## Unit 2: Constant Acceleration Particle Model

This second unit on the CAPM will proceed along the traditional modeling framework. I expect it to take approximately two and a half weeks. It will begin with ball rolling (or cart sliding) down and incline plane and whiteboard meetings to analyze the results.

From there they will proceed through the modeling materials for the Constant Velocity Particle Model as provided by the Modeling Materials. The first worksheet allows them to analyze additional data sets similar to what the saw in the lab. The second worksheet has the student create motion maps, position-time, velocity-time, and acceleration-time graphs for more complicated ramp systems. Worksheet 3 focuses on analyzing position-time and velocity-time graphs. Worksheet 4 has the student solve quantitative problems. We end with additional problems for review.

The students goals for this unit are:

SWBAT

1. create and interpret graphical and mathematical representations of objects moving with constant acceleration.
2. can correctly differentiate between acceleration and velocity.
3. correctly interpret the meaning of the sign of acceleration.
4. solve kinematic problems involving constant acceleration.

## Unit 1: Constant Velocity Particle Model

This introductory unit on the CVPM will proceed along the traditional modeling framework with only a few additions. I expect it to take approximately three weeks. It will begin with the Buggy Lab and whiteboard meetings to analyze the results. The only change from the traditional progression will be to first complete the “Graphing Practice” worksheet from the Scientific Methods unit.

From there they will proceed through the modeling materials for the Constant Velocity Particle Model as provided by the Modeling Materials. Thus the new worksheet 2 will be a worksheet that focuses on the students converting between the position-time graphs, motion maps, and verbal descriptions. Worksheet 3 will then add velocity-time graphs to the mix. Worksheet 4 brings back data analysis and converting to the other representations. Worksheet 5 does the same, but for slightly more difficult situations. We end with additional problems for review.

For those using Standards Based Grading, the first draft of may standards is as follows:

Students will be able to (SWBAT):

1. design an experiment that properly controls variables
2. report measurements and calculations with proper precision
3. develop a mental model that correctly explains and predicts an event
4. algebraically solve an equation for a given variable.
5. create a scatter plot of independent and dependent data points
6. linearize data points
7. create a mathematical model of a graph.
8. create and interpret graphical and mathematical representations of objects moving with constant velocity.
9. distinguish between position, distance and displacement.
10. solve problems involving average speed or average velocity.

I’m fully aware that this is a long list of standards, and quite possibly too many standards. Any feedback on whether or not the list should be adjusted (and how) would be greatly appreciated.

## AP Physics 2 Storyline

As I prepare for the transition to the AP 2 course, here is the story-line of how  I’m planning to teach my AP 2 students next year. Before I get into the details, I do plan to use Modeling Instruction throughout the course. If you haven’t had the chance to take a workshop, do yourself a favor and find one. Also, I plan to make future posts providing more detail for each unit.

For those that have drilled deep into the materials provided by the Modeling Community, you may have found the resources provided for topics such as fluids and ideal gas law. Within those materials, there is a recommendation to use computer programming to bridge the gap between systems with only a few particles (read: AP1 events) to systems with many, many particles (read: fluids and/or thermodynamics). With that in mind, I plan to begin the year with a unit on Computer Modeling. I hope to accomplish two things: 1) Review some of the major concepts from AP1, and AP2) Prepare the students so they can see how analysis of fluids, the Ideal Gas Law/Kinetic Molecular Theory all come out of the models we build in AP1.

From there, we move to a unit on Ideal Gases, which I call the Ideal System of Particles Model (ISPM). Within this model we will recreate some of the various classic gas experiments (Boyle’s, Charles’, etc.) to build a model for monatonic ideal gases. We will connect what we see in the lab, with what our computer models predict. We will also begin to look at what happens to that gas when changes occur such as a compression or an expansion. In so doing, we will enhance our model so that it can predict what happens to the energy within our gas with those various changes (read: thermodynamics).

