What should a school day look like?

I have been off-schedule for school lately. I am just having problems following the paths I have laid before myself. I have read tons of homeschooling material. I know the outcomes I want from school. I know that I want my kids to love learning. I know that I want them to excel. I know that I want them to have great imaginations so that they can be excellent problem solvers. I know that I want them to have a wealth of real experiences.

I know that by the time they start high school I want the girls to be ready for AP Virgil, have mastered Algebra, be ready for lab sciences, be strong readers, have a foundation in world and American history and literature so they can be ready to join the great conversation.

I know from experience with my senior year son, that I want them to not burn out on math too early, to do more writing, to have better handwriting, to incorporate art into their schedules, to be better at independent work, to be self motivated, to find something that excites them and motivates them to study more, and to do more community service. (maybe walk on water and learn to fly too?)

The problem with me is that how do those goals translate into a day of school for two very bright little girls? Of course only one of them is actually in school right now, but the school day really includes them both.

CC is in first grade and reads well, adds, subtracts, skip counts, divides, tells time,counts money and knows basic fractions and geometry. She cooks, cleans, is learning signing, swims, flips, sings, draws, and babysits. She loves history, science and art. She enjoys explaining animals to grownups at the zoo. These are all things that have happened without a "formal" school day or schedule and without any "teaching."

I think that for us, right now (at least this week), school will continue to look like it does currently. We will continue to read AO Year 1 selections. CC will continue to work her way through the Little House books. We will finish out FIAR and History at co-op. We will continue reading Story of the World Volume One. And most of all, we will get outside to play and explore every chance we get.