9 years old is a very difficult age for girls. I don't have a dd that age (my kids are babies, but I just happened in here) but taught 4th grade up until just a couple years ago. There are hormonal issues, self esteem issues, sort of a massive question mark in their minds around this age as they are not quite children but grown up either. This is an important age for communication and trying to get their input as much as you can. An excellent book that I would recommend is "Parenting with Love and Logic." The authors present ways that you can reach logical conclusions to behaviors and really get your child to think. 4th grade is a difficult year and the beginning of tumultuous times for girls (boys are often, but not always, trailing a little in maturity). Work on reasonable boundaries that you and dd both agree on and discuss freely. When the boundaries are broken (lying, for example) natural consequences are in order. She will need to make up whatever homework she lied about, for example, during a time mutually agreed upon, for example. Her interests could be changing at this age, and she might not be sure of what she likes. This would be a great time to try some new experiences out with her! You could also encourage her to keep a journal about things that are on her mind. I hope this is a little helpful. As I said, I have no parenting experience anywhere near this yet, but I wanted to offer you whatever thoughts I had on the matter.
Mom to Delia (5/25/07) and Alex (4/10/10) and 2 spoiled kitties