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 5: Multiplication

• Invention (p. i²) Compare the number lines given for multiplication and vectors. These will come up repeatedly in the lesson pages.
• The graphic for functions should look familiar from last week. I find this week’s easier to understand because they give an example. Attend to the elements of the Domain and Range to see how function and inverse function are related.
• For more experienced students, do they recognize any of the notation in the section at the bottom (Graphing 1D Intervals)? Is there anything unfamiliar? (This is where those Notations flashcards come in handy!)
• Memoria &Arrangement (p. i³) Personally, I find the method of using the “prime powers” to find the Least Common Multiple a bit confusing. TMM says it’s the most efficient method, and maybe for students who don’t have their multiplication facts memorized, this is true. Even if you’re like me and it’s not the way your brain works best, it’s always beneficial to learn other ways to do things, and this comes up in the lesson pages a few times, so it could be helpful to spend some time becoming familiar with it.
• Prime factorization also comes up in the lesson pages for many Domains, so I recommend attending to this section to make sure the students understand how to do it the way TMM has laid out.
• The first two pages of this week’s Charts are laid out in a similar way to last week’s. The first page (C5:1) has definitions, laws, etc. which can be a helpful reference. The second (C5:2) looks at multiplication in different domains.
• Page C5:3 has much of the same information as the i³ page, plus some information on “Significant Digits” that will be helpful when completing the lesson pages.
• Page C5:4 might be interesting to go through with older students at home, but I wouldn’t spend much time on it in class as a tutor, nor would I touch on it until my students have gone through TMM a a few times.

One of the frequent concerns I hear from parents about TMM is that there aren’t a lot of calculations. I feel like this lesson gives several opportunities for practicing multiplication, but if you feel like your student needs more, check out the Careful Calculations at the back, or just work through a few extra problems with them on your own.

On the subject of the Careful Calculations, I have to confess that we barely looked at them the first few times we went through TMM. My younger kids, who flew through their booklets in the lower domains, did many of them, but my Challenge A and B students were struggling just to get their lesson pages done each week. Over the summer, we did a quick run through TMM, covering one booklet each day. My kids went through last year’s books, either completing lesson pages they hadn’t done, or working through the Careful Calculations. Personally, I find these pages really challenging most weeks (at least from Complex and up.) Rather than struggling with it, this summer I had my rising Challenge I student walk through the following steps:

• First I had her look over the whole page and do anything she thought she understood.
• Then she checked the Careful Calculations solutions (these used to only be found in the Companion on CC Connected, but this year a printed copy has been included with each domain when you purchase it). If she had anything mistakes, she tried to figure out where she had gone wrong.
• Finally (and this turned out to be the best part for us), she looked at the solutions page for something she hadn’t done herself and tried to figure out how they had come up with that answer. Then she explained it to me. (I usually had her pick 3 things to explain to me this way). Working backwards like this made it less intimidating, but it also made her feel really successful because she knew she understood something that had seemed too hard when she first looked at the page.

Other help as you explore Lesson 5:

• 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 5: Multiplication (with episodes from 2023 to the present).