If you want her to "just sit and learn like they do in school," you might want to just send her to school. Is she ready to be taught? What do you want to teach her? What is her learning style? Does she have any special needs? Is she showing signs of being ready for "formal education?"
I don't use any "magic". My 4 1/2 yo can't sit still if her life depended on it. She learns while she is moving around and dacing and bouncing. She takes it ALL in! I don't expect her to be able to sit still. My oldest can sit still, but she unfortunately went to public VPK and then she did some public K. She is just a kid that NEEDS to sit still to learn. If she moves around to much or fidgets she isn't actually taking anything in.
Kids that age don't sit and learn very well. That's why preschools are usually all play. I suggest going and getting music CDs with fun songs. Checkout Starfall.com Most kids love it and it's free. It's an excellent resource. Read to your child every day. Keep the TV off during the day and do lots of crafts. 8)
At that age play is still important though that no longer matters to most public schools anymore. Do you know what her mulitple intelligences are and how she learns best? Children learn in three ways:
Sometimes it's a combination of all three.
Shorten 'lesson plans' into say 5-10 minutes. The best way is for her to play and learn that way. Do hands on activites. Jigsaw puzzles. Manipulatives like stringing beads on a piece of yarn counts as math. Helping mommy and daddy cook counts as science, math, and reading skills. Finger painting counts as Art.
No, she doesn't have to do much more. If she is absorbing everything that she encounters, then she is learning. When she is playing with her toys, ask her how many she has and what their shapes are and if they are soft or hard and what colors they are. That is how kids learn. If she likes to dance, then have her learn some music while she is dancing. Have her learn her alphabet that way too. If that is what she likes.
Fun and Interesting, is how you will be able to teach her. :)
She will sit for half page math either addition, subtraction. is that normal? does she has to do more in a day?
We don't use any magic. I don't make them sit all day (and mine are 5 and 7). We lay on the floor, walk around, sit on papasan chairs, dance to music, and so on. When they do need to sit (my 5 year old doesn't need to as sitting at that age for long periods of instructional time isn't age appropriate, but my 7 year old does have SOME seat work that he needs to be seated for) I give lots of breaks, move to subjects quickly, give some down time between subjects, give him fidgets to play with in his hands, and so on.