Force Diagrams — A Card Sort

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).

The style of this activity is somewhere between my kinematics graphs card sort and my momentum representations card sort. It has right answers, but it also requires more than just matching.

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.

Cards and Files

Here are some images of the pages of cards. And here is a link to the Google Doc:
BFPM Representations Card Sort Google Doc

As always, these are shared under a Creative Commons license, so please feel free to share, steal, modify, improve, personalize, etc. Just don’t take credit or sell anything based on these.

If you do use them, please let me know—and let me know how it goes!


This work is inspired by work done by Richard Wright during the Discourse & Sensemaking in Physics Class workshop in the summer of 2018 (through STEMteachersNYC).

Michael Lerner also contributed to this work by adding system schemas/interaction diagrams as an additional representation. Thank you, also, to Marta R. Stoeckel who has tested these in classes and given feedback.

Thanks to Mark Schober for some of the situation drawings which are part of the New Visions and STEMteachersNYC high school physics curriculum project. Some of the other situation drawings were done by my former physics student (and advisee!) Eve van Rens as part of an honors project (creating illustrations for my packets) after taking my class.

(And of course, thanks to Brian Frank for much of the inspiration for all of these card sorts!)

3 thoughts on “Force Diagrams — A Card Sort

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