## Physics #wcydwt – Indirect Measurement

While cleaning up after robotics class today, I noticed a statics problem involving an object hanging from a couple wires that was poking out from under one of my many piles of papers. We had looked at this question earlier during the week in class. A couple students were out for a volleyball tournament in Beijing, so I wanted to do something hands on and multimedia-esque that the missing students wouldn’t feel too upset about missing, but could somehow still be involved and connected with the class work from today.

I realized that we hadn’t yet used the spring scales during our discussion of forces. My obsession with #wcydwt lately has been on using the novelty of a minimum amount of information to get students to see a problem jump off the page/screen. I also wanted the students in class to get the joy of holding back information from their classmates to see if they could figure out the missing info. Lastly, I wanted there to be a simple physics problem that would serve to assess whether all of the students understood how to solve a 2D equilibrium problem.

So I grabbed the spring scales, some string, slotted weights, and told the students to put together a few pictures using these materials. We briefly discussed what information could be given, and what they wanted to leave out for the athletes to figure out on their own. I admit – I pushed them along, and given more time I would have given them more choice, but I don’t think my selfishness and excitement in doing this was too much. The other factor – the vice principal had given us an extra pizza to share – they were also really pushing for efficiency. It wasn’t all me.

And thus the spring scale picture project was born, thanks to one student’s iPhone and Geogebra:

The complete link of the assignment is at http://wiki.hischina.org/groups/gealgerobophysiculus/wiki/e495b/Unit_2__Spring_Scale_Challenge.html.

I’m sure I am not the first to do this, but it was so simple to execute that I had to give it a shot, and I am sharing it because I’m trying to share everything I can these days. We will see what happens when the results come in next week.

## “What can you do with this?” (WCYDWT) – Flood Gates Open

I’ve been making an effort to look for as much WCYDWT material as possible on a regular basis. This is not so much because I’ve had students asking ‘when are we going to use this’ though that is always brewing under the surface. Instead, I’ve been making an effort this year to spend less time in class plodding through curriculum, and more time getting students to get their hands dirty with real data, real numbers, and using their brains to actually figure things out. By recording screencasts, doing demos, and using Geogebrs, I’ve made some progress in getting the students to see the benefit of learning the routine skills-based stuff on their own for HW so we can use class time to do more interesting things. I’ve quizzed and am feeling pretty good about this thus far, but we’ll see.

During my trip with the ninth graders to Shandong and my week off due to the national holiday when my parents visited, I’ve kept my eyes open on reasonable, non-contrived problems that might serve as applications of linear functions. I’ve wanted some problems with non-trivial answers along with some low-hanging fruit that might give all of the students in the class a way in.

I’m pretty happy with how things have ended up with the top three contenders. There are some other things in the works, but I’m hoping to keep those under wraps for the moment. Click on the links to read the details.

This one I already started talking about in a previous post, but I spiced it up just a bit by putting images together and throwing the head image I’ve now used in a few places to be cute.

Ms. Josie and the 180 Days

I like this one especially since it has a good story behind it. My students know my wife, and I defer to her awesomeness quite a bit in class. Students certainly love it when their teacher is willing to knock him/herself down a few pegs, especially when it’s for their entertainment and for comedic effect in class. I think this challenge is a good combination of mathematical reasoning and drama – I don’t think I can lose!

Moving on up at the Intercontinental Hotel

I was looking for a third one that really jumped out as kinda cool and visually stunning since the others, though cool, weren’t particularly impressive visually. On the last day my parents were in town, we went to the Intercontinental hotel in Hangzhou and the problem smacked me in the face.

The videos aren’t all up yet – in addition to the two outside videos, the more enlightening videos (which I will post tomorrow before class) have a view of the elevator doors and the digital floor display as the elevator moves up and down. In addition, there is a nice reflection of the view out the glass wall of the elevator, beautiful in its own right, but perhaps a wee bit distracting from the really useful stuff in this problem. If I wanted to go the full-eye-candy route, I suppose I could have gotten a reflection of the elevator doors and floor display in the glass wall of the elevator. Maybe next time.

My plan is to let students choose which of the three projects they want to work on, and then give them tomorrow’s class (and finishing up for HW) to put something together. I plan to grade according to this rubric:

I think it gives them enough detail on what I want them to do, without being overly difficult to grade. I am even thinking of giving them a chance to grade each other since they will all be posting their work (from groups) on the wiki page.

I’ve had these things in my mind for a little while – I admit, after how this particular class made an impressive effort I am really excited to see what happens next.

## Climbing Mount Tai – #wcydwt edition

I am spending an amazing few days with students on this year’s class trip to Shandong province in China. We spent a couple days wandering around Qufu, the home of Confucius, and the location of the temple and mansion constructed for his relatives. There were some cool opportunities to think about mathematical thinking in Chinese architecture (more on that later) but nothing ready for prime time.

Today’s trek led us to the foot of Mount Tai, China’s #1 mountain for it’s cultural significance (not due to it’s height.) we decided as a group to trek up the mountain from the Heaven’s Gate which reduced the climb somewhat, but will descend the full height of the mountain in the morning after watching the sunrise.

From Wikipedia (to be replaced by my own pics when I get home, I promise.)

The realization that I might be able to do something really cool with this came after regretting that I had decided to leave two of my favorite data collection devices (heart rate monitor and hiker’s GPS) at home being unsure during packing if they would really be worth bringing. I had done this hike in March and had several conflicting reports of the exact height we climbed up and down. The students were asking me how many steps there were, and I vaguely recalled something around 7,000, but I wasn’t sure. This question actually popped out from a few different students as we passed the first set of steps. It got me thinking. Is it possible to take either one of these numbers (height or number of steps) and try to calculate or estimate the other? If the students were asking it standing at the bottom looking up, there might be a possibility they would be interested in answering it on their own if posed the right way.

I grabbed my camera and grabbed the best standard length measure I had on me: my iPhone.

(It probably isn’t necessary to say this, but this is just an example I took in the hotel.)

I took a number of pictures like the one above on way up the steps, trying to come up with a fairly random sampling of the size of stairs compared to the phone along the entire height. Through some combination of Geogebra, pencil & paper calculations, and some group discussion, I can see some height calculations for the climb coming out of this.

On the way up, there was also a perfect “answer” to this challenge posted in the form of a placard fixed to the wall that says both the vertical height and the number of steps – again, I will include a picture of this when I can transfer photos from the camera I used to take the good photos. I could see cropping this photo in a way that hides the answer, though I’m sure there is a more dramatic Act 3 to this challenge out there.

I think there is some potential here for some fun, as well as for good student discussion and writing about how close the number actually gets to the right answer. This is the second time in a week that I’ve been able to find something good that could work for a class activity, and I wanted to get the details out while still buzzed about its prospects.