After building a model for gases, we move on to a unit on fluids which I’ll call the System Flow Model (SFM). Again, I plan to use the modeling materials provided. For those that haven’t seen them, they in essence begin by looking at what is happen to a small volume of water. In so doing, we build the continuity equation and the energy density equation (Bernoulli’s Equation). We also look at the pressure at different depths, and how those with effect that small volume (buoyancy).

In unit four, we begin the a second major concept of the year, electrical interactions. We again will make use of the 4 units developed by the modeling community. First up for this concept, a model for an Electrically Charged Particle, which I will call the Charged Particle Interaction Model (CPIM). We build parallels to the other non-contact force studied in AP1, namely gravity. We develop a field equation and a universal equation (Coulomb’s Law), just as we did with gravity.

In unit five, we build upon that model to describe the energy changes that can occur, what I call the Electrical Energy Transfer Model (EETM). After quickly developing a model for the energy storage in electrical fields, we create a short-hand way of tracking energy changes by looking only at the product of the field with the distance through which it moved (electric potential).

In unit six, we now develop a model for the movement of charged particles through circuits, what I call the Charge Flow Model (CFM).  We begin by tying this model back to the third unit on flowing particles. Along the way, we also develop Ohm’s Law, and Kirchhoff’s Laws. We also  develop a means to predict the power dissipated by a resistor.

In unit seven, we begin by looking at a weird side effect of moving charges, namely, their interaction with other moving charged particles, the Magnetic Interaction Particle Model (MIPM). We show how this force a different interaction than the electric force, but also show how they are both based on the same fundamental quantity of charge. Along the way we build up a third type of force field, and look at the quantities that effect it and interact with it.

In unit eight, we begin our third major topic of the year, the study of light. In this unit we build a Particle Model of Light (PLM) to describe reflection of light. We look at both smooth and rough surfaces. Also study flat and curved surfaces.

In unit nine, we see the limitation of a particle model of light in understanding how lenses, diffraction gratings, and thin films. In the process we develop a new Wave Model of Light (WML). Along the way we develop a set of equations: one that relates the focal distance, image distance, and object distance; and a second that related the heights of the object and image with the distances of the object and image. We also develop ways of understanding total internal reflection, double slit or diffraction gratings, and the effects of thin films.

In unit 10, we encounter some events in which the wave model breaks down: photoelectric effect, atomic emission/adsorption of light. In the process we build a new hybrid “Photon” or “Quantum” Model (QM). By no means are we building the actual Quantum Mechanical Model through things like the Schrodinger’s Equation, but we are building the concept of photons and discrete energy levels within an atom which are further along than just the Bohr’s Model.

In the final unit, we will again do a mild “hand waving” to try to take our “Quantum” model and use it to explain radioactive events. Along the way we will develop our “Standard” Model (SM). Again, not the actual Standard Model developed of the last 5o years, but a rudimentary look into particle physics to study nuclear decays, Compton Scattering, and a very cursory look at the Strong and Weak Nuclear Forces.

As you can see, if you’ve made it this far, this course is not as completely developed at this point. I’ve taught some aspects of this. I plan to make use of as much of the advanced modeling materials as I can, but I’m guessing I’ll be creating some of the materials as I go. To end the year, I plan to have students do a second Video Project in which they must try to analyze videos using models from these second year  models to begin reviewing and getting ready for the AP2 exam.

## AP Physics 1 Storyline

As I prepare for the transition to the AP 1 course, I’ve taken this school year (2013-2014) to begin trying some things out. Based on what I’ve tried, here is the storyline I’m going to use with my AP 1 students next year. Before I get into the details, I do plan to use Modeling Instruction throughout the course. If you haven’t had the chance to take a workshop, do yourself a favor and find one. Also, I plan to make future posts providing more detail for each unit.

We begin the year jumping right into the Constant Velocity Particle Model (CVPM). The students at my school come out of chemistry, and for the most part have decent skills when it comes to doing labs. Although we don’t use modeling in our other science classes, they have a majority of the basic skills. So I save a little time by skipping the Scientific Methods Unit.

Our second unit, then progresses to the Constant Acceleration Particle Model (CAPM). As I mentioned, I plan to give more detail later, but for those familiar with the materials provided, I’m not doing that much different from those documents.

