Archive for the ‘Lab & Classroom Equipment’ Category
Student Created Lab
Posted on: January 6, 2014
I had been wanting to add a lab where the students determine friction on an inclined plane. Students seem to struggle with the complexity of the problem and I thought a good lab would help. I wasn’t really happy with any of the labs I found on the internet, but I also wasn’t really up for creating one of my own. (Having four preps really sucks the life out of your creativity.) What I decided to do was to put the kids into groups, give each group a variable inclined plane (exactly the one in the picture), a couple of blocks, and lab weights. On the board I drew the force diagram of the block on a plane being pulled upward along with the appropriate formulas. The goal of the lab is for the students to be able to calculate the coefficient of friction between the incline and the block.
I gave the class the following instructions:
“You are creating a lab for next year’s students. You are going to need to decide on the lab procedure, required data and graphs, and the analysis questions. You need to write up the procedure and the lab results, but I only want one per group. I am going to take the best parts of each of your labs and use it next year.”
I asked them to start with only a single block, but they could add another if they think it will improve the lab. We discussed setting the incline from 0 to 40 degrees in 10 degree increments. They are using their phone to take pictures to include in their instructions and write-ups. They have one more day and then the paperwork is all due at the end of the week. I’m hoping for work that is a step above their usual lab write-ups.
I’m thinking maybe I lied to them. I originally did want the students to create a lab for next years’ students, but I might just give next years’ students the same assignment.
Our school has added a number of iPad and Mac carts. The technology push is on and I’m not generally excited about it. You have to understand, I am the technology guy. I sold top of the line engineering software to the defense and manufacturing industry. I’ve presented technology solutions to the Secretary of Defense’s office, Senators, Congressmen, Admirals, Generals, and heads of fortune 500 companies. I am not afraid of technology, I love technology. I have an engineering degree; I can program in half a dozen computer languages, and I’m competent in 3-D CAD. But handing me an iPad and telling me to use it in class is like buying a 12-piece screwdriver set and hoping screws will suddenly get loose. It’s a solution in search of a problem.
It took a brain-storming session with my department head to realize I do have a screw loose, I have a problem that technology might just solve.
I have been really unhappy with lab reports. I’ve gone full circle with what I want from the kids. Here is a brief history:
- Year 1-2 – The students were required to have hard-bound composition notebooks. Students were required to type the report (3-4 pages) and the notebooks were graded. I had about 100 students – grading was a nightmare and the work was poor when it was even done. Many of my students didn’t have a computer or a printer a home.
- Year 3-4 – I changed over to one-page labs where the students would fill in responses as they went. They were much easier to grade, but the rigor was gone.
- Year 5-7 – Students purchased Carbonless Lab Notebooks. They were to record observations and show their work as they went through the lab. This never worked as planned. It was a constant battle to get them to only write in the lab notebook; they wanted their report to be neater, so they took notes on the handout. Reports were hard to read because I was reading a copy of unreadable students’ handwriting. Students didn’t like that they couldn’t edit, mistakes were to be crossed out.
It is time for a change, again. Maybe technology will by my answer this time.
Here is the plan as it currently stands (in my head). Students will be given a basic report layout on the Mac using iBook Author. They will build on the layout to construct a full lab report. Having the Mac in their hands during the lab will allow them to take pictures of the set-up and the results. Ideally, they will be able to record data directly into tables and turn it into graphs, charts, and anything they feel is appropriate. Reports will be turned in electronically. What they turn in will be a unique, well-documented report, hopefully of a much higher quality than I received in the past.
The down-side is quite significant. First, there is going to be a learning curve for iBook Author. Second, the students don’t have their own Macs, so the entire lab report will have to be created during class time. What was a one-day lab will probably turn into two or three days of class time. Third, I’ll have to figure out how to transfer data from the Vernier to the Mac. I’m hoping the quality the iBook reports will make up for the lost teaching time.
If you are a follower of this blog, you may have noticed I posted this entry and then promptly unposted it. I thought the software I saw demonstrated was called iBook, but I couldn’t find the application for the iPad. I spoke with my principal today and she confirmed that I had it right. However, the authoring app does not exist on the iPad, only on the Mac. When I went to download the app for my Mac, it said it needed to be running OSX 10.7.4 and I’m running 10.6.8. I tried to update my Mac but it says no update is available. I admit, I’m a bit confused. The tech guy from school is the one pushing the app, so I’m sure he will get everything taken care of once we are back. I was just hoping to spend some time this summer exploring this idea.
