Compass & Straightedge

Summer school right now involves six hours of Geometry instruction followed by three hours of planning for the next day’s Geometry instruction, which basically leaves me fully tapped for tweeting, blogging, smiling, anything but sleeping. I’d say something laced with regret here but the fact is I enrolled some truly incredible students who challenge me and crack me up for the better part of those six hours. These kids make for light work.

Their proficiency does cause its own kind of trouble, though, because my strongest and weakest students space themselves out dramatically over six hours, requiring all kinds of differentiation. My favorite recent method, particularly with today’s investigation of reflections, is to say, “okay, now do that with just a compass and straightedge.”

I had a method in mind but several students each did me one better.

One student made kind of stunning use of SSS congruency. Another dripped sweat all over the page constructing perpendicular bisectors, copying angles, copying sides in an incredible (but functional) mess. Another used the method I chose but did it in three fewer arcs.

I have five more days to enjoy this.

[BTW: I have determined that at least 20% of this is garbage.]

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. What made you determine it is “garbage”? I’m assuming you didn’t think this way when you posted it.

    Is it the content? The design? The way the students are asked to interact with the content?

  2. Its good to hear that other people do (and enjoy) summer school as much as I do. Although it is lots of work (I have split classes), the kids are wonderful and they are truly there because they want to improve! Its great to hear that an excellent teacher such as yourself gives up part of his summer to do this!

  3. How do you motivate these students? I taught summer school geometry a few years ago, where every single student had failed one or both semesters of geometry the first time around. I was able to help them with what they needed help with, but I know telling them to “do that with just a compass and straightedge” would not have gone over at all. In such a short time, how do you manage to have your students accept that task?

  4. @Jackie, “garbage” is overly self-deprecating but I ended up re-designing way more of my slidedeck than I would’ve expected just to keep up with a year’s worth of change to my pedagogy. I summarized most of that redesign here. Again, showing more, asking more, telling less, posing clear challenges with multiple access points for different learners, building from strong, clear images.

    @Brian, like I said in the post, I’m trying to differentiate activities between credit recovery students (who failed one or more semesters) and enrichment students (who are trying to advance early). The compass & straightedge challenge was issued at a couple of enrichment students.

    It would do my work a disservice, though, to say that these challenges only resonate with enrichment students. From day one, I’m doing everything I can to promote curiosity, promoting it higher than hard work, a good attitude, and correct answers. Those efforts are well-documented around this blog and the result is a class where kids know they can take a swing at the compass & straightedge challenge and their mistakes will be celebrated, their partial solutions analyzed, their cracked-out-but-functional solutions lauded, and the class will respect their efforts. It is oftentimes the kids who have failed multiple semesters of math who are most eager to embrace this kind of classroom culture.

  5. Dan Thanks for elaborating. I suspected it was the way the students interacted with the content.

    While I wholeheartedly agree this approach works well with students who have failed multiple semesters (and I’m sure it looks a bit different in your class than in mine), I think it is good for all students.