Let me give a little insight into what it's like to teach my eldest. Let me also write down a reminder of what homeschooling was like for him when he was 3 months past his 11th birthday.
"Addison, come here so I can make sure you understood today's math lesson." (He is working through/reading/self-teaching in math. His brother comes to me when he is stuck or needs clarification. Addison, not so much.)
He comes to the table, where I sit with the book. He does not bring his work. I don't ask him to get it. I am checking for mastery, and to make sure he's reading the instruction thoroughly.
"Ok, what about this problem?
Is exponentiation associative? That is, if a, b, and c are positive integers, must we have
"What about this one?
517 + 517 + 517 + 517 + 517
as a power of 5"
He throws out
without looking at his sheet. I ask him to walk me through, and he does.
He proceeds to tell me the answers to the other problems. I have no idea if he is remembering what he wrote, has a photographic memory, or is reworking them in his head on the fly. But, he is correct. On one problem, he explained what he put, initially, and that he read through and understood what he did wrong, telling me the way he then came up with the correct answer. I have always been amazed with this skill. Often, I will yell from the next room, "Addison! What did you get for that problem with all the 7's?" He'll look up from whatever Kindle book he's reading and not only yell back the answer, but can also remind me that it was problem 1.56.
I then get another problem.
"Express 1120,000 as a 10,000th power by finding the positive integer a such that 1120,000 equals a10,000
He tells me that he figured this one out. Before jumping in, he asks me (in a non-threatening, non-critical, completely nice way) "Do you know how to work through this one already?"
And here lies his biggest achievement of the school day. It was not understanding the math lesson. It was not his independent learning. It was the fact that he paused before spouting off a detailed disquisition to ask if I was ready, or if I was on the 'same page' as him. Most people would have missed this. I did not. I sighed, and smiled. I told him that I knew how to work it, and thanked him for asking.
He finished his schoolwork and never recognized this as a big deal. But, I did.
He's got the academics covered. It's up to me to teach him the rest.