If this works out, I should have some really nice files to post here in about two months. I’ll let you know either way.
New Free Fall Lab
Posted on: October 3, 2012
I had been using the archaic ticker tape device to do a lab comparing acceleration to constant velocity. Yawn. It was not my favorite. It wasn’t anybody’s favorite. Let me be clear – it was boring.
I recently picked up a Sony Bloggie camera on eBay for about $50. It’s the same thing as a Flip camera. Make a video, flip out the USB plug, transfer file. It’s just that easy. I set up a backdrop of black paper from floor to ceiling. Kids got on a desk and dropped things. Everybody had to drop a golf ball first. A golf ball will fall pretty close to an ideal parabola, very little air resistance over such a small distance. After that, they could drop anything that wouldn’t break. I have soft squeeze balls and practice whiffle golf balls, superballs and paper balls, and best of all, a coffee filter. The coffee filter is a must, it reaches terminal velocity almost instantly.
We are using Logger Pro software from Vernier. I suppose you could use Tracker, but I have Logger Pro and know how to use it. In Logger Pro, we insert the movie file and then use the tools to place a dot on the object as it drops. The software advances the frame, and in a few minutes we have a synched up video, graph and data table. The software allows the students to quickly see how the slope of the distance vs. time graph changes. They can replay the image and watch their data points in action.
Click for larger image
I have them use a quadratic curve fit to calculate the actual acceleration. Then the kids create a second curve and override the fit value with g/2. That puts the expected acceleration curve next to the actual. The effects of air resistance are instantly visible.
We just did this lab for the first time yesterday and today. Give the kids time, it’s going to take them a couple class periods to make this all happen. Initial feedback has been good. I think it’s making sense to them. They can see the effects of acceleration. They can clearly see terminal velocity.
Here is the lab they used. I expect there will be some changes.
I’ve been a member of American Association of Physics Teachers for about 6 years now. If you teach physics, please join! The journals and posters alone are worth the tax deductable annual dues. I attended my first AAPT meeting a couple of weeks back. I learned one or two great new things, met some super people, but I was also a bit disappointed.
Let’s get the negative stuff out of the way.
- I’m used to NSTA, so maybe my reference is unfair. AAPT was small, really small for a national conference. I felt like everybody knew each other because it was the same people every year. You could get through the entire exhibit areas in about an hour.
- It also felt like the conference was aimed at college educators. I know the organizers claim it’s not, but I’m giving my opinion here based on attending one day of a much longer conference.
- I had hoped that the talk on video in the classroom would give lots of useful tips; how to integrate video, success at flipping the classroom, etc. Most of the discussion was why video lectures won’t replace colleges.
Now the positives:
- The first timer special and lunch was a great idea. Lunch and the company was terrific, I’m glad I went. The first timer $75 one-day special is a great way to try it out.
- I got to meet some great people, some new, some who I had previously met online (Kathy, Frank). Everybody was warm and there to interact and learn from each other.
- I met local AAPT members who are trying to suck me in to local activities. I am interest, but they always do them on a Friday night and Saturday. I may submit, I do need local physics buddies but I love my weekends.
- Andy Rundquist demonstrated a great use of Jing. He has his students take a picture of their homework, then narrate the work on video. The video is their homework submission. Jing limits them to 5 minutes and when they talk, you can immediately tell if they know what they are talking about. Andy has them do this for every homework, I’m going to use it sparingly. Super idea.
- There is free software out there called Tracker that does video analysis. One cool use was to take a moving object, like a person jumping into the water, identify several points (hands, feet, head) through each frame, and let the software determine the center of gravity and plot the motion. Did I mention free?
- I really like the sessions where there is a new presenter every 10 minutes. Lots of great stuff, and if it isn’t, it’s only 10 minutes until the next one.
AAPT was worth my time, I wish I had done the entire week. It was close enough to home that I was able to take public transportation. Here’s the problem: if you can get your school to pay for you to travel to one national conference, which do you choose – AAPT or NSTA?
For me, it would be an easy choice. NSTA has so much more to offer, so many more strands, talks, exhibitors, and people to interact with. I would love to do both, I don’t see how. I will get involved locally, AAPT is too good of an organization to ignore, they are worthy of our support.
