I decided this year that if I was going to continue to take the time to teach students how to interpret kinematics graphs of motion (displacement-time, velocity-time and acceleration-time graphs) I was going to bring them up more often during the year. As we transition in my class from basic kinematics equations to projectiles I was looking for a lab that did just that. This is where it pays to keep more resources than you currently use in your curriculum. I found a pdf I had downloaded from Vernier using motion detectors and a ball. The lab looked simple enough and I tried to reproduce the results myself.
The original instructions had called for a wire basket to be placed over the motion detector to protect it from the ball's return. I tried this with a tennis ball and found it very difficult to get the tennis ball to go up and down directly above the sensor. After lots of attempts (seriously like 50) I was able to get three sets of data to work with:
I wanted students to see what happened at the max height on both the displacement-time and velocity-time graphs and understand what it meant. I wanted them to identify the time that the ball was still being accelerated upwards by their hand (easier on the velocity-time graph by the way). I wanted students to see a constant slope of the velocity-time graph to remember that gravity is constant. I liked how it was coming out but still wanted to make sure that students had an easier time than I did with this lab.
After tweeting to @VernierST I was able to get a few suggestions that made it basically fool proof:
1. Instead of a small tennis ball use a larger basketball (more reflective surface for the sonar).
2. Instead of a wire basket, which I didn't have enough of anyway, try putting two books on either side of the sensor.
Since my books are shorter I had students put two books on either side of the sensor as it was facing up on the table-top (above a picture from their lab). Students got great results and were able to focus more on analyzing the graphs using the tools in LoggerPro. Below is a sample set with the points I asked students to mark in their lab. Overall the lab was actually pretty quick and reliable. I think I could even move up the timing of the lab in my unit as an introduction to gravity rather than a review. Here is the lab I used.
Being in California my family takes the drought pretty seriously. We haven't watered our front or back lawn in years. And unfortunately it looks like it. To increase the curb appeal and still keep our water usage low we decide to convert much of our lawn to drought tolerant plants on drip with mulch. As part of the conversion we had to cover 792 square feet with cardboard, overlapping a foot or more at each transition, as a compostable weed block. Even with the start of school I couldn't collect enough cardboard boxes at school to do the job so we ordered a roll of cardboard 6 feet tall and 250 feet long. While it wasn't heavy per se, it was pretty awkward to roll out the 20+ foot lengths I needed. I had an old diameter wooden closet rod that was over 8 feet long so I shoved that through the middle of the roll and raised it up on two sawhorses.
Since it was above the ground I could easily pull on the end as far as I needed to and the cardboard would roll right off. But then I noticed that the whole roll, well, rolled. In the photo you can see the closet rod was pretty close to the back (right) of the sawhorse. It had started even closer to the front (left). Every few rolls I would have to readjust the rod on the sawhorse and bring it closer to the front. It didn't roll much but every 20 feet or so I would have to adjust it.
That got me thinking. This could be a great example for a Physics class that discusses the Mechanical Advantage of simple machines. Ask students why the rod rolled, why didn't it roll very much? Usually the "distance in" is the "effort force" which would be the axis in the middle, in this case the closet rod. The "distance out" is the "resistant/ result force" which would be the whole roll acting as a wheel. This may seem backwards for this example since I was moving the wheel and observing the axis roll as a result. Students could calculate the Ideal Mechanical Advantage using the radius of the closet rod (standard 1.25" = 3 cm) and the cardboard "wheel" (2 feet = 30 cm). We would have to assume the machine is 100% to calculate it using distances and not forces.
You could expand the problem for students asking them about the circumference of the closet rod (axis) and how many turns before the rod might fall off the saw horse (assume its 18" wide).
This is an example of a little idea that grew, changed and evolved and I'm still not done with it.
A colleague asked for some ideas about free fall and I remembered an activity often called Tin Pan Alley; here is a video demonstrating it. Usually done as a demonstration, hex nuts are tied to a piece of string and dropped from a tall height on to a pie pan or other metallic plate. The sound is better on a thicker reusable pie pan than the thinner single-use ones. First students are shown a string with the hex nuts equidistant, say 20 or 30 cm. When the string is dropped the sound of each hex nut hitting the pan gets closer to the next hex nut than the last. A second string has hex nuts that are at specific (increasing) distances so that when it is dropped the sounds are equal times apart.
After suggesting this activity to my colleague I began to think about it more and decided to use it in my own kinematics unit. In what felt like a stroke of brilliance I thought of turning this teacher-led demo into a student run inquiry activity. I wanted to hand students ten hex nuts, a pie pan and some string and ask them to determine the distance of hex nuts that would create even interval sounds through experimentation. In the first draft I dashed off I actually titled it "Free Falling Nuts." After remembering I teach in a high school I realized it needed a new title.
But there was a sticking point, how can students be sure that the sounds are in fact even intervals? I decided to try and implement some technology.
