In my opinion, you have received some really excellent answers, with the exception of one (you know who you are
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Now, here's how it worked for me...I got my first and only BB gun when I was six. My dad was a hunter and very safety conscious. One excellent control of a six year old with a BB gun, beyond attentive adult supervision, is to hand out BBs only five at a time. Five are fired, the gun is cleared, then it is cleaned and stored. As the child matures and advances in skills and safety consciousness, additional freedoms can be earned. By the time I was ten, my Daisy Red Ryder went every where with me. We were allowed to shoot birds but not song birds. Starlins were a favorite target and eventually, Bluejays were on the list also...
There are several documented incidents where BB gun accidents have killed adult bystanders, so SAFETY and ADULT SUPERVISION are the standards to live by.