mathnasium, beast academy, or tutor?

I have mathy kids so I have tried all of the above and more. If your kid can do well with online, or with paper and pencil, then it's worth starting with Beast or Khan Academy, as they are low cost (Beast) or free (Khan) and can be done at home. Beast covers grades 1-5, but goes into very significant depth. The problems on Beast, especially the starred and two starred ones, are really creative and hard. I would start with free Khan Academy, and also purchase a $100 Beast online subscription. Mathnasium and AoPS are pricey! Mathnasium is great for drilling, and may be really nice if your kid does well in the presence of other kids (body doubling) and likes rewards. It doesn't go deep. AoPs/Beast is the same company, but there's a huge discontinuity between the 5th grade, covered in Beast, and AoPS (all grades). The difference is the format. You lose all the games and cartoons, and most of the videos, and instead have a math casebook. I wouldn't start with AoPS for a kid that is behind the regular 6th grade program. I would probably instead start with Khan (5th or 6th grade), Beast (the online subscription covers 1-5, so I would have my kid start with grade 3, to gain confidence), and maybe hire a tutor if needed. I've had good luck with Caltutors. They charge $60 for online, and $65 for in person, which to me is pricey but a much better deal than mathnasium at $400 a month for up to 10 sessions I think. AoPS, FireCracker Math, and Russian Math are regular math courses, and those are options too, costing something less than mathnasium (but for fewer classes).

While I can't tell you what works for your daughter, we've been using beast academy for 2 years for my 6th grade daughter and 4th grade son. My kids both felt the school math was boring and the lack of homework in the early elementary years was concerning to me because I didn't want them to fall behind, especially in the summer. There are a couple of options that I like about Beast Academy, one is the sequence in which they can play through the games. You can set up specific topics (locking all the other ones), or make them do the whole game in the recommended order (no skipping ahead, must pass every level before the next one opens), or open up the whole game so they can do whatever math problems they want. With my son, I set it so he has to do them in order- he's at grade level competency. However, after a year, my daughter started performing above grade level, so I opened the whole game up for her. She likes to be challenged, so she skips games she finds too easy. This summer, we also bought her high school level math workbooks, because she said some of the beast academy is now too easy. I think it's supposed to run through 6th grade curriculum, so this is likely her last year using it. My kids say it's fun as it's a mix of lessons, quizzes, games, video explanations, and math puzzles. 

I also like the reports. When my son is getting a bunch of things wrong, it emails me and tells me where he is struggling, so then I can go and help. It also shows them why they got the problem wrong and has a detailed explanation of how their solution didn't work and how to fix it. I have them do 30 minutes a day on non-school days, and only occasionally on school nights, because of activities and school homework. 

I should note, we do the asynchronous beast academy online and have the physical graphic novels- I bought them as a bundle. There are also live online classes and physical locations for classes, but they never worked for us due to the timing of them. I like the asynchronous one, because we can do it when we have time. Other thing of note- you must have an internet connection when using Beast Academy, because it's adaptive to your kid, there is no offline mode. When we took a road trip last summer, I rented a hot spot from the public library so the kids could do it in the car. 

I noticed some math frustration happening when my kid was in 5th grade. Online did not work for my easily distracted kid who is plenty smart but who isn’t super mathy. He did Mathnasium for 3 years and it was great for him. Does Mathnasium not go deep? I don’t really know, but they have their own curriculum that they go through that is independent of what is being taught in class as they want to make sure they fill in any pre-existing gaps (although your kid is welcome to bring in schoolwork that they have questions about). What worked for my kid was that it was in-person, one on one, and done by hand. Yes, it's expensive (we paid $325/month) when compared to Khan but probably less expensive than the same amount of private tutoring. To my mind, anything you practice regularly, you will get better at and if online works for your kid, Khan is great and free, but if online does not work, we personally had good results with Mathnasium. I have no experience with AoPs or Beast.