Posted by: rdkpickle | 05.06.2017

spiraling squares

First, Jamie sees and saves the tweet:

Then, he sends it to me and Molly.

Molly and I spend the end of lunch/beginning of our shared prep block solving the problem (separately) and discussing our solutions and approaches.

We just finished a unit on Sequences and Series in Precalculus, so we decide to use the problem with our classes the next day.

I’ve gotten slightly better at framing stuff like this. I didn’t start with the problem. I started by having my (only 10 remaining with Seniors gone on projects) students count off into groups of 3’s. Move seats. *The mystery! The drama! What is Rachel going to have us do?*

Next I gave verbal instructions – get out a piece of paper and draw a (not too small) square. Then divide sides into thirds, draw next square. Shade. Etc. Students drew about 4-5 levels in and we paused.

Then I gave the question.

They started in seats on paper. Honestly, I think I could have left the room for 20 minutes and come back to find them still intently focused – I don’t think I’ve ever had a class quite like this before. After about 5 minutes, I made them get vertical and sketch ideas on the whiteboards. Here are some work-in-progress shots:

(The third group got bogged down with some algebraic/arithmetic mistakes. The black stuff got added as a student tried to reverse-engineer the math after knowing the answer.)

The engagement around the room was pretty great. I interacted with various individuals, groups, and students added notes and made comments as they took breaks from their work to observe others’ process.

The addendum, of course, is that after I tweeted out these WIP shots, Dan Anderson steps into the thread with an awesome OpenProcessing interactive that I just had to email out to my class this morning, even though it’s Saturday and it’s pretty unlikely any of them woke up thinking about this problem.

(I think I dreamed about this problem last night. Sorry, William – I’m still not dreaming in four dimensions. But for now, dreams about great days in class will do.)

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