Lead pencils don't just break. I got my first one in the 3rd grade and haven't used a wooden pencil since. I love those things, sharpening not required. Also, they are more dangerous than a wooden pencil because they have a sharp metal tip.
Give them all crayons, worst you can do with them is choke swallowing one. Or better yet, let them find out themselves and learn not to stick themselves again.
Had a teacher that always said don't stick anyone with the pencil because you will get lead poisoning. Guess that teacher didn't know the difference between graphite (carbon) and Pb lead. I wonder if that was an idle warning so we didn't stick each other or if she really believed that herself.