At 11 I was given a .177 pellet rifle that my parents let me shoot in northern Michigan (My mom actually said, "You'll shoot yer eye out!" way before "Chistmas Story" was at the movies). It was Crossman 760 and I shot it every day until my arm hurt from pumping. I set a soup can over a stick across the Muskegon river and sat on the dock, I'd go through a carton of BBs in just a few days. Every few weeks I'd row out and move the can further away or replace it as it became shot to pieces. I became a very good shot because of that experience. Then my father let me shoot his Ruger Mark? .22 into ice on the water. Without hearing protection, it was more violent than the BB gun and my first thoughts of firing gunpowder for the 1st time was that it was unpleasent. I think that carried with me and I developed respect for guns and learned to treat them different then my toys because of that.
A word of caution: an 11 year old boy, unsupervised is likely to test limits! How far will this shoot? Will it skip on water? What is the destructive power? The world was still new and there were many things to experience in the hundred acre wood. I never shot at a single bird or frog, but cat-tails in northern Michigan still fear me.