The third unit is where I make my first big adjustment from the traditional modeling curriculum. After reading numerous posts from some of the bloggers I admire the most (read Momentum is King, Kelly O’Shea’s blog, and more recently Mazur’s Physics Textbook), I decided to try out teaching momentum before Newton’s Laws. During this third unit, Momentum Transfer Model (MTM), we focus on interaction diagrams and the swapping of momentum as the mechanism of physical interactions. We stress the choosing of a system, and that momentum swaps within the system, or swaps out of the system as an impulse. In the end, we are building the concept of Newton’s Third Law. In addition to what I call Interaction Diagrams (others call system schema), we also introduce the Momentum Diagrams (IF Charts). We hold off on discussing collsions in great detail until after impulses are further studied with unit 5.

The fourth unit, Balanced Forces Particle Model (BFPM), then begins to bring in the concept of forces as the rate of swapping momentum. Here we introduce the major contact forces: normal, tension, friction (name not equation) and the non-contact gravitational force. We also begin using force diagrams to determine if the forces are balanced or not. We stress one way of understanding Newton’s 1st Law as “Balanced Forces -> no acceleration, Unbalanced Forces -> acceleration.”

In the fifth unit, Unbalanced Forces Particle Model (UFPM), we now get into Newton’s 2nd Law in two ways. One the classic:

$a=\frac{F_{net}}{m}$

And two, we build the parallel between kinematics and Newton’s Laws. In kinematics, the slope of a position-time graph gives velocity-time, the slope of velocity-time gives the acceleration-time. Finding the area allows us to go the other way. The same is then true of momentum and forces. The slope of a momentum-time graph gives Force vs. time, while the area under a Force vs. time graph give the change in momentum (impulse). For those students going on to calculus based physics, this helps lay the ground work. For the rest, it shows a nice connection between these different models. With this new information, we can now add a Force vs. time graph into the momentum graphs and make “IFF” graphs. Other features of the unit are the building of the equation for friction in relation to the normal force, and the independence of components by looking at 2D projectile motion problems.

We then wrap up the first semester with our 6th unit, Energy Transfer Model (ETM). After building the concept of energy storage through Energy Diagrams (LOL Diagrams). We discover that Energy storage is a “cheat” to help us solve more complex problems, since it is a second conserved quantity. We come back to collisions and find that, in elastic collisions, we can now build a second conservation equation: 1. momentum (IF charts) and, 2. energy (LOL diagrams).

As a review of the first semester, the students will then have to build a paper car that will hold an egg inside. They will have two tests: 1) a speed test to see who has the fastest car and, 2) a crash test to see who has the safest car. During the design, they must make use of all the models we have built this semester.

To start the second semester, we begin studying the Central Force Particle Model (CFPM), or what most people would call uniform circular motion. In this unit we also add in building the concepts of Newton’s Universal Gravitation and satellite motion.

In unit 8 we now move onto full rotational motion, the Rotating Bodies Model (RBM).  To be honest, I may try to split this up into two units, as it’s got a lot of stuff going on here. In short, within this unit we retrace units 1-6, but in the rotating or polar frame of reference. We begin with rotational kinematics ($\theta$  vs. t, $\omega$  vs. t, and $\alpha$ vs. t). Afterwords, we build in dynamics with angular momentum, torque, and rotational energy storage.

In unit 9, we move on to harmonic motion with the Oscillating Particle Model (OPM). Overall, we stay pretty true to the model materials here. We start with looking at a bouncing mass hanging by a spring. We later bring in pendulum motion.

In unit 10, we then move on to the Mechanical Wave Model (MWM) in which we build a mental model of coupled oscillators. From what I can tell AP-1 only focuses on one dimensional waves, so we looked at boundary effects: reflection (open/fixed) and refraction. We also build in wave superposition. We begin looking at sound waves and doppler shifts as further examples of waves. At least so far, I don’t build in diffraction through “narrow” slits or 2D interference patterns.

