Exit Slip (2025.10.2)

This week’s conics warm-up worked better than I expected. Starting with “where do circles/parabolas actually show up?” and letting us sketch and name our way in made the unit feel like a casual list of shapes. The hands-on locus demo was a nice one as it clicked that why “a set of points” is a useful way to think. Also, seeing the relationships among the conics helped: ellipses with eccentricity less than 1, the parabola as the boundary case at 1—that “family resemblance” made the equations feel motivated. The quick detour to our group's Gabriel’s Horn scratched the pure-math itch too: finite volume, infinite surface area is the kind of paradox that reminds people definitions matter.

Ed Doolittle’s Star Blanket patterns are basically sequences and symmetries people can hold, and scrabble was a smart reminder that games are rule systems we can tune to the language, not the other way around. Between that and the represent-in-many-ways exercise (draw, name), the through-line for me was pretty simple: pick representations that actually carry the structure—whether that’s a string tracing a locus, a blanket encoding a sequence, or a board game redesigned for morphology—and then give the formal math its spine once people can feel what’s going on, for the lower levels of math of course.