Ds11 gets up around 7am, eats breakfast (usually waffles or cereal), and then starts school. He does most of his independent work before ds7 and I get up. Ds11 prefers it this way. He says he can truly concentrate when it is so quiet and we are in bed.
Ds7 and I get up between 9 and 9:30. While ds7 eats breakfast, I work with ds11 on the things he that require my help/input/instruction. Ds11 finishes up his day and ds7 and I set to work on his school. Using this method, generally both kids finish their school day around noon. Then, we have lunch and the rest of the day is ours to enjoy!

ETA: The only chores the kids do before school is making their beds and getting dressed. They both have to put their own breakfast dishes in the dishwasher, but that takes literally 2 seconds.