One new change to my intro physics class this past school year was to replace the set of FBD practice problems with a card sort that would be done in groups. The card sort gives students a chance to practice FBDs with some scaffolding (especially choosing between options rather than creating everything from scratch), and it introduces a new representation that I hadn’t shown them ahead of time (force vector addition diagrams).
Please also see the credits at the end of this post for the folks who helped inspire, test, and make this set of materials.
How to Use this Card Sort
In my Balanced Forces unit, we started with a Newton’s 1st Law investigation. Then we did the stations for contact forces. I briefly introduced FBDs and system schemas (using the situations from those first two experiences). Then we launched right into this card sort.
There are 4 (or 5—I will get to that) types of cards: situation descriptions with pictures, FBDs (just arrows, nothing labeled), motion maps (qualitative), and vector addition diagrams (also just arrows, nothing labeled). Michael (see credits below) made system schema cards, which I replicated (again, nothing labeled). I used the system schema cards with my first class, but I found it worked better for my students if I didn’t give them those cards and instead instructed them to draw the system schema on the back of the situation cards.
Each group gets a set of the cards (and, if I’ve laminated them, a couple of thin markers to write on them). They need to sort the cards into groups of 4 (with one of each type). They also need to add in all of the labels (on the FBD and vector addition diagram cards).
For a follow-up at the end of the activity, each group whiteboarded one of the situations and presented to the class so they could check it against their own answers and reach a consensus. In their packet, I made pages with spaces for them to record their final answers. The blank spaces were just a side effect of the number of problems and could be used for anything they wanted (extra space for notes, a place to redo a problem if they messed it up too much in their first attempts or didn’t use pencil).
I think that doing the activity this way gave more students access to thinking about and trying these diagrams since they could debate between which of the options seemed to match their situation rather than having to create it from scratch. It circumvents the initial idea that students often have about how forces can’t be at angles (which means that with my old practice set, only some students had “aha” moments before whiteboarding and others had all wrong answers before someone else showed them a different way).
I liked the connection to the motion maps. Many students started with those. Even if they had found them difficult just a week or so before, they were now a familiar way into the problem, and they made the balanced/unbalanced forces connection much clearer and explicit.
I think the discovery of the vector addition diagrams worked pretty well. It’s easy enough to match them to the FBD you’ve chosen just based on the number and directions of the arrows even though you start out having no idea what they are for and what they mean. Then, they can start noticing some patterns about those diagrams for themselves. Helping students approach that part of the activity is probably the place for the next bit of improvement here, though.
In my Physics 10 update/upgrades, I built a new paradigm investigation for the Constant Acceleration Particle Model. The activity described here gets at the same things as my older activity, but it allows groups to do the investigation rather than the entire class together, and it gives more structure and space to the discussion. The students do more of the talking (and more of the students do talk) in this version, too.
Before this model, we have done Constant Velocity, Balanced Forces, and an introduction to Center of Mass.
In my Balanced Forces unit, students have practice thinking about and drawing qualitative velocity-time graphs when objects are speeding up and slowing down, so they have been primed for this work and discussion already.
Fan Carts and Motion Sensors
This activity starts off the unit. Students have already seen fan carts, so the “Hey, I want to show you something (relatively) cool” moment is to show them the motion detector.
We gather around a lab table. I have a student bring up their computer and set up Logger Pro. I show them the motion detector. Get everyone to be quiet enough to hear it click when we turn it on. We get to talk for a moment about what it is doing, then I show them how it makes the position-time graph. We move the cart back and forth in front of the sensor to get our bearings with how it all comes together.
I had out the packets, and they open them to the first inside page—the fan cart investigation.
At this point, they are set to do the first part of the page in groups, but it saves some time to have them talk for a minute about how to get a fan cart to slow down. At this point in the year, a lot of them still have a strong idea (whether they realize it or not) that everything starts from rest, so it isn’t very obvious to them how you could get one to be slowing down. A frequent suggestion is to “put your hand in front of it”. It only takes a moment to show them that if the cart is already moving, the fan can slow it down (depending on the direction it is facing).
Although the page only asks them to do slowing down once, since it doesn’t specify the direction, both directions will usually show up in the work among the different groups. That little bit of ambiguity adds to the discussion, and helps students focus (during the discussion) on the difference between how the velocity-time graph shows the direction of motion and how it shows speeding up versus slowing down.
The groups spread out and work through the three situations. Learning to use the motion sensors well takes a little coaching from me. As I move around to different groups, I help them identify which part of the graph shows the motion they wanted to capture and encourage them to sketch only that part on their papers.
Board Meeting and Discussion
After capturing graphs for the three situations, groups make whiteboards of the top portion of the page.
