My 10 year old had the same types of behaviors (and IQ scores!)and we put him on a low dose of ritalin mid year. He has always seemed sort of "borderline" ADHD. It is hard to tell what is anxiety, what is boredom, what is normal boy behavior He improved a lot according to the teacher after the meds and also his own self reports. He was accelerated in math and in a gifted program before and after the meds so I believe it was not boredom, it was ADHD. You can get a provisional diagnosis.