Why not read a book with them? I have been reading with my DGS (now almost 12) since the start of the first lockdown. Both his parents are WFH so this gave them a fixed time when they knew he was fully occupied. We both have a copy of the book (sometimes on kindle) and read out loud over FaceTime taking it in turns during the call. We have read several books that he wouldn’t have chosen for himself. His reading has improved and we have lots to chat about (other than football and cars and PS4) and the books have lead to us setting each other things to find out each day. DD1 bought us both the same book for Christmas so she must value it.
I have a granddaughter of 7 who is inclined to wander off during such calls. I did post an earlier thread on long distance grandparenting relating one call where she was truly engaged and ended up being told off by her father. (It involved putting his expensive phone at risk 😀) I have read stories, tried to do craft projects in tandem, but it is extremely difficult. I did have great success with her older sister a while ago when she was struggling with multiplication tables. We sang “one two is two, two twos are four,......” and she found it so easy to learn it as a song. It was how her father learned his tables and she wanted to learn daddy’s multiplication song. I tend to concentrate on widening their vocabulary. Learning new words to surprise daddy goes down well and I pretend to be impressed when my son tells me the elder girl used the words altruistic or fortuitously correctly. He reckons the school he pays for is doing a sterling job. I listen to music practice. (not for the faint hearted), check their rooms to see if they are tidy with bed made. The elder one gives the phone to her little sister for this. Curiously, by the time I am taken to the second bedroom it is miraculously tidy. I look forward to reading any hints you receive from other gransnetters.
Set her a show project. Give her a date for a Zoom meeting when she will have to put on a show for you. Suggest a few things she can do. -dance, song, poem if she can get her brother involved they can act. She can choose costumes etc. Turn on and watch. Mum & Dad can help her rehearse if they want. She gets all the attention she wants-she's the star of the show.
My son and DIL live in a flat in London with a son (10) and daughter (7). Our son is working from home, DIL doing freelance work at home. Grandson is embracing getting on with school work with almost alarming enthusiasm. Little one is NOT! When we do family zooms, she does her best to sabotage them. (This is a bright little girl who has been given school reports complimenting her on her academic abilities and achievements, and her niceness as a class member!) I would value suggestions about possible ways to make one-to-one zooms with her work, ideally, to make a positive contribution to her home schooling, but if nothing else to give her parents a break; but, since I imagine thousands of other families are struggling in the same sort of way, I'd be interested to know whether other people are as surprised as I am that professionals have not already broadcast guidance along the lines I describe. Perhaps there IS guidance out there, but I am not aware of it.