blue in...?", scanning the room for someone to call on."

leading question

noun. a question phrased in a manner that tends to suggest the desired answer, such as What do you think of the horrible effects of pollution? – Collins English Dictionary

Elicited

e·lic·it / iˈlisit/
v. (-it·ed , -it·ing ) [tr.] evoke or draw out (a response, answer, or fact) from someone in reaction to one's own actions or questions: they invariably elicit exclamations of approval from guests. (from The Oxford Pocket Dictionary of Current English, online at encyclopedia.com)

Since it seems to be popular from my comment, I'll submit as an answer prompted.

to ​help someone, ​especially an ​actor, to ​remember what they were going to say or do

Cambridge Dictionary

Although the definition does say "especially an actor" there's no reason you can't use this for a teacher who's trying to nudge students towards an answer. Alternatively, you have coaxed.

to ​persuade someone ​gently to do something or go ​somewhere, by being ​kind and ​patient, or by ​appearing to be

Cambridge Dictionary