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 8 Equations

• Invention (i² page) Most of us grew up learning the Order of Operations as PEMDAS, but the creators of The Math Map have created a new acronym (GIMA) that more accurately explains how we simplify different parts of an equations. You can hear Dr. Gilpin’s explanation of GIMA (and it’s reverse process AMIG) in this cued up portion of an episode of TMM Book Club. (I know everyone hates change, but after a few years, I appreciate the subtle differences between PEMDAS and GIMA, which really is a better explanation.)

• Memoria and Arrangement (i³page) There are lots of things on this page that will be looking more familiar by the 8th week through TMM. Rather than just asking, “What’s familiar?” I like asking my students if there’s anything they see that was totally unfamiliar when they first started TMM that seems more familiar now, even if they don’t understand it completely.

• Charts – In the Challenge Domains (actually, starting in Reals), there are a few proofs in the lesson pages that ask students to write the reasons for each step. The list of laws on C8:4 is the easiest place to look for these. (This chart also offers some explanation of proofs, which will be covered more in depth in Lesson 28.)

• What do you do when you don’t understand something in the lesson pages? I got stumped on a minor concept this week, so I thought I would explain the process I went through to find an explanation. (Call me dumb, but it’s been over 30 years since I took a math class, and I seem to have forgotten things I haven’t practiced since that time.)
  • Here was my problem as I worked through the lesson pages for Binomials. On page 3 (and its complements, pages 7, 11, and 15), the box titled “Plot the ray” instructs us to “confirm that the in/equality sign changes.” I couldn’t figure out why the sign was supposed to change, though I’m sure at some point in time a math teacher explained this to me.
  • The first place I turned for help was The Math Map Companion on CC Connected (be sure you’re signed in before you click the link), where there are videos explaining concepts for the first 4 pages. (Since these concepts are generally repeated in each set of 4 pages, they’re only given for the first set.) However, the Binomials video didn’t explain why the sign changed. I could have just copied from the Solutions and accepted the answer, but I really wanted to understand the “why,” so I kept searching.
  • Next, I scoured the charts (which are the same for every Domain), but still couldn’t find an explanation.
  • Frustrated, I went to the Lesson 8 videos from The Math Map Book Club (see below for a link to my playlist) but didn’t find any discussion of this concept.
  • (At this point I actually just ended up asking Grok and immediately understood that the sign flips when multiplying or dividing by a negative, but then I was determined to figure out how a student doing TMM was supposed to know that, that so I continued hunting.)
  • Finally, I worked my way back through the lower Domains and discovered that in Reals-Monomials, students are told to reverse the sign, but are not told why. (Dr. Gilpin did talk about it in the video for Reals, the first Domain that doesn’t mention the rule in the actual Lesson Pages.) I eventually found my answer when I reached Rationals. (It turns out that students are told this rule starting in Decimals and reminded in Fractions and Rationals.
  • These screenshots show what I saw as I worked from Binomials down:

• So if as student starts their journey through TMM in one of the lower Domains (Decimals-Rationals are for about 3rd-5th graders), they will be introduced to this concept and learn the rule, but the higher Domains assume they already know it.
• LESSON LEARNED: If you come across a concept you don’t remember learning, and you can’t find an explanation in the Companion videos for your current Domain or the Charts, pull up that same lesson page in lower Domains until you find an explanation.

Other help as you explore Lesson 8:

• While it didn’t yield the exact answer I was looking for this week, overall I have found The Math Map Book Club to be a great resource. However 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 8 Equations (with episodes from 2023 to the present).