What is the best way to clean a gray slate floor? It streaks every time I mop it, and the mop seems to shed on the floor.

It sounds as though your slate floor has a rough finish which catches the fibers of the mop as it is dragged across the floor. First, you need to deep-clean the floor to remove all dirt and grime. Next, apply a good-quality acrylic sealer. Several coats may be necessary. The acrylic sealer should make future cleaning much easier. Clean the floor with a neutral cleaner and re-apply the sealer as needed.

TIP When buying a sealer for slate, be sure to purchase a high solids type designed for stone surfaces. Do not over apply , any coating will need to be striped at some point. Applying too much sealer will make the stripping process difficult.