The Math Map Lesson 3: Comparison

Posted on August 26, 2026 by Deanna Leave a comment

Our Classical Conversations year has started, and as I take my Challenge class through The Math Map (TMM), as well as using it at home with my four youngest children, I’m sharing some tips each week from things I’ve learned over the last 3 years of using TMM.

Tips for Lesson 3: Comparison

On the i² page, note the top left box about 1D: The First Dimension. Compare it to what what said about 0D in Lesson 1 on the i² page. (Every time you move into a new dimension, it’s helpful to look back at these and compare.)
Note the special numbers listed on the number line (square root of 2, phi, Euler’s number, and pi). At some point (not necessarily your first time through), these are helpful to memorize.
The Graphing Axes won’t mean much until we get to 2D, but the Invention (i²) pages will always show both rectangular and polar coordinates, so it’s good to note.
Note that the “Rectangular Axis” (which is shown horizontally) shows Real numbers (though its labels may only be in a narrower domain), while the “imaginary axis” is shown vertically. Depending on which domain your students are working in, they will probably be asked to label these.
On the i³ page, the “International System (SI) of Units: Prefixes” has lots of patterns, so take some time to attend to attend to it and see which ones are familiar/unfamiliar.
For Challenge students, it’s especially helpful to discuss scientific notation and significant digits, as they’ll need to be familiar with these ideas for the Research strand. (For younger kids, or those brand new to TMM, I probably wouldn’t give these much time on the first time through this lesson.)
Depending on which domain you’re working in, there will probably be a few places in the lesson pages where you’d be lost without the Charts. When completing pages 3, 7, 11, and 15, C3:2 has divisions on a ruler that will be a great reference and C2:3 has a section on “Significant Temperatures” that will be needed as well.

Remember the Flashcards! If you’ve been doing them since Week 1, your student has probably mastered at least a few. Add 2-3 new ones in but keep practicing the ones that have become easy.

Other helps: Here are a couple extras that might be helpful as you explore Lesson 3:

Here’s my playlist of all the Book Club episodes that are about Lesson 3: Comparison: YouTube Playlist of Book Club videos about Lesson 3
What is e (Euler’s number)? Here’s a quick video to explain it.