Tag Archives: problem solving

Reassessment Experiment

CV.3 (A) I can solve problems involving average speed and average velocity.

That learning goal is the thorn in the sides of many of my students right now.

They took their midterm exam last week and many missed the question associated with that goal. The (A) denotes that it is a core goal.  Which means that, based on this grading scale:

their quarter grade cannot go above 69 until all core goals are met.

I handed the exams back in class yesterday.  Naturally, many students wanted to reassess on the spot. Since I have an archive of quizzes from previous years, it was easy for me to print out a bunch and let them have at it.

And most of them missed it again on the reassessment. No surprise there, really. Without any remediation, it was just another shot in the dark.

So as an experiment, I posted the following to our class’s Edmodo page today:

Does CV.3 have you Down? If so, do the following by Monday:

(1) Explain, in detail, the difference between average speed and average velocity. Simply writing the two equations won’t be sufficient.

(2) Describe in detail a situation where an object’s average speed and its average velocity have the same value.

(3) Describe in detail a situation where an object’s average speed and its average velocity have different values.

(4) Create your own physics problem involving average speed and average velocity that is NOT a simple “plug-and-chug” type problem. (For example, “A car travels 50 miles north in 2 hours. What is its average speed and velocity?” is NOT acceptable.) Write up both the problem and a complete solution. Feel free to use pictures, graphs (even video) as part of your problem. Check out this link for non-“plug-and-chug” problem types: http://tycphysics.org/TIPERs/tipersdefn.htm

(5) Cite all resources (classmates, parents, books, web pages, videos, etc.) you used. (It doesn’t have to be in proper MLA format. A simple list is fine.)

Submit you work HERE on Edmodo. You should upload a file (word, PDF, etc.). The work must be YOUR OWN. I can tell when “collaboration” is really copying.

I hope this provides both the necessary remediation and a unique opportunity to reassess beyond simple quiz questions. I am really excited to see what kind of problems they write. I have done student problem writing in the past, but was never pleased with the results. Perhaps by requiring them to create a TIPER problem, we can push past equation memorization and towards understanding.

This scenario has also raised a few more unanswered questions: Why do I have this goal in my course in the first place? Why do my students keep missing it even though all quizzes (and the midterm) are open notebook? And if so many students are missing it, is it really a “core” goal?


Falling Rolls

Rotational motion is my favorite topic in AP Physics C: Mechanics. Here’s one reason why:
[taken from Why toast lands jelly-side down: zen and the art of physics demonstrations by Robert Ehrlich]

We did this as a final problem in our study of rotational energy. After working through a series of long equations from energy and kinematics, we discovered the final answer is surprisingly elegant:

UPDATE 12/27/2010: Thanks to Dan Fullerton’s class for catching our error. They analyzed the problem using a torque approach and came up with:

I double-checked our energy approach and now get the same answer as Dan. We must have made an algebra mistake somewhere. This is why I love physics — there is more than one way to solve a problem!

H is the drop height of the free-falling roll, h is the drop height of the unrolling roll, r and R are the inner and outer radii of the unrolling roll.

Using large rolls of paper towels, we tested our prediction. Here’s the result, captured in slow motion:

(Despite our mistake, the demo still works. From the video, it seems the students did not release the rolls simultaneously. Perhaps this compensated for our algebra error.)

They were just a tad excited when it worked. And yes, that class is all boys, much to my dismay.

What’s your favorite activity or demo for rotational motion?

Speeding Problem?

The Problem:
New playing fields are going to be built on the lot across the street from our school. Unfortunately, people will need to cross Route 121 (a 2-lane highway) to get to those fields.  Currently, the proposed pedestrian crossing is a crosswalk with a flashing yellow light. Is there a speeding problem on Route 121? Do you think the proposed crossing is adequate?

The Solution:
We are videoing the traffic in front of the school with Flip cams and analyzing the videos in LoggerPro. Luckily, the fence posts are 10 feet apart and are perfect for setting the scale in the analysis!

(Feed readers may need to click through to view embedded video.)

If the school had put a police officer or a “Your Speed Is…” sign in front of the school, people would slow down, and the data would not be representative of real traffic. We hope that by recording traffic from a distance, drivers will be more likely to maintain their true speed. We also hope to collect lots of data during different times of the day (different classes) to help in our analysis.

This simple activity serves as an introduction to video analysis, so students will have another data collection and analysis tool at their disposal for future labs of their own design.

Fortune Fish

I’ve used these as the first lab of the year, like this teacher:

Reblogged from my post at wcydwt-science | http://wcydwt.posterous.com/

How Long is the Roll?

Note: Some readers may need to click through to view the embedded video.

My conceptual physics class was chugging along just fine the other day. Then a kid asked for some paper towel. When I took out a giant roll from under the sink, the day’s lesson took a detour which would make Dan Meyer proud.

Kid: “Whoa! How long would it be if you unrolled the whole thing?”