Let me start by saying that I have yet to take a course in teaching through modeling. I want to, and I will.
I never loved my pulley lab. I was never pleased with the learning, the kids seem to focus on trying to set up the pulleys and not on what is happening.
Two days ago I handed them this revised instruction sheet: Pulley Lab Rev D – Discovery Lab. The instructions are simple, “Your job is to come up with a set of rules that explains what is happening with the pulleys, ropes, and weights.”
Besides the ring stand, support, pulleys, weights, and string, I gave each group a Vernier and force meter. They set to work trying to figure out what is going on.
After they finished with the first setup, I asked them to tell me what happened. The weight was the same, so what was the purpose? Finally one of them said it changed the lifting up to pulling down. So a single pulley can be used to change directions. I gave them a few applications, like pulling something up into a tree or the mast of a ship.
Next they started on the other pictures. They noticed the force changed. I mentioned that there is a cost to the reduced force, what is the cost? Their response was less work. No, work is conserved. Keep going.
When they got through picture 3, I explained that they were experiencing Mechanical Advantage. If you hang by one arm, you hold all of your weight. Add the second arm and you are splitting the weight. Add a third arm… you get the picture.
As they got through the rest of the diagrams, two challenges remained: 1) what is the cost, and 2) figure out how to rig this up to get a mechanical advantage of 5. I gave them a hint – picture 2. They worked for a while without success. End of the first day.
I came into class and was pleasantly surprised to see all of the groups were already set up and working. They were twisting the ropes all over the place. I gave them 15 minutes to play. They still didn’t understand the cost, so I drew the solution for the MA of 5. We put a bunch of weights on the pulleys, almost 10 lbs, and I had them all take a turn lifting. I wanted them to experience the mechanical advantage. Then we measured how far the weights moved and how much string was pulled to make this happen.
That was all it took, they got it. In a perfect system, work is conserved. This led to a discussion of efficiency and how a lever also provides a mechanical advantage. It was a good day.
Note: Here is the solution to the challenge at the end of the lab: MA 5 Solution
Homemade Hooke’s Law Device
Posted on: March 5, 2012
I like saving money for my school. Nothing against Carolina Biological, we’ve been really pleased with their equipment and service, but sometimes their stuff is just way overpriced. Their Hooke’s Law Device is $35 each. I made a similar set of devices for a couple of dollars using what we already had in the lab and classroom.
My device is made with a ring stand and small rubber bands to hold a ruler in place. I used a pendulum clamp as the top support, but any clamp will do. To connect everything, I used a bit of chain that comes with a shop fluorescent lamp and opened up the links. These are in an S shape and twisted to be offset by 90 degrees. You could just as easily purchased a package of S hooks at Home Depot for a couple of dollars. At the top, I hang one side on the clamp and hook the spring over the other opening. Same on the bottom, the hook provides a place to hang a weight.
We use hanging weight sets, I just didn’t have them hand for the picture, this is one of my 500g medicine bottle weights. The springs come from Harbor Freight. They have a box set of 200 springs for about $5. Lots of springs to play with, many look alike but have very different spring constants.
My “indicators” were fabricated on the 3D printer, but you can just as easily make the same thing with two Popsicle sticks and some glue. Drill the holes or it will split.
That’s really the whole thing. I found that if I spun the whole setup one rotation CCW, the spring would try to rotate clockwise, holding the indicator against the ruler and making it much easier to read.
I’m planning on adding a scatter chart to this lab. The students will enter the points in Excel to create the chart and then plot a trendline. We can then use the first order trendline to determine an unknown weight based on the distance the spring stretched. This setup was inexpensive and effective.
Follow-on Toy Popper Lab
Posted on: March 1, 2012
Last year I gave all my physics classes the first toy popper problem (1st popper lab). I learned my lesson and only the honors group gets the inquiry version of the lab. This year I followed on to that lab with a second popper lab when we got to impulse. The non-honors class doesn’t get to play with poppers until they get to this lab.
I made it a lot easier for the non-honors group by explaining the steps to calculating the time and acceleration of the popper from just the height and the mass. The honors group got to confirm their methods with the help of my written procedures and they got to test the accuracy of their predictions. As a result, the lab works both as a stand-alone lab or as a follow-on from the previous lab.