Once they have put the graphs on the boards, the class circles up for a board meeting. The first order of business is to come to an agreement on what the graphs looked like. They move to translate the bits of messiness from the real graphs into simpler shapes that show the essence of what they captured. Their goal is to come to a consensus about the 6 graphs. As they listen to questions and comments from their peers, they update their boards to show their thinking. Sometimes they look back at their computers to check a graph. It’s easy enough to quickly run one again if we are having trouble coming to agreement. Was the line straight or was it a curve? Which way did the curve go? Were you drawing the graph just for when the cart was speeding up, or did you also draw the part when your hand stopped it? It takes a few minutes to get all of the whiteboards updated, but they can handle that discussion mostly on their own.
The next phase of their discussion is centered around the questions at the bottom of the page (as well as in the top right-hand corner of the page). Their new goal is to come to a consensus about what information about an object’s motion they can learn from a velocity-time graph. In this part, they are able to lead most of the discussion themselves, but I throw questions into the mix, too. By the end, they are in agreement about how to tell the direction of motion, whether an object is speeding up or slowing down, and what the graph looks like when the object is changing directions.
The last step is to see what we can say so far about the slope of the velocity-time graph. What would it mean if the graph were steeper? That part is easier—and we come to agreement pretty quickly that a steeper graph could mean, for example, that the object is speeding up more quickly (maybe the fan is set to a higher setting). The tough part is—what does the sign of the slope mean? They talk about it a bit, but come to realize that they aren’t quite sure what it means. Not yet. I don’t let them get stuck in this discussion for too long. We set that part of the question aside as something we can investigate later. This is only page 2 of a brand new packet, after all.
Finally, I ask them if they’d like to know the name that physicists give to the slope on the velocity-time graph. We define acceleration as the slope on the velocity-time graph—a definition that will be a helpful way of thinking about acceleration for some time to come.
The next day, we follow up on our ideas about the shapes of these graphs and the meanings of the features by doing a Walk-A-Graph activity where students practice being the object for a variety of x-t and v-t graphs.
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This model-building class activity fits well with Modeling Instruction pedagogy, and it is shared under a free and open copyright. Please feel free to use, modify, share, etc—as long as you follow the Creative Commons license on this page. Let me know if you try this with your students!
One might think that this would be more challenging (or even impossible) to do since these stations need to involve objects with changing velocities (so the handy flip-up index cards wouldn’t work for checking answers). Challenge accepted (and accomplished, I think).
Since this was our 4th unit, students were already comfortable using the force and motion sensors, so these tools could easily be used at stations without much or any additional instruction.
This course is an untracked 10th grade physics class with students in different levels of math, so I limited my first set of stations to situations with only horizontal and vertical forces to keep the focus on the physics concepts and not bury the point with more complex math. By the time we were finishing the unbalanced forces unit, a few weeks later, we had already been working force problems with angles in them, too.
Descriptions of the Stations
Balanced Forces with Angles
The only balanced force station, this one has a known mass of 410 grams and instructions to pull horizontally with a spring scale so that it reads 3 N.
The numbers chosen work out to make a 3 N – 4 N – 5 N right triangle in the force vector addition diagram. I hoped that by choosing those numbers (and no set of numbers screams triangle to high school students more than 3, 4, 5) it would help reinforce the idea of adding the forces as vectors.
Fan Cart Acceleration
Students use a force sensor (a push-pull spring scale would also work) to measure Fn(air) on the cart. Then they predict the acceleration of the cart. They check their answer with a motion detector.
In these photos, I have a setup that includes materials that are (frustratingly) no longer sold by PASCO, but any fan cart setup would work for this station.
For some of these stations, including this one, I included information about the mass of the object so that I wouldn’t cause a traffic jam or use up time with each group needing to use a balance to find masses at each station.
Pushing a Box
Students push an object with a push-pull spring scale or a force sensor. They are supposed to push with a constant force and make sure the object speeds up. Then they determine the friction force that the object experienced. Finally, they check their prediction by pushing the object so it moves with a constant velocity and measuring their pushing force.
This station turned out to be the “aha!” moment station of this set of problems. It’s a bit tricky to implement, so I spent the most time hanging around this station to help various groups get going with pushing the box correctly. They need to take data a couple of times. But by the end of this one, especially with the reinforcement of the balanced forces problem to check their work (the card prompts… “Think… why?” and students took that to heart), the understanding of how to work with unbalanced forces and acceleration was practically visible in their faces.
Dropping a Sensor
For this station, students predicted the acceleration of a dropped object. We don’t do projectile motion for another couple of units, so they don’t already know the answer to this problem. The setup is very simple for this one—just an acceleration sensor (I think the one pictured here should work, though we used a WDSS when I did this in class) and an instruction to CATCH the sensor before it hits the ground. (Teamwork!)
Cart on a Ramp
Students measure the angle of the ramp and predict the acceleration. They check their prediction with a motion detector.
