11/19 Phi Day (or winging it when disaster strikes)
This day was a bit humbling for me. After 2 weeks of competitive activities I really wanted to do something fun and low stress. I had just seen some cool Lucas number videos on numberphile that I wanted to structure the day around. That meant I needed to get my A/V story fixed. Last year, my host teacher let me use his account to get to youtube but this year that’s not available. So I borrowed a projector from a friend, found the public wifi password for the school. That’s worked in the past but in a fit of caution I also tried out Leawo video to capture one of the videos offline and put it on a memory stick.
Short Story:
- The school wifi network blocks youtube this year unlike prev. years.
- I forgot a 3 prong to 2 prong power plug adapter.
- The video I burned and verified up to the 4 minute mark, failed after the 6 minute mark.
- The school library was closed an we couldn’t get access to the videos there.
The only bright point to this is that I now know you can view videos on a memory stick even if a student logs into the classroom computer and that probably the non-trial version of Leawo also works but you need to confirm the entire video is there beforehand.
What I actually did through this rather flummoxing set of circumstances was replicate the video content myself on the whiteboard. I**n retrospect I really wish I had some notes pre-written down. **Once or twice I remembered a few details spottily and I actually delayed a piece of the explanation to look it up on my phone in the middle while the kids were working on some problems I had printed out. As I often repeat to myself its ok to make mistake on the board and its about modelling how you handle it. Nevertheless, if you had asked me how this all went I would have said dreadfully. But here’s where it gets interesting. I also had one of the teachers drift in and watch during the middle of this whole mess. I wasn’t paying a lot of attention since my focus was completely taken up with adapting to the circumstances. He stuck around for a while and before he left, he asked about what we were doing and complimented on how interesting the math was. I also realized that we were having a really good interactive session doing things like having the room calculating ratios of various numbers as they approached the golden ratio. So while I was thrown for a total loop, the day was actually going pretty well.
So here’s my outline of intended activities:
Introduction:
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Ask “What is the golden ratio?” I surveyed everyone for their gut free association.
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Draw basic window ratio illustration and the core ratio $\frac{a}{b}= \frac{b}{a-b} $
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Discuss the basic property that $ \phi^2 = \phi + 1$ and the value that results.
Videos:
(We ended up doing this ourselves: which actually works quite well)
Stop to experiment and prove on our own and then talk about the Lucas Numbers:
Look at the Pascal vs Lucas Triangle
!
Can you find Relation between the two sets of numbers?
3rd video:
This is actually my favorite of the set of videos.
Group Problems:
Suppose that chairs are arranged in a circle. Let
Ln” style=”background-color: white; border: 0px; box-sizing: inherit; color: #242729; direction: ltr; display: inline; float: none; font-family: “georgia” , “times new roman” , “times” , serif; font-size: 15px; font-stretch: inherit; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; word-wrap: normal;” tabindex=”0”>LnLn count the number of subsets of n” style=”background-color: white; border: 0px; box-sizing: inherit; color: #242729; direction: ltr; display: inline; float: none; font-family: “georgia” , “times new roman” , “times” , serif; font-size: 15px; font-stretch: inherit; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; position: relative; vertical-align: baseline; white-space: nowrap; word-wrap: normal;” tabindex=”0”>n chairs which don’t contain consecutive chairs. show that
Ln+1=Fn+Fn+2.” >Ln+1=Fn+Fn+2.
https://t.co/TVxhPBO4kI
Ln+1=Fn+Fn+2.” >
Ln+1=Fn+Fn+2.” >
http://boisemathcircles.org/bmc-sessions/fibonacci
P.O.T.W:
I went with a variant on Matt Enlow’s recent idea: link
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