About half of the students take calculus (with me) and I took the time to explain how the area under the impulse curve is really the impulse because it is the force (y-axis) multiplied by the time (x-axis). While they wouldn’t have seen that on their own, I think they all understood that the change in momentum (impulse) = Ft.
So here is the latest incarnation of the lab for you to use and enjoy.
Good Intentions, Bad Lab
Posted on: February 28, 2012
A couple of weeks ago we did a lab straight from the textbook. (Here is the Lab Instructions, typed up and put it into my words.) I’d been looking for a good Conservation of Energy Lab. I wanted to use the Vernier devices, but there wasn’t anything in their book that I liked. Rather than make something up from scratch, I decided to work directly from the Holt Physics textbook.
The lab had two parts; the first was to calculate the spring force constant using a Hooke’s Law device. I didn’t have that device, so I created my own by first designing a simple indicator on Solidworks (3D CAD Software) and then printing eight of them in the 3D printer. That worked out great. (I will try to remember to post my Hooke’s device design, you can build them for about $0.25 each.) Unfortunately, it was the only part of the lab that worked out at all.
We were able to use a ring stand, ruler, and indicator to successfully calculate the spring force constant. The second part of the lab was supposed to demonstrate conservation of mechanical energy by bouncing the weight and measuring the high and low point. Quite honestly, it just didn’t make sense. At first it did, but the more I thought about it, the less sense it made.
To begin with, it was nearly impossible to measure the bottom and top of the bounce with any accuracy. It was pure guesswork and the kids were really struggling.
This is a great bunch of kids, I warned them ahead of time that this was the first time using this lab, there might be some hiccups. They were understanding and really tried to make this work, but they were totally frustrated. I told them I would grade the lab on their effort, spring constant results, qualitative analysis, and attempt at explaining the results.
Clearly, I need a much better lab for next year. I was originally thinking of calculating the spring force constant, then determining the weight of an unknown object based on distance the spring stretches. That makes sense for the chapter on oscillations, but not for Conservation of Mechanical Energy. I don’t have an air track, but I’m really good at McGuyvering solutions, as you all well know.
Please throw your awesome labs my way, I need help.
Last year, the course was actually called Robotics and Astronomy, or Robostronomy for short. The intent was half-year of each. The result was more like three weeks of astronomy and robotics all year-long. Don’t get me wrong, I love astronomy. It’s just, well, Robots took over the Earth. Between the great things we could do with the MindStorm, and then the SeaPerch competition, we were all robots, all the time. This year we are adding the First Tech Challenge. Yep, Robots have taken over the Earth, and it looks like they landed in my classroom.
The goal here is STEM, that’s what opened the door for the robot invasion in the first place. Clearly missing from our program these days is what we called in the old days, ‘drafting.’ Drafting isn’t done on a board with a T-square anymore, but you all know that. Today, 3D mechanical Computer Aided Design (CAD) is available for free from Google (Sketch-up), and from a number of companies who cater to the high-end. I actually know this industry well, I spent 25 years in the CAD/CAM/CAE industry (M for manufacturing, E for Engineering, meaning simulation).
So with some guidance from some friends at Drexel University, and a little research on my own, I decide to go with SolidWorks software. All of the vendors have aggressively priced programs for the educational market, I think we are paying just $1000 for a 10-seat license. What makes this software connect to the students is what we spit out of it. The school invested in a 3D printer, specifically uPrint Plus from Dimension.
If you have never seen one of these, think Star Trek Replicator. The replicator creates parts from ABS+ plastic directly from the output of the 3D CAD. How better to teach engineering principles than to give the students a design challenge, have them work through designs and then fabricate it in the printer. Here is a great video from a customer talking about how they use a 3D printer in their engineering design work.
My new printer is due here any day and I’m pumped up. Yep, geek boy has a new toy. Tea, Earl Grey, Hot!
Coffee Shop Physics
Posted on: August 29, 2011
I would like to have coffee available for the students while they work, but my administration frowns on kids having food and drink in the classroom. But that is not where this story is going.
Last year, one of my students came into class second or third period and said how much he loves coming to my room. I thought it was odd because he wasn’t a particularly enthusiastic physics student. Then he said he loves the way my room smells.
