How functioning student and board in class.

Ds is too young to have this yet but as a teacher there are several things you see from students who get bored with the material. Some end up acting out and some zone out. When I was working with my music students and they hit the ok got it phase, I always had an extra "higher level" activity they could do that was a step or two beyond what we were at and let them try to brainstorm answers. Of course that is easier to do in the encore classes. In a classroom I would think the teacher should have that same concept. If they are already to the point of doing multiplication up to 10 why not let them try by 12's 13's or so. I was one that got stuff fast and I was very excited when I could get the bonus work to try. Did I always succeed at those? No. But I was challenged to critically think more. Plus switching up how it is approached helped me.
 

I think there is a difference between being bored and being inattentive. Everybody gets bored, some things simply are not exciting. However, being inattentive is not always an option, and I think people do it because it's easier than trying to focus on something you have no interest in. I believe that attentiveness is a learned behavior, and like most student behavior it is something that is learned at home first. How is she at focusing on things at home? Is she able to focus on her homework or chores, can she listen well during conversations or does she go off in her own world, etc. I would try to work on it home in preparation for the new year. When she is doing something I would insist on her giving it her full attention. Try to limit distractions and multitasking until she is able to handle one thing at a time without tuning out.

If it's because she finds the material too easy, there's a simple solution - teach her harder material. There's no reason you can't move her along faster if she is learning it faster. (Assuming you are home schooling).  She doesn't need to do repetitive homework IF she knows the material.

When my DD was being tested for her IEP, the Social Worker observed her in the classroom. At the time, the teacher was doing a whole class lecture on some subject and my DD was being very good - quietly sitting in her chair and sometimes looking at her teacher, but she was picking at her skin the whole time. The Social Worker asked, "Are you sure she isn't ADHD?" No, she isn't ADHD. She just has a bad habit of picking from OCD (something we're working on because it could lead to cutting or other destructive behaviors.) She was picking because she was bored.

My DD is pretty stand up about boring work. Over the years she has learned to do it quickly and get it out of the way so she can move on to more fun stuff. Math has been a particular problem this last year because DD is operating at a high school level in math and there she was repeating a year to strengthen her reading. Since DD missed the testing period to put her in the advanced placement classes, her teacher instead had her "tutor" kids in class who needed extra help.

As for the videos, I'd let her fast forward through the boring parts and/or allow her to do other work while they are playing in the background. There is no reason she has to suffer through a video on a topic she already knows.

You said they do not have a GT program, do they have any type of enrichment?  That really stinks if they have nothing.  dd9 is in enrichment for math and reading and it really helps.  She is still bored, reads a lot when she finishes her work.  Last year she was allowed to help other students when she finished her work.