Week 2 Activity Reflections

I recruited my older daughter (grade 9) to help me explore mathematical possibilities with mini candy canes that I had leftover from before winter break. Our analysis ideas included: broken:unboken out of the box (6/36), and even:odd red/green swirl pattern (21:9). When we tried to use them to build geometric shapes, we were disappointed to see that the shapes were not uniform. We envisioned being able to hook and hang them but only some could hook together, some were formed to narrow and could not. Some were alsolonger in length, some shorter. This made shape exploration tricky. But, these differences sparked the idea that they could be weighed to find the average mass of each individually wrapped candy, the range of sizes, etc.      

For the virtual fair in 550 I hosted a workshop with Möbius strips because I had not heard of them before that class. As you can imagine, I was excited to try making one out of a bagel. However, I only had bagels that were presliced, and those did not work. With creative willpower I used cucumber chunks instead. I cut segments and hollowed the center. In thinking about making the paper Möbius strips, I knew that you take a flat 2D strip and then looped it into a ring and made a half twist (180o) before taping it into a loop. This was different because I couldn’t twist the cucumber, that motion needed to be made with the knife instead. So I tried several attempts at cutting around the segment while rotating the knife 180o. Many attempts in, I was worried that I wouldn’t be able to do it with the amount of cucumber I had (which was a whole cucumber) and frustration kicked in. I felt like I needed a knife with two sharp edges - how could I twist one knife without needing to cut backwards? Taking a breath, I took a step back and just practiced moving the knife in my hand 180o. Start with palm up, finish with palm down. In my second to last chunk I got it! Then broke it apart trying to get the photo…I easily reproduced the motion a second time, with my last segment, but it was the tapered end so still not the clearest shot. I was so pleased with myself for persisting. Practicing the movement pattern I wanted first was the ticket. 

In her Supersmarties video, Vi Hart said, “sometimes it’s just more fun to let my hands solve their own problems.” After this week’s experiences, I think this is true. My daughter and I came up with more ideas than I thought we would by dumping the candy out and exploring with it. We also had some ideas (like the hook together building) that didn’t work but we couldn’t tell that until we tried it. My brain conceptually knew how to get a cucumber Möbius strip, but I couldn’t get my hands to replicate that concept without deliberate practice of the movement. (I was doing a 360 instead of 180.) In these cases my hands found more problems, and solved more problems, than my eyes/brain could alone. I see these experiences broadening perspectives and deepening understanding for all learners.