Original post:
> three 6th graders I work with ended up acing the AMC 10, which is a contest that American kids take in the 10th grade. One of them even made the AIME cutoff,
This is 100% impossible. How could you "ace" a contest and not qualify for the lext level? No one did better than "acing" and there is no lottery.
Do you mean "100" on the AMC 10, not "acing" ? That's impressive and plausible, but "acing" is 150, which is achieved by only about 10 people in the world each year, and takes years of intense study, and all of them qualify for the AIME.
Also, AIME is currently top 2.5% of AMC 10, not top 1%.
Score reports at: http://amc-reg.maa.org/reports/GeneralReports.aspx
Sorry, I meant acing in the "scored way above what I'd expect 6th graders to do" sense. One of them made the AIME cutoff, two missed that cutoff but quite narrowly.
> "acing" is 150, which is achieved by only about 10 people in the world each year
Agreed, that is pretty impressive.
> Maybe host a math contest forum for working adults where we can work on interesting integrals & suchlike :)
I'm sure you must know about https://artofproblemsolving.com/community They have a huge collection of problems, and sometimes solutions.
I'm somewhat curious about the logistics of the courses. How many students are in your classes? Do you run one-on-ones online? And are they really one-on-one, i.e. only one student at a time? Or is it more like office-hours?
Also how much time does it take you weekly to prepare the course materials and to check the homeworks?