I had downloaded the free Physics Toolbox app a few months ago and started to play with its many functions. Its an awesome app I strongly recommend downloading. There is a sound meter on there that records decibel levels over a time axis. I wanted students to use this free app to capture their hex nut hits so that they could compare the intervals between them. I also had Vernier Microphones and wanted to try using them as well. I wrote the whole thing up but before I decided to do it I thought I should try it. Turned out to be a good thing.
My colleague Matt and I decided to try it out before we gave the task to our students. We calculated the distances required for even time intervals with 0.1 s or 0.2 s, etc. and made a few prepared strings. We found that the sounds were so short that neither the Physics Toolbox sound meter nor the Vernier Microphones could pick up the sounds well enough to determine the time intervals. We tried amplifying the sound on a large stool, tried recording and slowing down the recording, etc. Without a 1:1 classroom we didn't want to rely on video analysis. We were forced to abandon the idea of students determine the distances by sound. And given that we wanted to use this as an introduction activity we didn't want students to calculate the distances between the hex nuts yet.
So I was back to the idea of a teacher-led demo. I decided to ask students to predict, discuss and then explain what they were hearing. I wrote this google slide presentation to guide the activity. The background data for calculating the distances for different time intervals is here, first calculated out by Matt. The larger the equal time interval, the longer the string. I was limited to a few meters given my ceiling height, something to keep in mind.
My regular Physics class starts the year with basic graphing skills and learning how to interpret graphs of motion. Tuesday we used Vernier Picket Fences and Photogates to determine the acceleration due to gravity.
Usually the next day I have students create another planet or moon in our Solar System to create the same graphs based on their acceleration due to gravity (activity here). Starting with the acceleration-time graph (constant horizontal line) students find the area under the curve to plot the velocity-time graph (line with a positive slope) and the area under that curve to plot the displacement-time graph (a power curve).
By this time in the unit my students understand the relationship between the three graphs for something moving with a constant acceleration. They've even graphed something similar by hand; and they saw the same shape with their lab (above). So I found myself wondering, "Why am I making them do it again?" I gave a small quiz last week and noticed that students were having trouble with tangent lines to approximate the slope of a curved line.
So I re-evaluated what I wanted students to learn/ practice with this activity:
- Students need to practice drawing accurate tangent lines and determining their slopes.
- Students should understand that while a constant acceleration creates a positive linear velocity-time graph and a power curve on the displacement-time graph the acceleration will not always have the same value.
- Students often find the area under the curve to find velocity from acceleration-time graphs but need practice finding the slope of a displacement-time graph to determine the velocity and eventually acceleration.
After reflecting on this I changed the activity. I took the acceleration due to gravity at the different locations in our Solar System and worked the data backwards to create the displacement-time graphs for each one. (data here) I printed out enough copies for students to work in pairs and laminated them; I also laminated graph paper. Students were given the displacement-time graphs Wednesday and asked to practice their tangent skills to determine the instantaneous slope at several points. They used these values to create a velocity-time graph on the graph paper using dry erase pens. Note: Overhead projector pens work as well and since they are finer tip would probably have worked better.
Students dove into it, determined to get very close values to the actual acceleration due to gravity. I soon found however that many were trying to use power regressions to solve it; I have quite a few students in AP Calculus. Others found the slope at the beginning and end of the curve, connected those two dots and called it a day. Students were calculating accelerations due to gravity for Mars or Mercury at 400+ m/s2! After some help around the room most students were better about using the tangent method, finding five to six points, paying closer attention to scale, and felt pretty good about their calculations. Yet as students came up to check their answers with me they were consistently twice as high as the actual value. Enough students had almost twice the values that I went back to check my data.
I had calculated d = at2 not d = (1/2)at2.
As my students would say, *face palm*; I totally blame the toddler-induced lack of sleep. The students were doing it right (good) and they didn't really know the acceleration due to gravity on other planets anyway so they didn't catch my mistake (even better). In the end I decided it would be a good way of introducing the equation next week and discussing why it is so important to include that (1/2).
I've fixed the data (available again here) and the printing pages (pdf or google doc) and plan to do this again next year. I have very sparse grid lines; depending on your students' math level you might want to give them more grid lines. In the end students were able to practice a skill, broaden their understanding of a concept and I didn't have to grade anything. Aside from my miscalculation, it was a win all around.
Back in June I wrote a Blog of Phyz post about the social media textbook reading website Perusall. I set up a Perusall class for teachers to try out. I posted a reading assignment, a paper by Joe Redish called Changing Student Ways of Knowing. I invited teachers to create a student account and participate by reading and commenting on this article. I promised to release grades on September 1st. Thirty-two teachers registered for my Perusall class and took a look at what Perusall can do. Seven teachers left a total of 18 comments. The artificial intelligent agent that scores comments on Perusall gave twelve the maximum score of 2, six received a score of 1. There were no zeros! These were pretty good scores compared to what my students averaged.
