I have a DD8/3rd as well. Does your DD have a desk that's open near her lap/hands? My DD hides little things at the edge and plays with them with one hand and has the other hand out for whatever...turning pages, holding up her chin. She's learned through trial and error what works and what doesn't. She isn't aloud to hold any fiddling thing and she could really use it to relax her.
The girls in class get reprimanded for twirling hair and playing with those feather barretts they're all wearing, the boys get reprimanded for flicking things at each other.
I think they're just going over and over and over the material because of the assessments and it's pretty excruciating.
I remember doing all-class reading when I was in school and the poor kids that would get called on for their turn to read out loud, when the teacher obviously called on them because they had a spaced-out look on their face. Then the kid was so embarrassed.
How is your DD able to go to school for 3 hours? Is that per day? Is it a public school? How did you manage that, I am a little jealous.