Measure and cut a piece of fabric to cover the exposed back of the board. You can do this by tracing the board onto fabric with a pencil and then cutting just inside the line; this way the cut piece of fabric is slightly smaller than the board.
When the glue is dry, apply a thin, even coat of clear chalkboard paint in a horizontal direction over the top of the placemat. Wait one hour and then apply another even layer of chalkboard paint, this time in a vertical direction. Allow the paint to cure for a full 24 hours. Depending on the fabric you use, you may need to apply two more layers of clear chalkboard paint in each direction.