Generally she would love to work at her own pace but doesn't want to do it after school as she will still have to sit through math at school. She dislikes her school math class which is very slow. Her sister suggested to her that she could do 7th/8th grade online this summer and then go into algebra next year and now she really wants to do that. I have no idea if that is possible, who to do it with and if the school would go for it.
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My only wish is for her to be more engaged with math and a bit more challenged as I've seen how natural it is for her and how she gets into it. I want her to have a solid understanding of math...
What a great suggestion from her older sibling who cares enough to consider her sister’s situation and come up with a practical way forward. The very fact that your daughter is keen to do it when she was previously reticent to work on maths at home is good reason enough to give it full support. Whether or not the school accepts her into the algebra program next year is a secondary issue which can be dealt with in the future, if it even becomes necessary - mastering the 7th/8th grade content from the online resources fulfils your main goals now, of getting her to become ‘more engaged’ and having ‘a solid understanding of maths’.
Teachers are more likely to make an effort to extend/accelerate a student when the latter can actually demonstrate that they’ve mastered content, rather than on assertions of capability without formal demonstrations of proficiency. In the ‘worst case’ scenario that she is not skipped by two grades and is placed in the compacted 7th/8th class, I suggest trying to negotiate for her to participate in the group teaching part of each lesson (revision never hurts) and work further ahead on the online materials during the time allocated for individual exercises. My son has always been in classes with similar aged peers and works on differentiated content (3-4 grades ahead) during the time allocated for working on individual exercises. It worked well for him and he has never complained of boredom.
