Thanks to Matt Greenwolfe from North Carolina for having me think about using the bowling ball/broom lab in this way.
Traditionally modelers have used the bowling ball lab as a introduction to the Balanced Force Model, however in reality this lab has so much more to offer than just balanced forces. In reality it has EVERYTHING an intro mechanics physics course needs. Granted we won’t be able to dive into and develop all of the models of physics at play here, but the students will have a sense of them anyways.
I gave my students the following set of “Official Broom Ball Rules” as published by the United States Broom Ball Association (USBBA). Broom Ball. Before we started any competition I gave all the students about 20 minutes to practice their techniques. Once I felt they knew what they were doing we divided into teams of two. Each team took a timed run through the course. I found a student to be the official timer, and I was the keeper of any penalty time that needed to be assessed. I felt the students had a great time playing the game and competing for the pride of being the fastest broom ball team. Here are the final results:
After the competition each team discussed questions about the motion of the ball, how to produce that motion, challenges and recommended strategies to succeed. As a large group these same questions were discussed. During the course of the discussion I served as recorder of ideas. I tried to write down as much as possible and attempted to organize all the ideas into 7 big physical models. Constant Velocity, Acceleration, Balanced Forces, Unbalanced Forces, Circular Motion, Energy, Momentum.
At this point it’s unnecessary that the student understand any of these models fully, but I can see the benefit from having the words at least “out there.” Sometimes I feel modeling tries to “hide” the terms from students like it’s a big secret, when in reality they already know these terms and its now our job to break them from what they think they know about each one and model the correct way to apply the models in different physical situations. I was excited to start the year this way, and hopefully it sets the tone for a great year.
It’s amazing what some students have heard and believe on “school faith.”
As the first activity in my Physics 2 class we do the Pinhole Camera with a light bulb and view the image on a screen. The first day I showed the class how to create a simple pinhole camera out of a box and some aluminum foil (if you want to see what mine look like let me know.) This year I rewrote the lab to be totally inquiry based. They made a number of general observations and wrote 7-10 “I wonder…” statements or questions, they then experimented and tested their “I wonder…” statements and made observations. This rewrite to an inquiry lab was great. All of the groups wondered about and tested the same things I had on my previous version of the lab (move the screen, move the bulb, make a bigger hole, make multiple holes, use two bulbs, etc). So that part of this process was excellent.
The next day after a brief discussion about some of the observations we saw I instructed each group to create a model on a WB for the situation. I reminded them that the model should be simple, but yet be able to explain ALL of the observations they made. Here are two of the models I got:
Student justification: “Light travels in waves”
“I was told light is a particle that travels in waves.” Thus the dots in wave form here. I find it interesting that the waves keep getting bigger. The student had no particular explanation for that, just that they were waves.
I keep trying to ask “what about this lab shows that light travels in waves?”
“I don’t know, but it does.” was a common response.
It took myself and another student group about 20 minutes to finally convince the bottom group in particular that we don’t need to model the light as waves. And even now I’m not sure if they bought it or just wanted to be done with the conversation so they gave up.
“Why can’t we use straight lines.” another group said. Their board did show a linear model for the light, and they had the arguments to back it up.
“We have no evidence to back up the claim that they are waves.” I said. “Straight lines explain the behavior and it’s a lot simpler to use then draw crazy wave forms.”
I went on to say that “we haven’t “disproven” the idea of light as waves, but we surely haven’t proven it. Science comes with the burden of proof.”
So as I analyze this class discussion a couple of questions come to mind:
1) Do other modeler fight this battle of using a model that we have evidence for vs. what they have been told. (I find it A LOT in chemistry too, especially with the atomic model)
2) Was this a lesson for my students about science at its finest? Did I end the discussion too quickly because I wanted to “keep moving?”
3) Should I let them use their mental model until it totally breaks down and/or becomes too difficult to use?
If you have any answers or thoughts about these questions, please comment below.
This week if finals week at school so our normal cycle of learning gets interrupted. I’m lucky this year however that we are in the process or building our constant acceleration model.
I know it seems late in the year that I’m just starting constant acceleration, but I went with the a “Unit 0” to start the year, and then Constant Velocity and Balanced Force before Acceleration. I definitely like the change in order but it has taken me a long time to be comfortable to move on when students were still working through understanding everything. By using SBG I’m able to track that as well.