Every morning I make a pot of coffee, often flavored with vanilla or hazelnut. I never thought about the impact something like a nice smell has on making a student feel relaxed. I’m still making coffee every morning, but this year I picked up a bunch of scented tea lights from IKEA. These things smell so good, my son and I bought a pack of every flavor they offered.
I have heard stories of real estate agents putting a drop of vanilla on a warm oven at an open house to make the home subconsciously remind the potential buyers of home-made freshly baked cookies. Maybe getting another one of their senses involved improves learning.
Homemade Hooked Masses
Posted on: May 26, 2011
I needed unknown masses for my Torque Lab. Good thing I don’t seem to ever throw anything away. I’ve been taking Prevacid for about a year now, it comes in a really handy sized bottle. (Now let me just say, if you have a chronic indigestion problem and you don’t try this or one of the other drugs like Prevacid, you are missing a life changing drug… seriously.) Anyway, these cool little bottles tend to stack up rather quickly. I took a small screw hook and tried to put it into the top but found it difficult to center it and drilling was too much work. Instead, I turned the bottle upside-down and inserted the screw hook into the bottom of the bottle. This worked great and I like the look. By changing the contents to lead, I can make these much heavier.
I wanted to put lead shot in the bottles, but I didn’t have any. I was going to purchase fishing weights, but for what they cost I decided to just use pennies. They are mostly copper, fairly dense, and I can fill a bottle for about 20 cents. It turned out to be cheaper to use money as a weight than to spend money to buy anything else. In some of the bottles I put odd screws and other metal bits to increase the density. I made sure none of the masses were at even values, and they are all different values. In other words, the mass of one bottle was 87.2 grams, not 80.0 grams or 85.0 grams. For some reason, my students believe all answers should be whole numbers. Of course I don’t believe that. I numbered the masses #1-#12, weighed them on my gram scale, and recorded their mass on a note card and stored it in my desk drawer. During the lab, I refused to tell them the values of their unknown masses, and my gram scale was locked up, but I did tell them their answers should be in the range of 75 to 120 grams. I did find the unknown weights would work better if they were more in the range of 150 g. I’ll have to see what lead shot costs, maybe a bag of it is in my future.
During the lab, I instructed the students to make note in their lab notebook of which unknown mass they used during the lab. I explained that each mass was different and they needed to stick with the same one each day. Despite the explanation, about half the groups didn’t make note of which unknown mass they used. Some of them just said it was white. Well, at least we have colors down.
Toy Popper Lab – Update #1
Posted on: January 5, 2011
We finished the lab today. I gave the kids two days to do it. Most of them figured out the initial velocity by the end of the first day. The start of the second day, I put two hints on the board. For question 2, I put up t=d/Vagv. For question 3, I told them they needed to calculate the acceleration of the popper.
I decided to be only somewhat helpful. At the start of day 2, I told them the initial velocity should be in the range of 5 m/s. I told them I would not answer questions about their numbers if the formulas were not there and units were not shown. I generally only told them they were either on the right track or wrong, nothing more. Most of them had a tough time making the leap to the distance in part 2 was how far the inverted popper moved from rest to the calculated initial velocity. Once they got that, they were well on their way to solving the problem.
Force v. Time Function for Toy Popper
I did an interesting experiment while they worked. I set up a LabQuest to sample at 1 ms intervals. I build a tiny tray from cardboard and string and attached it to the force sensor. I set the meter to trigger at a force greater than 2.5 N, zeroed the sensor, and let it rip. It showed a nice impulse function that took 23 ms and a peak force of close to 7 N.
I could use some help with my interpretation of the graph. I believe the integral of the Force v. Time curve gives me the impulse (the LabQuest gave me a value of 47 N*ms). If I divide that value by the mass of the popper (9.1 g), I get a delta v of 5.16 m/s. This is in agreement with the numbers the kids got in the experiment.
Now if I divide the delta v by the time, I should have the acceleration. The LabQuest samples every millisecond and there are 23 points, so I think the time is either 22 ms or 23 ms. The acceleration works out to be 235 m/s^2. Doing this, I only get a force of 2.1 N, but the graph shows close to 7 N. The students calculated forces in the 6-7 N range. I think the discrepancy has to do with using the integral (which should be more accurate) and getting a peak force compared to an average force. Can someone either confirm this or correct it for me please?
