I'm a confused by the way Mick used the indefinite article "a" in his comment:
You could say that the child is playing at basketball, or playing with a basketball.
Why does the phrase "at basketball" not have an article, whereas the phrase "with a basketball" has the indefinite article "a"?
My guess would be that the key point here is the preposition (at) that in the first case prevents its use, whereas, in the second case the preposition (with) calls for its use, but I'm not sure either whether there's such a thing in English as the preposition to be decisive in the indefinite article use or what other rule may govern this situation.