For example, the teacher's preferred answer to this question was false:
5. True or False: When several traits are combined they can
be used to distinguish one racial group from another.
Technically, the answer is true. It's only false if trait only refers to the caricatured stereotypes of some particular racial classification system. But even if trait means readily identifiable phenotypes, you absolutely can break global populations into identifiable groups using traits like ear wax & perspiration, eye color, hair color & type, skin elasticity, and various other traits. The groups may not perfectly reflect traditional racial classification systems, but that's of no matter. The old Victorian system is but one among many around the globe, and all cultures are adept at redefining the contours of race. The racial classification system of modern American culture is nothing like the Victorian system. Disproving the inconsistency of Victorian-era race is like disproving phrenology--nobody cares. (We say "race" was a Western invention but that's just because Western Europe was the birthplace of modern phylogeny and biology. Race is a meme that was and is easily adopted and localized.) A shallow approach risks piquing students interest without dispelling the notion that any system of socially constructed racial categorization is broken and unproductive.The counter-point to typical racial classification systems about the degree of genetic diversity of African populations doesn't resolve the question at all, because once you open the door to sophisticated genetic variations it becomes trivial to track populations.
There's just too much complexity for a high school biology class to really wrestle with. It would be awesome if it was explored in a science-centered high school class because it's a perfect way to really drill down into fundamental concepts in science, but it'd have to be a seminar with a low student-to-teacher ratio. And the subject is a minefield, particularly in an age where people are primed to be outraged. It's just not practical for most schools.
Incomplete and inconsistent answers are the perfect environment for breeding pseudo-scientific concepts. There's something to be said for not asking the question unless your prepared to invest yourself in finding the answer.
I don't really like the term race anyway. It's not a proper biological classification and really shouldn't be taught in biology. We're all the same species with a good amount of genetic variation that comes from lots of things. Teaching anything about race in a science class seems unscientific to me.