I’m still waiting for someone to answer the OP’s question.
Please, please sign in, wise men of the CR, and tell us where the beautiful Minhag of teitching the passuk “Va’Ani” together with the Rashi in that warm niggun originated.
(And in case you’ll want to ask me the same question you asked Queen, -no, I didn’t learn it in Bais Yakov. But I remember it from other little boys, and some big ones.)