Now that we've solved the pencil sharpening problem, I've also solved the problem of having pencils stay on desk (not on the floor). I was published last year for an idea in the Scholastic Teacher magazine.
I buy the big roll of velcro at the beginning of the year at Walmart. I then cut off 1/2-1 inch strips. I take the rough part and put it on the top corner of students' desks (on the right for righties and on the left side for lefties). Then you take the soft part and wrap it around the base of the eraser, right under the metal part. Then the kids always have a place to put their pencils and they don't roll off or end up on the floor (this was especially great when I was pregnant and couldn't bend over to constantly pick them up).
I hope this helps. Let me know if I need to clarify anything.