We are currently finishing up our first year of homeschooling, after we realized that school just wasn't an option for my "kindergartener" because he was done with kindergarten, and most of 1st grade at 4 years old without ever really working with him. My son is a reluctant learner if someone is teaching him. He had a horrifying 1 month school experience where he was pushed and required to work on things that he hated and had zero interest in and he is in a lot of ways healing still even a year later. I have found that with these academically precocious children they learn in spite of us. They have an incredible drive to learn, and learn seemingly by osmosis. My son knew things, but had no idea how he learned them and frequently would say "I just have it in my head" or "my brain told me". After we pulled him from jr. kindergarten I told myself that I would not require anything formal in terms of learning until he was ready. I stuck to my guns, and didn't offer him anything enriching until he asked for it and it only took him a week. An extremely traumatized, reluctant learner. As a homeschooler, I only "require" that he do 1 page for math, write in his journal daily, and read. He isn't ready for writing, so we don't formally work on it I just have him write one sentence and praise him highly even if all of the words are mispelled and I can't decipher them. All of this work, takes him about a 1/2 hour sometimes longer sometimes less depending on how quickly he feels like working. We don't watch television in our home, and although he has a computer we really limit computer time. Our home is incredibly learning rich, and we are constantly offering up new experiences. Even though I didn't require much of him academically this year he gave me so much more than I asked by my backing off. The days that I get the most out of him, are days we play mostly games. We play Yahtzee and he adds the 5 dice up in his head. He looks for combinations of 10's, and then works the dice in that manner. He will play for 1 1/2 hours if I let him and I make it really fun and encourage him constantly in a fun exciting manner. We play chess, checkers, boggle, scrabble, dominoes, and many other games throughout the day. All of these games require skills that I expect of him when we do school work but it's fun because it isn't in a workbook and it involves fun and he doesn't see it as learning.
I think sitting for 1 1/2 hours and working on curriculum AFTER preschool for 1/2 day is a bit much for a child of 4 (I'm guessing the age based on preschool), but if your child is asking for this amount of work at that age than it's fine. If you're asking of this of your child I think it's too much to ask because there will be plenty of time for academics the older they get. Now is time to have fun, meet their inquisitive minds, and let them learn about the world around them.
If you're looking for specific recommendations on curriculum we use Miquon Math, and I really like it. It teaches advanced concepts to children at an earlier age and uses Cuisenare rods which are colorful and great for children this age because they tend to be more tactile. In the first book, addition, subtraction, multiplication, solving for missing numbers, and fractions were covered. I believe they consider that kindergarten math, however state standards are not nearly close to that. Personally I think state standards are way too low, and fussy and even though we homeschool through a charter and they give me a set of state standards I never even look at them. I just make sure my children learn what they are capable of, and let them lead me in what they are interested in. Currently my 5th grader is obsessed with Greek Mythology, and has been for several months. I never introduced it he just glommed on to it on his own. I provide several books per week, and many resources and his interest has exploded into studying Roman, Norse, Celtic, and now Native American Mythology...all on his own. I would more than anything encourage you to follow your child's interests. If she is interested in anything, feed her books and materials to help her learn more about her favorite topics. It doesn't matter what the interest, the act of learning about it and feeding her interest is more important at these younger ages. My son is really interested in locks, and any sort of technology. I leave books around the house constantly that I feel would interest him, and most of the time he picks them up and just starts reading. We also use audio books quite often, and the boys will sit and listen to audio books while doing art, or building with Legos.
