Intro to Math: Circles and Squares

School is back in session! One of the students I tutor apparently has no homework tonight, otherwise I don’t know when I would have had time to put this into writing – things got busy in a hurry.

I’m doing the whole #teach180 thing so if you’re desperate to see more frequent updates from the classroom you can follow me on Instagram, @multiplefactorsi. I’ll be posting every day, held accountable by a reminder on my phone. I hate tiny little red numbers on that screen, so you know I’ll be following the rules.

Anyway! The first week of math class I always do “intro to math.” We started with some talk about what topics in math we were going to do over the year, and then we spent some time on an arts integration project inspired by these tasks for small children. This would have been awesome if we had more time, or maybe they would have gotten old – who can say? A couple students finished them beautifully at home, and others have kept their unfinished projects in case of momentary boredom. I’ll attach that whole assignment.



PDF of the assignment: day-1-arts

The second day was all about seeing things from multiple perspectives and integrating multiple viewpoints into collaborative work. We started with a number talk, something I loved when I first saw it but just never used. I took the one from YouCubed’s “Week of Inspirational Math,” week 2 day 1. I had been very nervous that our conversation would be nothing like the thought-provoking and joyful example video, but this went amazingly. Here’s our board:


Inspired by Sarah at Math = Love, who was in turn inspired by other bloggers, we then launched Broken Circles. That was great! I love hearing students talk about math, but I also loved the no talking rule. It’s also an inspired touch that one circle completes itself. In one group, the person with the “A” pieces sat there, self-satisfied while the rest of the group struggled, and it was kind of glorious. It’s almost like the point of this task was to show that working together and paying attention is crucial.

Between that and our next collaborative task, we went over our group norms. I translated them into Spanish for an extra touch, and perhaps that will inspire me to do more group work in Spanish class? Time will tell.


The end of Wednesday we started the Pentomino task – I blogged about Pentominoes last time I did it, SO long ago! This year I didn’t leave as much time and consequently they didn’t come up with quite as many combinations, but I do still think it was a useful exercise in visualization and pattern recognition. I’m kind of in love with my independent reflection for that task, attached. Why indeed can you not build a 6×6 square?

Independent Reflection PDF: pentomino-ir

Things are shaping up, but I already know I won’t have nearly enough time to blog as I’d like : 0

Fractals Task

I had wanted to do a unit about fractals for a long time, and this year I finally got the opportunity! I had originally envisioned my Math Four class as a traditional fourth course through more of a visual lens. Fractals involve some complicated mathematics, mainly exponentials and infinite sums, but also some complicated intricate designs.

We started with an exploration task. I would have assigned this in groups but I definitely burned them out of group work earlier in the year – live and learn. It started with Sierpinski’s Carpet, an increasingly-dense set of squares with an easily-recognized exponential growth pattern. sierpinskis carpet

They then explored the Koch curve, finding the proportion of the area of triangles added in successive iterations. koch curve

As a group, students created a big giant Sierpinski’s Pyramid! Credit where credit’s due, I got the idea from this school in Winston Salem. Excellent idea!

I kept tripping on it because my room is not exactly large enough to accommodate a large pyramid, so I moved it into the administrative building. There, it encountered this guy and met an untimely demise.

cat pyramid

To wrap up content for the entire year (?!!), students used grids to draw their own fractals. First we used triangle grids to draw the Sierpinski arrowhead curve, then regular square grids for the Dragon Curve. Vihart has an excellent video about that – a few students finished early and I had them watch it.

Next week is review week and then it’s exams – I’m starting to reflect on what I’ll be changing about this open-ended course next year, but mainly to avoid thinking about writing and grading exams! Although I will admit I secretly do enjoy exams in some ways.