They were split off in big slabs. One side left as split. The chalkboard side was ground flat and finished to use as chalk board.
Slate (real rock black slate) was also used as bottoms of tropical fish tanks.
IIRC the black boards in Marshall grade school on the West Side 3200 W. Monroe had boards about 5’ x 5’, that raised up to reveal the coat racks on the hall side of the room. Fixed b’b’s arcross both front and back of room. In the mid 30’s Mrs. Jesse Root was 8th grade teacher & principal. She ruled with an iron hand and the 8th graders loved her. 
Any OT Dopers remember her?