So today served as a silver bullet for me and my students.
I gave my students the following guidelines for their task today:
Basically I asked them create a whiteboard that will both review what the graphical models of constant velocity show as well as to extend those ideas to the graphs we looked at from carts speeding up and slowing down on a ramp. (We used Motion Detectors prior to this to see the graphs and shared whiteboards about the data collected, but we didn’t finalize ALL of our thoughts.)
I said they can organize it anyway they wish that makes sense to them, and will help them review and hopefully draw connections between the two models. Groups will share their boards tomorrow during our “semester review” time. (I will try to post some pictures of what they come up with). I will let you know how that turns out.
As always, if you have done something like this, or have some ideas for me to improve, or have questions about what I’m doing PLEASE comment below.
It was almost impossible to not pay attention to the Red Bull Stratos Jump this last week. Especially being a physics teacher. I knew this was a big deal, and an exciting deal, even for high school students.
As information and analysis was flying all over the Blogs, Listserves, and Twitter I tried to figure out how can I use this? My students are just finishing up the Constant Velocity Model, so their understanding at this point is limited. Then I came across Peter Kupfer’s message on the Modeling Listserve. The link is here: http://blog.peterkupfer.net/2012/10/15/using-the-red-bull-stratos-space-jump-in-physics-class/
I found that Peter used the speedometer shown in the video to create a velocity vs. time graph! Sweet, thanks Peter! The graph is below. The way Peter used it was to calculate the jerk experienced during the time of increasing acceleration. My students are no where near ready to do that yet, so I focused on the segment between 45 sec and 60 sec.
A link to the worksheet I created with this data is here: Felix Space Jump CV Analysis
Basically what I did was created a “How Do You Apply the Model” problem as well as a “Goal-less” problem. I wanted students to be able to draw other representations of his fall during the 15 seconds in which he was falling at constant velocity. They were able to draw x vs. t graphs, and motion maps. Some even wrote written descriptions and mathematical models!
As students were drawing these they noticed that the speed is in mph and the time axis is in seconds. Only a few took it upon themselves to do the appropriate conversion to miles/second. I ended up showing the class how that worked out on the front board, but once I did that they were able to solve for distance covered as well as correctly scale their graphs and motion maps.
Most students were amazed that he covered 3 miles in this 15 seconds. “That’s ridiculous” was a common quote.
Overall I really loved how this current event fit so nicely in with the unit we are studying. The fact we were able to analyze even a portion of the data with our limited skills was awesome. I did get a lot of questions about other aspects of the entire fall and how to analyze those, including the “why did he travel at a constant velocity.” It was a perfect time for me to explain that our current model is quite limited and we need to work on developing some new models. WIN! I do plan to pull this data out again as we get into forces and acceleration. It should be fun.
Even through all this fun and excitement (for me) there are always a couple of students that do not appreciate the sweetness of this analysis. One young man went so far as to jokingly say, “way to ruin the coolest thing I’ve seen in while.” (At least I hope it was a joke).
I’m always looking for news ways to change up the whiteboard process I use (almost daily) in my class. Whiteboarding is amazing, it gets and keeps everyone involved in the process of scientific thinking and problem solving. However, early on each year I struggle with getting the students involved in the questioning and discussion process during WB presentations.
My theory is that it is an intimidation factor. Students have a hard time adjusting to being able to questions their peers in front of a larger group of peers. Usually in my Chemistry classes it is the first time students have been exposed to “low pressure”/”conversations starting” presentations such whiteboards. Most have experienced the dreaded report presentation but that is it.
This year I tried something different to get the conversation started while my Chemistry students were whiteboarding the Modeling Chemistry worksheet on density.
I split the class into groups and gave each one problem to work on (students were to work on all of these problems individually before they came to class). The problems on this WS consist of a mass vs. volume graph and several questions relating to that particular graph. I gave the groups about 8-10 minutes to work on their problems.
As groups finished up working on their problems I rotated the boards themselves so that each group was looking at someone else work on a different problem than what they just did. I gave them the following instructions:
- Do NOT change any of the work on the board.
- Write at least 1 relevant chemistry question about something that was on the board (Not why did you spell this wrong?)
- Even if you agree with everything on the board you need to write 1 question you would like to ask the group about why or how they did something.
