English is not my first language, so I'm not sure what you commonly call one of these:
I'm trying to choose between blackboard, white blackboard, or maybe just 'slate'.
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I most often hear these referred to as dry erase boards.
I refer to it as simply a whiteboard.
Also in common use is the generic term "the board", since most rooms only have a single whiteboard or chalkboard so there is no need to disambiguate between them.
For instance: "Student, please go write the answer on the board."
"Blackboard," has a nice archaic ring to it. I started in elementary school with blackboards, then they turned green, and we still called them blackboards. Now they're white, but to me it will stay a blackboard no matter what color it is.
"White blackboard," I've never heard used, except by sarcastic teens mocking my age.
"Slate," would confuse Americans, and, I belive, is not techincally correct since a "slate" is an individual item that one writes on, like a tablet, not something that is big enough to nail to the wall and show the room; that would be a big chunk of rock indeed.
So, if you want to be accurate, "dry erase board." But accuracy is boring and ugly.
The dry-erase boards are called simply "whiteboards" or I've heard "greaseboards."
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