In the last unit, we then look at circuits in what I call the Charge Flow Model (CFM). We begin by looking at sticky tape activities to introduce the electric force and electric energy. During that discussion we bring in the concept of gravitational potential ($gh$), to help understand the concept of electric potential ($V$). From there, we have them build simple circuits with lightbulbs, then move onto simple circuits with fixed resistors while measuring the current (flowrate of charge). We eventually get to adding multiple resistors in series and in parallel and try to create a model that explains how the resistors add in these two different ways.

To review the entire year, we then do a video analysis project in which the students must analyze movie, tv, or internet videos and determine how feasible those scenes actually are. Here is an example from which I got my idea:

## A Message to a Young Man

On October 25th, 2013, I was honored as the University of Notre Dame Alumni Association National Teacher of the Year. This was my way of saying thanks to everyone who helped me reach this milestone:

One of my first memories of Notre Dame was visiting my sister for Sophomore Sibs weekend. My sister is four years older than me, so we were both sophomores, her at ND, me in high school. While visiting, we went to Mass in my sister’s dorm. The overall message that the priest talked about in his homily was that we are all called to do something by God. Moreover, the Holy Spirit will act through friends and strangers to let you know what you’re called to do. If you’ll give me just a few moments, I’d like to tell you how the Holy Spirit has interceded to guide me through my life.

During a visit my junior year, my sister was taking my brother and I to a party in Grace Hall. What I remember most was on the walk to the dorm, we could hear music playing in various dorms nearby. All of a sudden, one of the parties started playing my favorite song growing up, Kermit the Frog’s “Rainbow Connection.” To me, that was the sign that ND is where I need to go to college.

Fast forward to the summer between my sophomore and junior years at ND. While working at a pizzeria in my home town, a repairman came and talked to me about how great it is to be a teacher. He went on and on about how we need good, intelligent teachers to shape the next generation of citizens. I honestly didn’t think much of it at the time; merely that this crazy stranger wouldn’t shut up about teaching for the 45 minutes he was working on the broken fridge.

During my junior year, during a class called Transport Phenomena, a two semester course on how fluids move through pipes, the class hit a sticking point. The professor, in his Italian accent, was going on and on about several simultaneous equations that describe a particular situation. Without going into the gory details, this final point was that the graph of all of the equations had a minimum in it. He proudly stated, “That is what engineers live for!” I honestly didn’t see the greatness of this, and this was the moment I started to think maybe engineering wasn’t for me.

Amazingly enough, as I was walking in my dorm later that day, a flier for the Alliance for Catholic Education popped up. I remembered my sister talking about ACE and started thinking about looking into it. I also remembered that crazy repairman I and thought maybe I should think about teaching.

Amazingly enough, one of my roommates got a new girlfriend. As we started getting to know her, she told us that her cousin was the director of the ACE program and that he was always asking her to bring friends over to his house to try to convince them to apply. After doing just that a few weeks later, I was excited to apply. I’m grateful to say that I was accepted, and soon learned that I would be heading to Jacksonville FL and teaching chemistry at Bishop Kenny High School. Throughout my experience in the ACE program, I encountered the best teachers I ever had. They still inspire me to this day.

During my first year at BK, the volleyball coaches, one of whom was my housemate, asked for some help with the volleyball team. I was already helping with the soccer team, but after some arm twisting, I was convinced to help that team too. A few years later, a few of the volleyball team moms found out I was single, and took it upon themselves to find me a significant other. For the most part I humored them, and just went about my life. At the end of that season, one of those moms was very adamant that she knew “the one.”

It turns out, she was right. Stephanie and I hit it off right away, and 10 months later I was lucky enough to be engaged, and a year after that, I was married to the most amazing woman I’ve ever met. That same year I was to be married, my principal asked me if I would be interested in taking over the physics program at BK. Part of my fear of teaching physics, which I’ve never told anyone, was that I would be teaching the same subject as my favorite ACE teacher, and I wasn’t sure if I could live up to his standards. However, after talking to my department chair about it, I accepted.