Although you (obviously to physics teachers) don’t need the mass to do this problem, for students who don’t yet know trigonometry and need to solve by drawing the vector addition diagram to scale with a protractor benefit a lot from knowing the mass. (It’s still possible, of course, without the mass, but it adds a level of abstraction to their work that most aren’t ready for in November.)
Two Exit Ticket Stations
The exit ticket station was useful last time, so I included two exit tickets this time around. In both problems, Fnet is not equal to any one force. The images of the pages and the editable files are included later in this post with the station cards.
Overall Logistics
Most groups were able to spend time at every (or almost every) station. Everyone did at least one of the exit tickets, and most students did both. This all happened in one 65 minute class period.
I made sure that I had more stations than groups so that I didn’t have to make each group spend the same amount of time at each station. The groups chose when to move and which station to attempt. That arrangement worked for the size and nature of my classes, but could easily be adjusted in a different situation.
Follow Up
After my Balanced Force version of this activity, it was clear from the exit tickets that students “got it” from the work that day. After this activity, with the more complex problems and the forces at angles, I wanted to make sure everyone got a second chance to see and discuss the problems and solutions, so we whiteboarded the stations during the next class.
Here are some whiteboards with their (awesome) work, excellent annotations and notes, and very important doodles.
The cost is $25 for the day and includes food. You don’t need to be a current member of AAPT or attend any other part of the summer meeting (though we encourage you to look into both—especially the HS Physics Teacher Day on Monday if you’ve never been to an AAPT meeting before). Everyone who attends the camp gets to share and learn from each other, and we even include work time at the end so that you can start turning your new ideas into action before the day is over.
In my (admittedly biased) opinion, there is no better 1 day professional development for HS physics teachers. I have learned something every year, and my students have definitely benefited from this event because of my improved teaching and classes.
Here are my blog posts about the camp from 2017, 2016, and 2015.
After my first card sort activity, I was eager to design more. Quick heads up—this card sort is VERY different from the kinematics one that I designed.
Some Inspiration
I had this tweet from Brian Frank in mind as I started to work on my revised packet for the Momentum Transfer Model.
Leaning toward trying something like this for momentum representations. Stacked graphs. This is a generic explosion. pic.twitter.com/1AzEBWnyoR
At the same, I have also been incorporating the really nice work on thinking in terms of systems and center of mass from the group of Ohio teachers (Kaar et al). Michael (one of those teachers) has the link to all of their materials (intended to be extensions to multiple units throughout the year rather than one self-contained Modeling unit) in this tweet:
As I rewrite my packets, I am (of course) customizing them for my school and the students in my classes. We have limited class meetings (3 classes per week, 8-10 weeks per trimester), untracked classes with the entire 10th grade taking physics (I am very happy about this, and it is also a factor in thinking about the design, of course), and students who have taking a full year of Modeling Chemistry in 9th grade (also yay!). We definitely do a good amount of quantitative problem solving, but there is also a strong emphasis on writing an argument, designing experiments, discourse in the classroom, and multiple representations. (In other words, this is an AP Physics 1 style and depth class, but not quite at the AP Physics 1 pace.)
For the Momentum Transfer packet, I wanted to replace worksheet-style problem solving practice using momentum bar charts with something more activity- and small-group-discussion-based. I also wanted to introduce additional representations, including a new-to-them graph—the Fnet-vs-time graph.
The Cards
Here is a gallery of the pages of cards that I made. These are meant to be cut up and mixed up before students see them. There should be 6 blank cards. The grayed-out and/or missing cards are meant to be discarded before giving the cards to students.
Here are the pages as a Google Doc so that you can edit them yourself: CARD SORT FILE LINK. Of course, please make any changes you want, modify, expand, improve, etc. (Just please don’t take credit for my ideas or my work. I hope you won’t, but it doesn’t hurt to say it!)
How to Use the Cards
Here is the idea: There are 6 “problems”. Each problem is represented in 6 different ways (verbal (written) description, momentum bar charts, momentum-vs-time graph, Fnet-vs-time graph, velocity-vs-time graph, equation). The catch is that one of the representations is missing for each problem. Since there are 6 problems and 6 representations, each problem is missing a different type of representation. (And in my class, there are usually 6 groups, so this setup continues to pay off all the way through the whiteboard discussions at the end of it.)
After sorting the cards into the 6 different problems, the group needs to identify which representation is missing and draw/write/replace it by creating their own on one of the blank cards.
Finally, they should “upgrade” their cards by: (a) solving the problems (if they haven’t already), (b) drawing in the total momentum (for the system) graph on the momentum-time graphs, and (c) drawing in the total Fnet (for the system) on the Fnet-vs-time graphs.
Each group signed up for one of the problems and created and shared their whiteboard of the problems, and we looked for patterns and insights from the overall activity. We spent about 3 classes on this activity, including the whiteboarding at the end.
What went well
Overall, it was a really engaging activity with lots of discussion in groups and lots of different skills and abilities needed for working through a lot of new ideas and information all at once.