His Treasure Seekers

Our Classical Conversations community starts next week, and as I prepare to take my Challenge class through The Math Map (TMM), as well as using it at home with my four youngest children, I thought I’d share some tips each week from things I’ve learned over the last 3 years of using TMM.

Tips for Lesson 1: Ex Nihilo

• The Lesson 1 booklet is really helpful because it explains the different components of TMM and what to expect. However, it’s laid out differently than all the other booklets, so it tends to throw people off. I encourage parents to read through the entire Ex Nihilo booklet before attempting to do it with their students.
• Be sure to spend some time attending to the top left corner of the Invention page (p. i²). Every lesson that introduces a new dimension (Lessons 1, 3, 9, 19, 23, and 27) will follow this format.
• Note the way the domains are listed using a different font. Once students are aware of this, they’ll see them popping up throughout TMM.
• If you have younger students, make this a light week. Pages 1-16 are normally the lesson pages that the students work on (usually 4 pages each day), but in Lesson 1, it’s a lot of reading. Just pick 1 or 2 things to discuss each day.
• Page 6 discusses place value and introduces some of the ideas around base 10, which is helpful to understand before heading into Lesson 2, which will look at other base systems. I practiced this with my Foundations students by pulling out some math manipulatives. I told them we can only use 0-9 in each place, and then we have to move over to the next spot. So we played around with a thousand, hundreds, tens, and ones.

• Be sure to introduce Lesson 29 Seeing the Unseen, which is a blank booklet intended to be worked on all year. Lesson 1 Ex Nihilo explains how to use it on p. 1, and then the bottom portion of each of the remaining pages gives examples of the kinds of things students might add to their Seeing the Unseen booklets. In my experience, this takes a lot of practice and encouragement (few of my students did much the first year until the last minute), but it’s also a great way for the kids to engage with math in the world around them. My first year, I tended to see things online and I would copy and paste them into a file, which you can see here. (We all got better at noticing things and thinking about adding them to our Seeing the Unseen booklet. I’ve already added 3 things to my book for this year.)
• Don’t skip the Flashcards! See p. 4 of Ex Nihilo. Even just 5 minutes a day makes a huge difference. We set a timer and everyone goes through a set of 5-15 cards they’re working on. It’s important not to do too many at one time! On Thursdays, the kids give me the ones they think they’ve mastered, and then on Friday, I meet with each of them and check them on ALL the cards they’ve mastered so far. (Well, once they’d finished memorizing their addition facts, we dropped those. But we review multiplication facts if they’ve just learned them in the last year, and then any Notations cards they’ve learned. (I love the sets sold by CC. My ChB student has memorized all the Fractions and Notations cards, so now he’s working on the Trigonometry set.)

Other helps: When I first started to dive into TMM, I jotted down notes of things that might be helpful as I taught each week’s concepts.

• I wanted to review some of the concepts for Lesson 1 by watching the corresponding Book Club videos. I decided to make a playlist of all the episodes that are about Lesson 1 or 0D, and I figured I’d share it. So if you’re looking for videos discussing Lesson 1: Ex Nihilo, you can find them here: YouTube Playlist of Book Club videos about Lesson 1 or 0D. (The Book Club has gone through The Math Map several times, with a different focus each time. I’ve made a list of all those tours with a brief description in this post: “The Math Map Book Club Videos: Where Do I Start?“)
• In one of the Book Club episodes, someone recommended eventually memorizing the table on p. i³ of Ex Nihilo, starting with the first column (a list of dimension characteristics). I recorded a simple song to help us get started with that. (Looking back, that was way too ambitious for our first tour through TMM. But hey, someday I might find it helpful!)

Just for fun:

• In the very first Book Club episode, in discussing the idea of zero, someone brought up Zeno’s Dichotomy Paradox, which could make for an interesting discussion about how an infinite series can be contained in a finite sum. (I think this paradox could be fun to tie in to the idea of an asymptote, which is introduced on p. 8)