To the original post:
In my DD13's current school district, I'm not sure what the actual criteria are for elementary or middle school. My DD came into the district fresh off skipping 6th grade and was put right into the gifted program. No one seemed to question that she should/would be in the program, so we didn't worry about how high or low the bar was. Looking at the website, it seems the CogAT (one of the seemingly few tests my DD did not take) is used along with staff observations of students and achievement testing (almost certainly the ITBS and/or Iowa Assessments).
To qualify to take 2-3 high school classes while still in 8th grade, a student needed to have earned a national percentile rank of 90 or higher in math and reading on the ITBS/Iowa Assessments. There is also a separate algebra readiness test for those wanting to take algebra.
In practice, it seemed the cut-off for the HS classes was a little low as some students did struggle. In my DDs observation, it seemed there were more girls than boys in this program. My DD also noted that, even though she was in one of the more diverse middle schools in the area, there were very few minority students in the program.