7/8 is 3 and a half one-fourths, and 10/12 is only 3 and a third one-fourths.

I don’t have easy access to a laser cutter, so I would absolutely commission some. Thank you so much! I’ll send a dm.

Thanks! I would love to acquire a set of wooden ones, is that what you are thinking about? I’ve used a laser cutting service I found online before, but I am not (yet) very good with the tools necessary to create precisely the file I want, so I’m looking for a shortcut.

I see two overlapping 3x3 arrays. Two nines is eighteen, then I’d subtract the 2x2 I double-counted.

Can I include your poem in a math newsletter for our elementary students? I didn’t realize today was Fibonacci day, but I was just writing about the Fibonacci sequence yesterday for the next edition!

Absolutely. I’ve found effectively consolidating learning after a BTC-style work session is hard enough even with some background with the five practices, I’d be lost without it! That connecting phase is so crucial.

I agree. I think the pedagogical overlap depends on the specific goal (inquiry, skill development, knowledge acquisition etc), and for math a thorough understanding of conceptual progressions across grade levels is especially helpful for supporting access to grade level content.

Hi! I’m in year two as a math coach, and I’d love to hear others’ perspectives on this too. What is your current thinking?

Here’s where they live now: talkingmathwithkids.com/wodb/

Math Education-Middle Grades. I feel like it was roughly 50% math courses and 50% methods and math history, but it’s been a while.

I did. It was incredibly convenient and inexpensive, albeit not my favorite way to learn and less rigorous than I expected. I appreciated being able to quickly complete courses that covered content I was familiar with and move on to the next. It was very doable while teaching full time.

Thank you!!

Thank you for sharing your reflections here. I’m working with a 4th grade team around math instruction, and they are using many of the same materials and working through the same sequence. I’m new to fourth grade myself and I really appreciate the additional perspective!

And there are many fascinating and creative things a person can explore with larger cubes that are not accessible to me yet because I haven’t built a flexible understanding of how the cubes work. I don’t really know how to solve a cube, I know how to unscramble one-most of the time.

I experienced something as a learner that we talk about in math ed all the time: it’s incredibly difficult to reverse engineer conceptual understanding when you’re entirely reliant on memorized procedures.

But I had no flexibility. I learned algorithms to rotate certain pieces clockwise, but couldn’t break them apart to complete the counterclockwise moves without losing the flow of the steps. And I often forget steps-if I didn’t pick a cube up for a few months I would inevitably have to look some up.

But with a good bit of practice I could reliably unscramble a 3x3 cube reasonably quickly. I then explored the 4x4, 5x5, and the megaminx, a regular dodecahedron. All have a lot in common with the 3x3 cube, so I could apply a lot of what I already knew and memorized a few new algorithms for each.