Intellectually gifted children - distance education K-8 "Stanford EPGY Open Enrollment" (Math and English):
EPGY
The cost is extremely low: $135 for 10 months (lower for 5 months).
See the flyer at
http://epgy.stanford.edu/pdf/soe/EnrollmentWebPost.pdf .
No entrance exam, but need a group of at least 8 students to register. (This is where a group of interested parents would be useful.
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You can call their office directly to find out more how it works.
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Regular Stanford Education Program for Gifted Youth (EPGY) and John Hopkins University Center For Talented Youth (JHU CTY) are both well-established, popular programs (JHU CTY goes back to 1980's as far as I know) and provide distance education. They both require an application and some kind of entrance exams, though, and have much higher costs than Stanford EPGY Open Enrollment (Stanford EPGY: $495 per course, time-limited to 3 months; JHU CTY: $690 per 3 months, any number of courses sequentially).
So Stanford EPGY Open Enrollment is way more accessible than the regular EPGY/CTY and may be a good place to start.