I believe this process is similar to a “Whiteboard Museum,” but my classroom is not set up well for that at all, and I’ve never seen that done where students actually write questions right on the boards.
Here are a couple of examples of the boards I got. (These aren’t the best ones I had all day, but I forgot to take pictures during my first couple of classes):
Overall I really liked the way this whiteboard modification turned out. There were a couple of benefits my students gained from this WB modification.
- It gave everyone a sense of what I am looking for during the “questioning” phase of whiteboarding. The whole idea of asking a question even if the answer is correct and they agree with the answer is foreign to them. This forced their hand a little bit, to understand I’m more interested in the overall process of them “getting” a problem.
- It allowed the shy students that have a lot of great questions and insights a chance to ask a question without asking in front of everyone else.
- As groups presented the boards we were able to skip them explaining some of the WS problems they had been assigned. Since all groups already looked over the boards and didn’t have an questions on a particular problem we saved that time.
- As the groups presented they were able to focus their explanations based on the questions written on the board. It gave them a sense of “direction” for their presentation.
I don’t think I will do this every time I whiteboard (especially not for labs), but when WBing a set of worksheet problems it seems as if it could be an effective way to change things up.
I would be interested to hear your thoughts and comments about this. Have you done something similar? What could I do better? Different? Please post below!
To me measurement is one of those topics that doesn’t seem like is should be a challenge. BUT every year and every teacher I talk to finds that measurement is a HUGE PROBLEM with students. I’ll let you form your own theories as to why this is the case. This post is to describe the process I use to “reteach” students how to measure correctly, with the emphasis being on using a system of 10 divisions.
I personally treat this activity as a lab, but it can be done any number of ways. Here is the handout I use: How Many Nerds Lab. The lab begins with me giving each student a ruler that looks like this:
They are asked, what do you notice about this ruler? Things such as “no markings,” “a 0 and a 10,” “10 inches,” and many other things come up. First thing I tell them is that this is NOT 10 inches or any other unit of measurement they have ever used. So I have given the units a name: NERDS! I tell them that since I’m kind of nerdy I wanted a unit of my own.
In reality the credit for this name and the rulers goes to Mr. Ryan Peterson of Brillion High School. Any unit name you see fit can work.
From there I ask: “What is this ruler good for.” The usual response is “not much.” I usually have to hold something up and say “really, you can’t tell me anything about the length of this object?” Someone usually realizes they can tell the object it either shorter or longer than 10 nerds. “Ok, so what should I do to report the length of the object?” “Guess” seems to be a popular response, but I quickly say guessing is random, like how many Jelly Beans are in a Jar. Someone will finally say “Estimate.”
“Ok, now go and measure 8 things around the room. Try to get at least 2 or 3 things that are longer than 10 nerds.”
I give them about 5 minutes to make their 8 measurements. Then I hand out this ruler:
After a very brief discussion revolving around the fact that this ruler has the whole numbers marked, and that in science WE DO NOT USE FRACTIONS, I send students to remeasure the same 8 objects.
They are off to remeasure the same 8 objects they have already measured.
Before I explain my discussion, here is how these rulers were created. Again credit for the original Excel file goes to Ryan Peterson.
Nerds Rulers. This Excel file contains 3 tabs, each containing 6 rulers on each tab. Print from each tab. I then copied enough sheets to make a class set of ruler on colored paper. Finally I sent the pages through the laminater and cut out each ruler. The set I made 5 years ago is still going strong. The only real issue I’ve had is kids fold the blue ruler in half.
Back to the lab.
Once all measurements are made the students see a pattern of increased precision with each ruler (they don’t call it precision, but that’s what it is). We quickly discuss things such as which ruler is best for measuring different objects, what makes a measurement “correct,” and how to handle measurements that we right on a marking. The next thing is to have small groups discuss and whiteboard a rule or rules for using a ruler.
I give groups about 10 minutes to discuss some things and come up with what they think we should consider as “rules.” Most groups come up with things like:
- Start at zero
- Measure the same object
- Measure twice
I tell them that those are good and true and all, but how do make sure we are using a ruler correctly? I sometimes have to give them the hint about what they did with the 3 different color rulers. Most of the time that helps them realize that they ESTIMATED something in the answer. Ultimately, after all groups have shared their rules I want the class to agree that we should:
- ESTIMATE ON PLACE MORE THAN WHAT THE RULER TELLS YOU FOR SURE
This usually makes sense to the class, and they agree this the #1 rule. PERFECT!
