To me this sounds like a learned behavior; especially since this is 1st grade and he hasn't been in school long, I would agree that this is probably his primary strategy for getting what he wants at home and it works and is tolerated. Honestly the first thing I would try is extinction. Completely ignore the student while he is crying and then immediately provide attention when he stops.
That's a reaction during the actual behavior event. To prevent, take the student aside and let him know politely and firmly that while it's ok to cry, awesome students don't cry over little things, and that you want to see him working on his problems instead of crying about them and that will make you very proud of him. Don't reinforce how smart he is, there are tons of studies coming out right now that students who are "smart" won't take risks for fear that if they fail they won't be smart anymore, but students who are praised for working hard understand that if they fail they can fix it.
If extinction doesn't work, try a contract. Something like if he starts crying but stops when you cue him, he gets a small reward, something as simple as a sticker, (or a star on the Super Improvers Wall, if you implement it.
Dave Sudia
WBT Intern 2011-2012