Here's some more detail on one of the activities I use to teach race. It's called "Race is in the cards", and it comes from Strategies in Teaching Anthropology (Graber 2000).
I made "decks" of cards, four cards to a deck. On each card, I drew a stick figure. In each deck, two of the figures are short, and two are tall. In each deck, two of the figures have curly hair, and two have straight. In each deck, two of the figures are drawn with an orange crayon (technically, the crayon was named "mac n' cheese"), and two are drawn in purple ("purple mountain majesty").
Here's the difference: In one deck (marked "c", for concordant), the traits are correlated. That is, the curly-haired figures are all short and orange, while the straight-haired figures are all tall and purple. In the other deck (marked "d" for discordant), the traits are not correlated. So, there is one figure with curly hair and a short, orange body, while another figure with curly hair is purple and tall, etc., etc. The students are given the two decks, and asked to create "races" from them. In one case, this is easy. In the other, it's hard, because any choice they make will be arbitrary. The idea is to convince students that dividing discordant physical variation is arbitrary, and based on social rules, not biological ones.
This exercise only works for about half the students, even though we talk through it in great detail. The other half write the damnedest things when asked to reflect on the exercise. I get some truly bizarre answers (like, "this exercise shows the racial prejudices of our country." Yes, that's so true. When, oh when, will we ever see a mac n' cheese colored president?!) Most of the students who "go wrong", though, seem to have gotten caught up by the color issue. They assume that color is the only way to divide figures into races (that's what we do, right?), and therefore, they don't really get what I'm trying to say, other than "gee, the different races are more diverse in deck "d" than in deck "c"."
I've decided to change this exercise next year, and use plain black stick figures on a white background. The third variable be something unrelated to color, like squiggly bellies, or something. I hope that will help get the point across more effectively.