I extend the discussion with what that estimated number means. I show them how the number they estimated is really reporting a range of numbers. So for example a measurement of 3 is likes saying somewhere between 2 and 4. A measurement of 3.6 is the range of 3.5 to 3.7. Reporting 3.65 is something like 3.64 to 3.66 (this range might be a bit larger depending on the ruler). Something I don’t stress at this point.
The next step is to introduce our more typical units of measurement: METERS! Students know it is coming but they grumble and complain, and raise a fit over why we can’t just do it the “easy” way (inches, feet, etc.) I then proceed to ask them something like; “so what increment comes after 7/32?” Someone says 8/32. “Ok, but I’m not going to find a wrench marked that.” 4/16, 2/8. oh 1/4. “Congrats that just took you 1 minute to figure out.” “What wrench comes after 7 mm?” 8mm. “1 second, nice job, now which way is easier?” I will then of course have the discussion about english vs. metric.
I usually like to get on my soapbox a little bit and complain about how “the US is the greatest country in the world, and by gosh we aren’t going to change our ways for anybody.” I play that angle up a little bit, and we get to the point that metric is easier to work with, just not as common for us in America, but they hopefully see the point.
I now show the class a dowel that is marked as 1 meter long, but that is it. Kind of like the blue ruler from above. I then discuss and demonstrate how you can split a meter into 10 equal sections called decimeters, show them a ruler with only dm marks. Each decimeter into 10 centimeters, show a cm ruler, and finally centimeters into 10 millimeters, show a typical meter stick with mm markings.
My lab hand out is here: How Many Meters
Basically, I have a set of different metric rulers, and whatever the smallest markings are on the ruler is the “type” of ruler it is. So a standard metric ruler is a mm ruler even though the numbers are cm. This is just another complication in the process we have to deal with. I have each student measure the same stuff with the same type of ruler so that we can compare results.
This is all for practice, and the whiteboard discussion is pretty minimal. I usually focus on the different prefixes used in the SI system. Why it is called SI and why it is important we have a standard unit of measurement for scientists.
Uncertainty of Measurement Activity
The questions I usually get about all this emphasis on measuring is “Why is this important?” To me this activity nails it and relates why estimating measurements is so important as well as demonstrating exactly why significant figures work the way they do.
I distribute a index card and blue ruler to each student. (something smaller than 10 nerds is a must, otherwise the uncertainty becomes too great.) Each student measure the length and width of the card. They then calculate the area, and I instruct them to write down exactly what the calculator says.
They remeasure with the pink ruler and again calculate and record area exactly as is displayed. Finally they measure a third time with the gold ruler.
After all measurements and calculations are made I have each student list their calculated areas on the board. One column for each ruler. I forgot to take a picture of the entire set of class data, but it was something like this:
Notice how sweet this data is! The discussion revolves around where the uncertainty in each calculation shows up. For the Blue ruler it is in the tens place. The Pink ruler the ones place, and the Gold ruler is in the tenths place. Coincidence?! I don’t think so.
Because of our “rule for using a ruler” the significant figure in each measurement comes out to be where our uncertainty shows up in our calculations! Amazing!
Bottom line is the blue ruler gives us calculations that are uncertain plus or minus 10, thus we can only report an answer that is rounded in the tens place, which just so happens to coincide with 1 sig fig!
The pink ruler is uncertain plus or minus 1, thus rounded to the 1s place; 2 sig figs!
The gold ruler is uncertain plus or minus 0.1, thus rounded to the tenths place; 3 sig figs!
I think it is really cool how nicely the data comes out for students to “see” significant figures really work out. In all actuality I not huge on make significant figures a huge issue as the year goes on, but I tell students, you better never ask me: “Where do I round?” That is one of the biggest pet peeves I have and when the do I’m going to tell them to look at sig figs.
WOW! That is a lot of information in one post. Please use it for your benefit, and as always, if you have any questions or comments please leave them below.
My journey towards Standards Based Grading started about a year ago (Fall 2011). It just so happens that is when I discovered the Physics Education Blog world. As I have stated in previous posts I give a lot of credit to Frank Noschese and Kelly O’Shea for many things I’ve picked up in the last year. In terms of SBG I give these two ALL the credit! I started reading their blog posts and ideas about what SBG is, how it works, and most importantly how to implement it.
