Last lesson they were in Unit 10 of level 1 Lesson book and next lesson they will be using 2A Lesson book.
My son likes to go ahead and try new songs himself. About 3 weeks ago, he already went through all songs (at least right notes and rhythm) in three level 1 books (Lesson, T&A and Performance). His teacher knew it and gave him another book (Alfred All in one book 3) so he can try new songs (with eighth notes).
During lesson, my son plays a piece and the teacher will show him what he needs to do differently (like downbeat, melody v.s. harmony, hands and fingers technique to sound better). Then he will try again and usually he can do what teacher asks him to do. Then they will play duet if there is one. If time were not limited, they could go on and on (no skipping, also went through all three books).
She said she has higher standard for him and would demand stuff she usually won't do for this level. Even though she knows he can play the whole books, she still wants him do it one by one in front of her.
So they don't skip at all and if time is allowed, they can probably be on unit 10 of all three books.
I wouldn't use the word prodigy at all. I think my son just has good memory and above average music instinct. He can memorize those songs easily after playing it several times. Say if the next lesson will start from unit 8, he can play songs (about 10 pages) from unit 8 one by one in order without looking at the books. He showed this to me in practice, but I told him that he still want to look at the book so his sightreading can be better.