Today one of my seventh grade classes wrapped up their investigation of the question “How many triangles can you make using six lines?” Here’s the chart that they made. They found ways of making everything from 0 to 20 triangles using straight lines, and also found up to 80 when using a circle! Some folks made diagrams where they counted 21 or 22 with straight lines, but I hope to convince them next class that this isn’t possible. Also, some students today used Geoboards to explore the problem some; I think this could lead to some interesting extensions.
Previously I was thinking that we’d head into a unit about logic next, but now I’m thinking of switching that around and doing combinatorics first. On the other hand, maybe it would be nice to leave this here for now and come back to it later. Yeah, I think that seems better.
These are fun kinds of decisions to have on one’s plate. 🙂