During our discussion, she recommended I look into a new lab based curriculum developed at MIT. Since I was the only physics teacher, I only had to convince my admin to adopted her recommendation. Not an impossible process, just a necessary step BK has to ensure our students receive a good education.

A year or so later, a few students asked me about adding an AP physics class. While discussing the possibility with one of the academic deans, she recommended I look into what other teachers do for their AP classes. In my searches, I stumbled on a few blogs talking about Modeling Instruction.

At about the same time, we had a workshop day where teachers shared some of their best practices. One of those mini-workshops was on how that teacher uses twitter to find lesson plan ideas. With his help, and a little searching, I found a great group of physics teachers that blew me away with what they were doing in their classes. For the first time, I had other physics teachers to bounce ideas off of and even have weekly meetings online. Many were also singing the praises of Modeling, so I decided to look into going to a workshop.

While at the workshop, not only was I fully convinced of the power of teaching through Modeling, I also had a fellow participant share a news story about what would become one if my favorite books, “The Last Lecture” about Randy Pauch celebrating his life as he was dying of cancer. Those three weeks proved to be a very transformational time for me.

When I returned to school the next year, I set about trying to convince my admin to switch to that way of teaching my classes. Just about the time I received their ok, my wife and I found out we were going to be parents. As we were to begin preplanning that next year, Dillon, you overachieving son of mine, decided to come early. So instead of me starting the year as planned, I had a sub with no experience teaching physics, trying to introduce my students to this new way of learning. After returning to the classroom, I set about trying to recover from that crazy start while balancing the joys of fatherhood.

For the most part, that brings us to this award I’m being honored with tonight. I think it’s important for you to know all these steps throughout my life to share how I think the Holy Spirit has guided me to this amazing award. To me, humility isn’t hiding your accomplishments, but rather celebrating them as gifts God has given you. I can’t begin to thank all the people that have helped me get to this point, but what I can say is this: Dillon, when you’re old enough to read this letter, I can only hope that you realize that God has a plan for you too. Have the courage to be open to the amazing people that enter your life, so they, with the help of the Holy Spirit, can help guide you along your path. Most importantly, take time to enjoy the steps along the way, as I’m sure God has a plan for you to experience your own amazing ride.

## Momentum is King!

One idea that has been gnawing away at me is Andy Rundquist’s awesome notion that, “Momentum is King.” One quick link to see some of his ideas in greater detail is here. My issue is how exactly to make that stick in a modeling class, or stated another way, how does the storyline for mechanics change? The main issue I’m going back and forth over is if you teach momentum before forces, when and how exactly do you introduce the concept/term force?

Here are my thoughts so far:

I’m planning to progress though Constant Velocity Particle Model and Constant Acceleration Model as set up by the modeling content. (As a brief aside, if your not familiar with Kelly O’Sheas blog on modeling, go there ASAP!) From there, I’m planning to use a modified version of the Momentum Transfer Unit (Impulsive Force Model). After that is where I’m stuck, but here’s what I’m roughly thinking:

1) Jump to Balanced Forces, and don’t make the explicit connection between momentum transfer and forces. Basically begin creating a second parallel concept. Progress through the modeling materials for balanced forces (Free Particle Model is the official name) as designed and wait until unbalanced forces (Constant Force Model) to make the connection.

2) Recast the balanced forces model as multiple transfers model and remove the discussion of forces. Continue to reinforce the idea of momentum swaps, but now discuss the fact that the swaps can balance out. Focus on the system schema and stress that if there is not net momentum swap, the momentum must stay constant. Instead of hammering home “no net force, no acceleration; net force, acceleration” recast it through momentum. Then introduce the concept of force in the next unit, Unbalanced Forces Particle Model (which may or may not need/get a new name)

3) Jump to Unbalanced forces first and show the connection between impulse and Force. Begin by showing that a force is the rate of momentum change and that the area of a F vs t graph.  You could build the IF bar graphs in the momentum unit into IFF bar graphs. In the process focus on how each object has the same momentum swap, but different accelerations; that the forces are the same, but the effects may be different. (I’m looking at you bug on windshield problems!). Once complete, go to balanced forces and show that you can have multiple, simultaneous interactions, which can balance out. Now bring in things like system schemas and force diagrams.

