His Treasure Seekers

Since Classical Conversations released The Math Map in 2023, I’ve gone through the 30 lessons at least 5 times in various forms, as a tutor, a teacher at home, and “lead learner” trying to understand concepts I never learned in school myself. This year, as I prep each week (taking my Challenge class through it on Community Day, in addition to using it at home with my four youngest children), I’m writing a post on each lesson, sharing things I’ve found helpful or offering some suggestions in hopes of making it less intimidating to those just getting started.

Tips for Lesson 13: Circles & Ellipses

• Invention (i² page)
  • See “Measurements of a Circle” in the top right corner. If students did Foundations, the formulas for the circumference and area of a circle will sound familiar. Use what’s familiar to discuss the other formulas in this section.
  • ATTEND to the “Circle Parts and Properties,” as these will come up in the lesson pages.

• Memoria and Arrangement (i³ page)
  • Back in Lesson 10: Intersected Lines, I mentioned that it would be helpful to memorize the degrees and radians for each of the angles, starting with the multiples of 90°, then adding in the 45°, etc. This lesson shows the context for those relationships within the Unit Circle.
  • Eventually, it would be helpful to memorize everything on this Unit Circle, which will probably feel doable after a few cycles through The Math Map

• Charts – Here are a few things that might be helpful to know before diving into the lesson pages:
  • C13:1 I recommend making note of the DEFINITIONS as they correspond to the diagram of “Circle Parts & Properties”
  • C13:2 The top of the chart (“Degrees vs. Radians”) provides a bit more explanation than the Unit Circle on the i³ page. Also, the lesson pages will talk about “inscribed” and “circumscribed,” which will probably be self-evident, but this chart explains the concepts if needed.
  • C13:3 Note the DEFINITION of an ellipse, as well as the difference between vertical/horizontal ellipses and parabolas.
  • C13:4 All Domains look at the graphs of the functions on this chart to some extent, so depending on the level of your students, it might be helpful to spend some time ATTENDING to this page.

Other help as you explore Lesson 13:

• I have found The Math Map Book Club to be a great resource, but there are so many episodes out there, it can be a bit overwhelming. If you just want to focus on this specific lesson, here’s my YouTube Playlist of Book Club videos about Lesson 13: Circles & Ellipses (with episodes from 2023 to the present).

Just for fun: Here are two books that would fit in with this lesson for younger students:

• Sir Cumference and the First Round Table by Cindy Neuschwander

• Sir Cumference and the Dragon of Pi by Cindy Neuschwander