2011-12 School Year
By about November last year I was convinced. This is the way I needed to go. The problem was of course changing “in-year.” However, I am lucky because I just so happen to teach a Physics 2 class which is only 2nd semester. My roster for this class was entirely seniors. So I decided to experiment. I presented the grading system to my 13 students as just that, and experiment. My principal supported my idea without needing much convincing. He just warned that I had a well documented plan to have on file. Their wasn’t really any initial backlash from students or parents, so I considered that a victory.
I did run into some initial struggles, but nothing too major. Our school has really pushed student and parent involvement through monitoring grades online, so when I didn’t have a good way for that to happen I had some issues. I ended up printing paper copies for each student ever couple of weeks. I used ActiveGrade from the beginning to monitor and track students progress for myself, but I never explored it enough to figure out all the details (like how to allow students to login). This is something that I have since resolved.
The other problem I had was creating well worded and good standards for units on Light and Waves. I found plenty of good examples for mechanics, but not these. I ended up relying mostly on the “Unit Goals” from the Modeling curriculum. I did this in-semester rather than planning ahead, and that proved to be a challenge. This will be much better this year, as I have my goals written going in.
Overall, my 13 seniors liked the idea of NO HOMEWORK and a weekly quiz for me to see where they were at. They realized the quizzes were low pressure, but still worked to do well and get mastery scores. I didn’t do official “reassessment requests” each week, but a couple of time during the semester I gave the class larger assessments, where all the problems were optional. Students opted to complete only the questions that were relevant to the goals they hadn’t mastered yet. I also did a reassessment assignment that included students video taping themselves working through a problem. Only a few took me up on this offer, but those that did did a nice job of explaining what they knew. I was able to tell if the truly “get it” or exactly where their conceptual breakdown occurred.
By the end of the semester students saw my grading system in a positive light, and I never had to defend it once to an enraged parent!
2012-13 School Year
This fall I have expanded my use of SBG to my Physics 1 class. This class is a year long and consists entirely of Modeling Mechanics. A lot of work has been done by other already to establish a system and standards for the Modeling Mechanics material, so naturally I relied heavily on that. Below I have links to my Student/Parent Handout as well as my Goals for each mechanics unit.
If all goes well this school year I am planning to make the total change over to SBG next year, expanding to Chemistry as well. I plan to continue to post idea, questions, and thoughts as they come up this year.
2013-14 School Year
I have again expanded my use of SBG to my Chemistry 1 classes in addition to Physics 1 and 2. I’m really excited about using SBG in chemistry this year as well. I saw how much it helped and focused my physics students last year, so to see that extend to chemistry will be good.
The one big change I’ve made in my system is that I’m going to a 3 point scale for feedback purposes as opposed to using a 2 point scale. The scale is defined as:
3 (Green) = Mastery has been demonstrated
2 (Yellow) = Developing Mastery – This indicates you are missing a minor piece of conceptual understanding, and/or that you have made a minor error in your reasoning process.
1 (Red) = Minimal Mastery – This indicated you are missing a major piece of conceptual understanding and/or you have made a major error in your reasoning process.
0 (Black) = No Data/Attempt
I’m going to use the colors on students quizzes and other assessments to try to get away from the “points-system” altogether. The point values will simply be for ease in entering scores into ActiveGrade. Although the scale changes students will still need to reach the “green” level for me to count the goal as mastered. The yellow and red levels will better help me provide feedback for my students. Giving them a more quantitative measurement of if they are close or far away from mastering the goal. Last year I used the Yes/No scale and No was everything from minor mistakes or thinking to complete lack of understanding. I wanted a better way to help students know exactly where they stand. We’ll see how it goes.
I’m also attaching my revised document explaining Learning Goals Based Grading to my students and parents, and my Goals for Chemistry 1.
Last week was our first week with students for the school year. For the first time (I think ever) I’m actually quite pleased with how my classes went. This post will outline my week in Physics I class.
Physics I is class that consists of Juniors and Seniors. All have taken Science 9 (mostly physical, but other as well) and 10th grade biology, some were in Chemistry last year but not all. Mathematically the range is from Algebra 2 to Trigonometry to Pre-Calculus.
