Yes, you are looking specifically for slate.  A couple of ideas:

  1) There was an article some two or three years ago in _Yankee_ magazine
about a slate quarry that had just reopened in Maine.

  2) You should be able to use the slate from beneath the felt on an old
billiard table.  I wouldn't know if that would typically be "blackboard
grade" but it would have a planar cleavage and I would think would fill your
needs.  It would certainly be large enough.

Kevin McCartney, Ph.D.
Associate Prof., Geology
Director, Northern Maine Museum
  of Science (opens October 5)
University of Maine at Presque Isle
Presque Isle, ME  04769