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Elizabeth Gire - It seems that the activity would go more smoothly if the students who play Kirk and Spock knew what they were supposed to say. It might be nice to have a conversation with these students before the activity begins, or to hand them a synopsis of what they are supposed to know

David Roundy:

I chose to do this activity *before* doing the “one thing you know about the dot product”, partly because I thought that doing the dot product first would lead them to immediately jump to the law of cosines. As it turns out, this is precisely what one student did anyhow, and I just promoted him and asked how we could solve this with vectors. Based on Liz's suggestion, I very briefly instructed Kirk and Spock what to do (basically to answer any questions posed to them, and to make up reasonable answers).

When describing where they were, there was some confusion as to whether Spock was northwest of the red building, or if the building was northwest of Spock. A student later chose to draw vectors from Kirk to the red building, and then from the red building to Spock. I just asked him to reverse the first vector. Then later, we had a discussion of the red building serving as the origin, and talked about the trouble we had had with signs, who was north of whom.

Doing the dot product second allowed me to phrase the derivation of the law of cosines in terms of the distance between Kirk and Spock, which I think was helpful.