One Resource a (Week)Day #3: Math and Simple Machines

So far, summer has been pretty great but pretty busy. School only ended last week, but it sure feels like I have been on summer break for a long time. In no particular order, I have:

* Gone on a glorious evening bike ride with a local bike group
* Checked out the annual Solstice parade, which included naked bike riders, costumed dogs, marching bands, and everything in between!
* Shopped, ate funnel cake, and all around enjoyed the Fremont Solstice fair -- on a side note,  I fell in love with a local project to help low-income and homeless youth get some real job training. http://cmdprint.com/ trains these young people through design internships and empowers them by giving them real ownership and a sense of accomplishment in designing, printing, and selling their own t-shirts. I bought two of Sydney's awesome blue shirts after talking to her and finding out that she's an intern in this program, and I only wish that there were more sustainable options like this for helping young people get on their feet!! 
* Celebrated my husband's birthday with a really fun group!
* Finished reading my first summer book (just in time for my book club meeting)
* Slept and napped and exercised and watched a good deal of TV. I feel pretty relaxed and wonderful. :)

Anyhow, I am also trying to stay on track with my goal of One Resource a (Week)Day. Today I found some interesting activities in a book called More Mathematical Activities, by Brian Bolt. I'm frankly not as enthusiastic about this book as I am about the two previous resources for straight teaching purposes, but I do think it has a lot of promise as a resource for math circles or math clubs, that do primarily recreational mathematics. The book has lots of puzzles (some of which I have seen elsewhere), and although some of the language can be a bit confusing, it also comes with a  solution key to help elucidate the instructions.

Here's a simple activity from the book that I liked, because it tied to an interactive exhibit I have seen at the Museum of Math in NYC. The activity calls for drawing parallel line segments and then cutting/translating the paper along the diagonal slit. What you observe is that one of the original parallel segments "vanishes", much like the monkey in the MoMath rotating wheel exhibit. And, similar to that exhibit, what is observable here is that each remaining line segment gained a fraction of length in order to compensate for the loss of the extra segment / monkey. For students, I think this activity is easier to wrap their heads around than the monkey display at MoMath, and would accompany the MoMath exhibit nicely.

This (below) is also quite interesting. The book has a discussion about how mechanically you can construct something that will turn circular motion into linear motion, which is useful in engine design and other such applications. The students' task is to construct such a machine. The reason why I like this is that it seems to tie proofs and the idea of "geometric validity" into an everyday application. Is the proof doable by students? That would really enrich this task to bring the learning to the forefront. It's something for me to look into/think about a bit further.

This (below) is also interesting. Here the book goes through various ways to scale something via a physical construction. I think as math teachers, most of us are familiar with the idea of gears and gear ratios, but notice the variations they have, even to include pistons and sliding ramps! Those applications are less familiar to me. Eventually, the students' task is to construct a black-box machine that accomplishes a specified ratio in input and output rates. I think the examples are great, but the task is a bit too simple. It seems like the kids can just duplicate the designs without much further thought. In order to incorporate this meaningfully into your classroom, you would have to re-think the structure of the teaching or the assessment in order to up the cognitive level.

 

I have always liked these mathematical paradoxes involving infinite iterations of recursive definitions. I liked the way the author paired these two similar examples together. But, again I think the author could have used a bit more variety in their tasks.

I hope you've enjoyed this installment of One Resource a (Week)Day! More to come tomorrow. :)