If you own a chalkboard and children have access to it, sooner or later, you're going to find marks on it other than those made by chalk. Here's a very easy way to remove not only pencil marks, but oily fingerprints and crayon as well.
Use a felt eraser to erase the entire chalkboard surface.
Wash the entire surface of the board with a mild, organic, non-oily, non-abrasive cleaner, according to the directions on the bottle. Apply by either spraying the solution or using a soft lint-free cloth or chamois.
Rinse the cleaner thoroughly from the chalkboard with warm water, using the cloth or chamois.
Dry the chalkboard immediately with a soft, dry, lint-free cloth or chamois. This is very important, as it will discourage the water from compounding with chalk--which would result in a slippery, glassy, veneer-like surface that would be impossible to write properly on.
Allow the chalkboard to air-dry for a couple of hours.
Lay a stick of chalk on its side, pressed against the chalkboard, and rub it until the entire surface of the board is covered with chalk.
Remove all of the chalk with a clean, chalk-free felt eraser. Wipe the surface of the board once again with a dry, soft, lint-free cloth or chamois.