T.S.
I have dealt with true ADHD and ADD kids. There is a huge difference between the two. The violence you are thinking of is what becomes prevalent in ADHD kids as they struggle to express their frustration with a world that moves at a difference pace than they do.
ADD is a much overused term. Having boys that were both on that edge I can tell you it is very common to have some first graders that are not 'into' school work.
My first suggestion is to learn your child's learning style.
I have an auditory learner. He only needs to hear it, thus he would play with anything on hand (paper, paperclips, rubber bands, pencils, etc.) while the teacher was instructing. But he could still repeat concepts, pass tests, etc. To keep him on track we (he is now in 10th gr) try to work with his teachers and tell them in the beginning that he is an auditory leaner. He needs only verbal instructions. making him do 100 word problems rather than let him help someone else that is struggling, let him do a fun project, or let him work ahead in the book is much better. He can get as far as 4-6 chapters ahead of the class and still do well.
My other son is a doer. He needs to hear, but then also be able to move and do it with his hands. Work sheets are fine for him, but he cannot be expected to sit at a desk for 7 hours at school without a lot of release for that energy. He is not ADHD however because he can truly hold his attention, if he can just stay focused and have a goal. We kept him in soccer and other activities. The teachers learned to let him run errands or move around.
Another child I had was ADHD, she needed full time supervision. She did get angry. She would absolutely pace at times. She could not focus. She was on medication just to get through a school day. She could stay at her desk, but she just could not focus on anything at home, school, church, for more than 2 minutes. She was truly in need of meds and is the only one that was medicated.
I suggest you work to learn how your child functions best and then find the academic situation to help her. All my kids have been at different schools to help them succeed. A good teacher wants to help all students succeed and will find a way to make that happen if at all possible. She will also communicate a lot with parents and not make the child feel like a failure because they are different. If a teacher can't do that, then you may need to find a different teacher, school, or consider options.
But meds should always be a last resort in my opinion.
Good luck,
ts