Party Popper Lab
Posted on: December 31, 2010
Am I the only teacher that spent half of the holiday break grading papers and working on lessons? Here is a lab my students will be working on when they come back from break on Monday. I figure it will give me a day or two to settle in without having to get up front and teach.
We just finished Newton’s Laws before break, what better way to refresh their memory than making them think. I got this lab from the NSTA regional conference in Baltimore, it is called “Inquiry in a Box” and presented by Deborah Roudebush. I put the instructions into a format my students are more familiar with and I expect they will need two days to get their arms around the whole thing. What is very different about this lab (compliments to Deborah) is that the students are given only the problem to solve, some minimal tools, and no instructions. They need to figure it all out on their own. It could be a disaster, I fully expect a lot of whining.
The basic idea is that the half ball Party Popper shown above is a cool little science experiment. Giving them only a ruler and access to a gram scale, they need to figure out how to determine the velocity, time, and force exerted by the popping event. At the conference, we were put into groups of four and set about solving the problems. It didn’t take us too long, but there were some very good discussions on when the time and acceleration actually occurs. There will be no answers posted here, some of my students know about this site. If you need some help, email me.
Here is the lab handout: Popper Lab Handout
Now, you would think these little poppers are easy to come by… good luck! I went to many toy stores and party stores and found none. I ended up online at Oriental Trading Company. Their 1.5″ poppers are great, their 0.75″ are going back, they don’t work at all. I found another place selling them; Century Novelty. I’m ordering 1″ poppers from them. The key here is you have to plan ahead for this lab, you can’t run out to the store the day before and find them easily. I won’t have the 1″ poppers in time for this year, but next year I plan for them to analyze different size poppers and compare the results.
This is a follow up on the first pass of a lab I created about a year ago. You can see my first post here. This year we purchased a whole pile of new technology including the LabQuest from Vernier. If you have these in your lab, you know just how cool they are. The kids love technology, this lab grabbed their interest.
When I came up with a lab last year, we used spring scales to attempt to measure the coefficients of friction on all different surfaces. Let’s face it, doing this with a spring scale was mostly guesswork. I enhanced the lab with the digital force meter, made a few quick modifications to the instructions and gave it to the kids. The results blew me away.
The graph you see below was printed directly from the LabQuest. I tried exporting it as a file, but the export file wasn’t an image file, so I scanned it for all of you to see. Click on it to see it full size. The red line shows the force required to pull a painted steel plate across linoleum. You can clearly see the spike where the pulling force overcomes static frictional force. The next horizontal data set shows that the object was pulled at a constant speed. We can read both the static and kinetic forces directly on the LabQuest.
I included a shrunken image of this graph on today’s test. I gave the students the weight of an object and they had to calculate the two coefficients of friction from the graph.
Here is the handout: Measuring the Coefficient of Friction – LabQuest, feel free to steal it and use it. If you have ideas to improve it, leave me a comment.
Here is an interesting finding – shoe rubber seems to have a static coefficient that is the same as the kinetic coefficient, pretty much regardless of the surface. On linoleum, it’s around 0.60.
Free Astronomy Resources
Posted on: March 30, 2010
At NSTA I met an earth science/astronomy teacher named Jay. In one of the lectures Jay attended on the Chandra, there were playing cards showing the steps of stellar evolution. He told me the cards are free and I found the site and ordered a set of them for my classroom today. One way the cards were used was to ask as question, like “What are the steps to a star becoming a white dwarf?” You can then choose a subset of the cards and have the students create the proper order of the star’s evolution.
http://chandra.harvard.edu/edu/formal/stellar_ev/cosmic/
To order the material, the bottom of the page has a link saying “request.” You must be an educator to order this material, so if you are just a space nut, sorry, find a teacher friend or give up your high paying job to become a poorly paid teacher so that you can get free stuff for your classroom. There are additional links and request forms for posters, you will find it on the first order page.
Whoever is responsible for the Chandra site has a real clue about education. There are actual lessons and activities that a teacher can use with little or no modification. I’m finding this to be a rarity; usually the sites have quick activities or thoughts they post as lessons. The link to the Chandra Educational site is here:
http://chandra.harvard.edu/edu/formal/index.html
There is an awful lot here, I plan on spending more time digging when I have some reading time.
Physics & Physical Science Demos, Labs, & Projects for High School Teachers 
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