Update: I've added a link to the data in Desmos and TI lists below.
Yes, I jumped on board the "if you can't beat 'em, join 'em" boat.
Inspired mostly by Harry O'Malley's site, I brought a fidget spinner* and my phone to grade 11U math class one day and the students modelled the spin. The above graph is the one of my student's results. It's a bit wonky because in the two days since I had bought it, one of the end caps had fallen off, which made the central bearing ring shift off centre. This made it slow down a lot; the above graph shows a few tries at spinning. The student at the top of the post took an average of the cycles while other students just looked at the first.
To make a good video, mark one of the edges of the spinner so you have a reference point to track. The app I used is VidAnalysis Free for Android (for Apple fans, Vernier has an app for LoggerPro that lets you do the same stuff, if not more). Don't spin it too quickly unless you have much better equipment than I do -- I tried to analyse that lovely first video and got goobledeegook because it's spinning too fast for the video to capture properly.
You then pick reference points (known length and origin of coordinate system) and track your mark. You can skip forward and backward in time to get to the section you want to analyse. I goofed because I forgot that I had made a spin without my finger in the way; by the time I remembered, I had already invested too much time getting the other data. Hence the starts and stops.
I didn't want to take up class time getting the analysis ready, so we discussed what equation we were likely to see, and then worked on other problems. Before the next class, I made the analysis and turned the data into graphs in Google Sheets. The next class, I put the x-distance graph up on the screen and got the students to figure out the model. When they had an equation, I graphed it against the data (if you do this, remember that spreadsheets do trig with radians, not degrees).
It was a really good exercise, considering it's the first time I've officially used the VidAnalysis in class. We had some great discussions about the vertical translation (did I deliberately make the coordinate system off-centre? no, but I will next time because that led to interesting math); how to deal with the increasing period; how the amplitude of our function compared with the actual measured distance.
I've since shifted the centre bearings back and made another, better video analysis. The screen shots are below:
 |  | What I like about this, mathematically, is a) how it shows the spinner slowing down; b) how it shows that I didn't hold the camera completely still -- notice that the "zero line" of the equation shifts up (nice for composition of functions!); and c) the x- and y-distances are essentially translations of each other (sin vs cos). I could have really expanded on this activity and got them to break the functions into different domains. |
 |  | The velocities show the same math effects as the distances; this could be used to show that the derivative of sinusoidal functions are still sinusoidal (and how). If only Google Sheets would get their act together and let us connect points in scatter plots. |
 |  | More screenshots. What I really like is that you can upload the data as a csv file to Drive. Copy-paste makes it simple to create a spreadsheet. Note that the Free part of the app means ads. I was still giving it a trial run, but I think I will upgrade to the premium version because it's a great little app. |
I started the trig functions section by creating a periodic wave using a salt-shaker pendulum (an idea I cribbed from someone on Twitter -- I can't remember who it was, but I'd love to give her the credit). I now wish we had filmed the pendulum at the same time so we could compare our rough model to the data. Future ideas!
I have a graphing calculator assignment that grabs tuning fork data from a microphone; I get the students to model the function and work backwards to determine the frequency of the fork. We didn't get to it this year, but it would go well with this exercise.
If you'd like to use my data, feel free to make a copy of fidget spinner 2, or download the csv file.
*I meant to use one of the students' spinners in my MCF3M class, but ran into difficulties because that student wasn't in class the day we were supposed to do the model. Since I wanted a permanent mark on the spinner, I decided to not buy trouble and get my own. Plus, they're fun.
I did this exercise with the 11M students as well, but we wound up doing it as a class instead of individually.
I was wondering how you captured your data! Great use of technology. Free app also means that you could put them on a class set of ipads, ipods, or android devices without breaking the bank.
ReplyDeleteclass set of iPads? Do secondary schools have those these days?
DeleteHah. That would be the dream. The Vernier app isn't free, but there is an educational discount (and you can import video directly into Logger Pro anyway, so that's an option).
Delete