I was a little disappointed by the amount of participation in the teacher trial of Perusall. Because the default for automatic grading is 15 students, I had to ask their tech support to grade the assignment. The discussion would have been more interesting if we had a group of 20 commenting like I used with my students. Perhaps I didn't pick an interesting enough article. I still believe in the potential of this tool that encourages students to read textbooks by making it more relevant and useful for them. I am about to start using Perusall in this year's classes. I will use it for the full year and collect data about students use and perceptions. Perusall is free if you upload your own readings, I use the OpenStax physics textbook. Look for another update about Perusall next summer and maybe another teacher trial.
The Resource Area for Teaching (RAFT) was mentioned in a recent discussion on the PTSOS email list. I decided to contact RAFT to see if they could support PTSOS in some way. RAFT Site Manager Ofelia Delgadillo soon replied to my email inquiry with several ways RAFT could help PTSOS, our program for new physics teachers. I won't mention specifics here because I don't want to give away any of the surprises for those coming to the 9/17 PTSOS workshop (registration is still open). I do want to describe my experience visiting the San Jose RAFT location and how they can support physics teachers wanting to do more hands-on activities.
I easily found RAFT on Ridder Park Drive because it is a little past the Santa Clara County Office of Education. I went to the membership desk and joined. The $40 membership fee might be an obstacle to some teachers but it is only $25 to renew. If you can gather a group of 10, the new membership price is only $20 each. Many teachers should be able to get their school to pay for a membership. Either way, it will probably pay for itself on your first visit. As I waited for them to complete my registration, I noticed several teachers making use of the teacher "maker space" called the Green Room. It contains a lot of the equipment teachers need but don't always have access to like laminating machines, book binders, and button makers. After getting my membership card, I went back outside to get a shopping cart.
My first goal was to see if they had some whiteboards for modelling activities. I had to resist looking at all the lab kits as a passed through the front aisles, more on those later. I soon found several boxes full of framed 2' x 3' whiteboards donated by Silicon Valley companies. They were only $5 each. You can make your own for less money but some teachers would find that difficult and/or time consuming. The frames made them look more professional and sturdier. Many still had writing from the last time they were used. Who knows, maybe there is a billion dollar idea still on one of them! I picked out a class set of 10 of the lighter ones and navigated my now loaded cart through the back aisles. These contained art and office supplies, books, extra chachkies from corporate events, and numerous random surplus items like old VHS tape containers and biotech vials. A more creative teacher could work wonders with many of these items but I loaded up on sidewalk chalk.
In the very back is an area where volunteers work. They sort through donated items, update inventory, and package and price items. This would be an ideal place for high school students to get some community service hours. I also noticed the volunteers were assembling the lab kits that drew my attention when I entered. I decided it was time to take a look at those.
The lab kits covered many areas of science but many would be perfect for elementary, middle, and high school physics students. Each kit contains everything you need to build a hands-on device including detailed illustrated instructions, NGSS standards, "To Do and Notice" instructions à laExploratorium, a description of the background science, and links where you can learn more. I saw many variations of old standbys like roll-back cans, hoverpucks, Benham's disks, and simple motors. There were a few intriguing ones that I was unfamiliar with like roller racers and static merry-go rounds. You can purchase single kits or lab packs of 10. The single kits averaged about $1 and the 10 packs $10. I had to restrain myself from buying them all and managed to leave with 6 of the 10-packs covering a variety of physics topics. Here are some pictures I took of the lab kit displays:
Another great resource RAFT offers is professional development. I have not participated in it but a quick look at their website shows they have a useful program worth exploring. They have scheduled workshops and will customize training for your school or district.
After taking a good look at what they have to offer I am sure you are asking, how can I get in on this? There are 2 RAFT locations in the lucky San Francisco Bay Area and one in Denver, Colorado. Sadly, the Sacramento location has closed. That is hard to believe knowing that the top supporters of education in California, the governor and the state legislature, spend a lot of time there. Perhaps the Sacramento RAFT will return in the future. If you are within driving distance of any RAFT location I highly recommend you plan a visit soon. If you are not, you are in luck, you can order many of their items online. I noticed that there were over 100 of the lab kits available plus many more items in their online store. If you are having trouble visualizing this amazing place, here is a video tour:
My only criticism of RAFT would be to maybe get a better membership card machine:
I decided this year that if I was going to continue to take the time to teach students how to interpret kinematics graphs of motion (displacement-time, velocity-time and acceleration-time graphs) I was going to bring them up more often during the year. As we transition in my class from basic kinematics equations to projectiles I was looking for a lab that did just that. This is where it pays to keep more resources than you currently use in your curriculum. I found a pdf I had downloaded from Vernier using motion detectors and a ball. The lab looked simple enough and I tried to reproduce the results myself.