Me: “I don’t know…you want to find out?”

Kid: “Yeah!”

Me: “OK. But you’ll need to make a prediction first.”

How long is the giant roll?

Takin' data with a smaller roll

Class data. Groups measured different amounts of paper towel. Who will be closest to the actual roll length?

Time to unroll!

Final analysis with an attempted shot at evidence-based reasoning.

Eratosthenes 2.0

In case you missed it, fellow physics teacher John Burk blogged a post-mortem of our collaborative lesson in which our students brought Eratosthenes’s famous experiment into the 21st Century: Measuring the Earth with Skype and a Stick. The feedback from his students were overwhelmingly positive! Check it out! (And be sure to subscribe to his blog while you’re there!)

Raising the energy level of my physics classes

Measuring the earth with skype and a stick

Win? Fail? PHYSICS!: An introduction

(Note: Feed reader users may need to click through to view embedded videos.)

A simple question

Real or fake?

Physics win or physics fail?

Inspired by Rhett Allain’s physics explanations at Dot Physics, Dan Meyer’s blog series “What Can You Do With This?”, and Dan’s TEDx plea for a math curriculum makeover, I have been collecting video clips that are prime for my physics students to analyze. The website is Win? Fail? Physics!

Videos are categorized by topic to help teachers locate videos for the concepts at hand. Several videos are listed under multiple topics. For example, the World Jump Day video above can be analyzed using Newton’s laws or conservation of momentum. The videos are presented without any further questions other than “Physics win or physics fail?” Kids watch the video and have an immediate visceral reaction. Now they just need evidence to support or refute their conviction.

What are they good for?

A WFP video can be the hook for the whole unit. The analysis will take several days as the students explore and experiment to develop an appropriate model. At the end of the unit, they return to the video to answer the question “Physics win or physics fail?” For example, my projectile motion unit starts and ends with the Kobe Bryant video (above), which I’ll outline in a future post.

A WFP video can also replace a textbook problem and the analysis can be done in a class period. Here’s a parallel end-of-chapter “problem” for the World Jump Day video:

How fast can you set the Earth recoiling? In particular, when you jump straight up as high as you can, what is the maximum recoil speed that you give to the Earth? Let your mass be 76.0 kg and your maximum jump height be 0.250 m. Model the Earth as a perfectly solid object.

(a) Based on your maximum jump height, what must be your push-off speed?

(b) What is the recoil speed of Earth due to your jump?

(This is a WebAssign numerical version of a problem from Physics for Scientists and Engineers, 6th edition, by Serway and Jewett, where it appeared as an order-of-magnitude estimate-your-own-data problem.)

The plug-and-chug version gives students assumed values and guides students to the solution. Students lose out on important problem solving techniques as this style reduces a rich learning experience into an exercise in formula substitution.

Cognitive Weightlifting

The WFP video version strips the problem to its core: Win or Fail? Students do the cognitive weightlifting.  Working in groups, they must generate their own follow-up questions to solve and determine the knowns and unknowns. You can consider a good WFP to be a video version of a Context-Rich Problem.

Group A asks, “If every person on Earth jumped at the same time, how fast would the Earth move in the other direction?” while Group B asks, “How many people would have to jump in order to change the Earth’s orbital speed?” And in order to do solve their own questions, students will often have to make assumptions about certain values or conduct simple experiments to get those values.

Group A will need to know the mass of the Earth, the mass of a typical person, the number of people on the Earth, and a person’s typical push-off speed when jumping. A quick Google search yields the Earth’s mass and population. Group A assumes a typical person weighs 150 pounds and converts to mass in kilograms. However, they have no clue what a typical jump-off speed would be, so they decide to do an experiment to calculate it. One person jumps as high as they can, while group members measure the jump height, which they can then use to calculate the jump-off speed. Now Group A has what they need. They compute the recoil speed of Earth and compare it to Earth’s orbital speed via Google. Win or Fail?

Group B, on the other hand, looks up Earth’s orbital speed first and assumes that a 1% increase may be just enough to move the Earth slightly. They then do a similar analysis as Group A, but they compute the number of people needed to create that 1% increase and compare it to the Earth’s actual population. Win or Fail?

And, of course, there is Group C. They say gravity pulls the Earth and the people back together again anyway. Win or Fail?

Of course, the whole time I’m circulating around the room, helping groups and tossing questions back at the kids. Then we have a mini-conference where groups share their solutions on whiteboards and field questions from classmates. Finally, we reach consensus as a class. Win or Fail?

What it’s not

  • WFP is not  a demonstration.
  • WFP is not a talking-head documentary.
  • WFP is not a lecture or tutorial.

Want more?

Check out these sites for more possible WFP videos:

If you have suggestions for a WFP video to add to my online library, contact me with the URL. However, I do not have the time to take movie scenes from DVDs to upload to YouTube. Thanks!