My quick \$0.02:

1) If I’m making the effort to put momentum first, it doesn’t seem right to then ignore it when introducing the concept of forces.

2) Seems to flow a little better than (1), but when do you build in force diagrams? Adding them in the unbalanced forces unit make that unit really big, but I’m not sure I would feel right calling them momentum swap diagrams (especially if no other physicists do so).

3) Part of me is really drawn to this storyline, but in the end, that means I’m teaching Newton’s Law in the reverse order (3rd -> 2nd -> 1st). There is probably a good reason why no textbook or the modeling materials do it that way.

I’d love to hear feedback, if you’ve got any.

## Modeling the NGSS Physics Course

As this year draws to a conclusion, and I look ahead to the coming changes in physics education (yes I’m looking at you college board and NGSS), I’m beginning to look ahead to how I might change what I’ve done to meet these new standards. Please note, I’ve only taught with Modeling Instruction for one year now, but maybe my fresh eyes will be beneficial in bridging the between the traditional modeling curriculum and what will be needed in the future courses.

Over the next few weeks, I’m hoping to add more posts to fill in more details, but here’s what I’m thinking so far the what I can put together for a physics class (assuming there is still such a thing) from the NGSS:

### Unit I: Scientific Methods/Intro to Modeling/Constant Velocity Particle Model

Paradigm Lab: Buggy Lab

Objective: to determine the graphical and mathematical relationship between position and time for a toy buggy.

### Unit II: Constant Acceleration Particle Model

Paradigm Lab: Cart on incline plane

Objective: to determine the graphical and mathematical relationship between position and time for a cart moving down a ramp.

Here’s where I possible get a little crazy. In an effort to break up two big projects I think I’ll need to do for NGSS, I’m splitting momentum from energy. The two big projects are an Egg Car project and a Rude Goldberg project. I’m thinking by doing this, I’ll have 1 project each quarter instead of two very close together. I’m not definite about this, but figured I’d throw it out there and see if I can get any feedback positive or negative from more experienced modelers.

### Unit III: Momentum Transfer Model

Paradigm Lab: Cart Explosion

Objective: to determine the graphical and mathematical relationship between the ratio of velocities to the ratio of masses when two carts explode apart.

### Unit IV: Balanced Forces Particle Model                         (w/ universal gravitation)

Activities: bowling ball games, Universal Gravity Simulation

Paradigm Lab: Gravitational Field Lab

Objective: to determine the graphical and mathematical relationship between mass of an object and its weight.

### Unit V: Unbalanced Forces Particle Model

Activity: Ball toss

Paradigm Lab: Modified Atwood Machine

Objective: to determine the graphical and mathematical relationship between Force, mass, and acceleration

### Unit VI: Energy Transfer Model

Paradigm Lab: Cart “Launch”

Objective: to determine the graphical and mathematical relationship between compression of a spring, maximum velocity, and maximum height of a cart launched up an inclined plane.

### Unit VII: Oscillating Particle Model

Paradigm Lab: Bouncing mass on spring

Objective: to determine the graphical and mathematical relationship between amplitude, mass, and spring constant with period.

### Unit VIII: Mechanical Wave Model

Paradigm Lab: Snakey Lab

Objective: to determine the graphical and mathematical relationship between pulse length, pulse amplitude, and tension with wavespeed in a snakey spring.

Activities: water tray waves, speaker interference

### Unit IX: Electrically Charge Particle Model

Activities: Sticky Tape

Paradigm Lab: Balloon Lab

Objective: to determine the graphical and mathematical relationship between charge, distance, and electric force

### Unit X: Magnetic Particle Model

Paradigm Lab: Field cause by a current carrying wire

Objective: to determine the graphical and mathematical relationship between current, distance from the wire, and magnetic field for a wire carrying a direct current

Activities: Mapping the magnetic field of a bar magnet