This year I’m trying Unit packets (i.e. Kelly O’Shea), so on Day 1 I handed out my Unit 0 Packet. More on Unit 0 later. Using a packet will free students from individual Lab Notebooks and hopefully guide them to focus on lab content rather than organization. The strategy allowed me to by pass all the Lab Notebook setup stuff I’ve done in the past. So I was able to just get started.
I began with a circle drawn on the board. My first question was, “How could you describe this shape, WITHOUT using the word circle.” Things such as ’round,’ ‘curved,’ ‘360 degrees,’ ‘all points equidistant from the center,’ were stated. Good enough.
Since I introduced this lab as and exercise in measuring I next ask the students what could we measure about the circle. The usual things were brought up: radius, diameter, circumference, area, and maybe something else. Next I said we needed to narrow our list down to the two easiest things to measure. We agreed upon circumference and diameter. I have a classroom set of 10 meter tape measures, so from there I let them go.
I made sure to emphasize that this lab was a MEASUREMENT lab, because a few students always try to get away with calculating circumference. One thing I did not mention was whether to measure in inches or centimeters. I got about a half and half return. I set students free to find circles around the school building, with the goal of measuring between 10 and 12. This takes about 30 minutes.
The next day the students returned to class with all of their measurements. From there it is time to graph. In the past I’ve gone directly to LoggerPro, but this year I decided it was important to at least draw a couple of graphs by hand. I gave them the following guidelines:
One your Graphs be sure to:
- Use Pencil
- Label your axes with symbols and units
- Give the graph a title (“[vertical axis variable] vs. [horizontal axis variable]”)
- If the data is linear, draw a Linear Fit line (don’t connect the dots)
- Find the slope of the line using points on the line (not data points)
- Write the equation of the line (EOL) using the variables from your axes (not “x” and “y”); make sure the slope and intercept have the correct units attached to the numbers.
- Put units on numbers, but never on variables
I did NOT tell them which axis which variable need to be on. I again got about a half and half return, which is good for the whtieboard discussion. I did have to do some “teacher talk” regarding the Linear Fit line and the EOL. Since these are things that we will be doing ALL THE TIME I feel it was important to spend a few extra minutes to introduce common terminology and expectations. Hopefully it makes my life easier in the future.
Once graphs are drawn by hand on paper each group transfers their graph to a whiteboard. It doesn’t need to be a perfect graph, but something that shows approximate locations of data points, and most importantly the Linear Fit line and the EOL.
The final piece to the puzzle is the whiteboard discussion. We take our time presenting and discussing things such as methods of measurement, variety of sizes measured, why they decided to put C and D on the axis they did, how they calculated slope, etc. We then compared all groups graphs to each other.
The first thing that was noticed by the students was that graphs that were C vs. D were different than D vs. C. GOOD! Then they realized that the graphs that were done the same all had slopes that were very close to each other.
Me: INTERESTING, why would that be?
Students: Because we all measured circles.
M: Oh, ok, so what does this slope mean then (looking at the C vs. D graph)?
S: Well they are all around 3.
M: Exactly 3?
S: No, just a bit more.
M: Who had pie? I like pie.
S: No the slope is pi.
M: Cool, what about this one? (D vs. C graph)
S: Inverse of pi
M: What does that mean?
S: 1 over pi
S: The variables are graphed on the opposite axes.
Ok, you get the idea, but more importantly SO DID MY STUDENTS!
Based on all of this discussion we are now able to write and mathematical model for circles. From the C vs. D graph we get C = πD. From the D vs. C graph we obtain D = (1/π)C. Someone usually notices that these models are one in the same. This is awesome, because most students realize they have seen these equations before in some form or another, but never had the experience of knowing where they come from. Thus I give them one of my favorite sayings: “Equations come from experiments NOT textbooks!”
The very last thing I added this year was a quality addition. I took time the next day to do a summary of how models were used in this lab. On the whiteboard I created a summary that looks like this:
The final thing I wanted to do was come up with a definition for the term Model. With a little guidance both of my classes agreed on the fact that a MODEL IS A REPRESENTATION. I can now refer to this simple definition anytime students wonder what the heck I’m talking about when I call and equation a model. It simply represents the situation in a mathematical form.
I absolutely love the way this lab introduces my students to just about everything we are going to do in physics this year. Defiantly worth the 3+ days to complete.
WOW! How can something as simple as measuring circles turn into this ridiculously long post?