Multiple Representations of Momentum Transfer — The Card Sort

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.

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:


Rewriting the Momentum Packet

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.

Momentum Card Sort Instructions

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.



The momentum-time graphs were great. When they presented their work, the idea of the total momentum of the system staying constant was very clear and explicit. The total Fnet for every system was zero, of course, and that set us up really well for our next activity in class (where we investigated what would happen if that weren’t true).

And we looked at ∆p for each object in 2-object systems and saw that when 2 objects interact, they change each other’s momentum by the same amount, but in opposite directions. (And that sounded really suspiciously familiar.) The symmetry in the momentum-time graphs but NOT in the velocity-time graphs was really striking.

I am sure it wasn’t ONLY the card sort, but this year’s students developed the best understanding of momentum that I’ve seen in my classes so early in the year. (Usually they understand it this deeply when we come back for a second pass in the spring.)

What remains to be improved

This set of cards is really the B/B+ version of this activity. (My first class got the B/B- version, but I fixed some of the mistakes they caught before printing the cards for my other section and before sharing them here.)

The problems are mostly ones that I found in quick online searches for conservation of momentum. When I have time for the 2.0 version, I will write my own problems with numbers that overlap a little more.

The Fnet-time graphs were a really interesting thing. I idealized them a little less than I did the velocity- and momentum-time graphs, which prepared them for seeing what happens when something bounces off of the force sensor. On the other hand, the first thing every group did when looking at the cards was to say, “Well, we know the slope on the velocity-time graph is the acceleration, so let’s find that and then we will be able to find Fnet.” Oops. But the conversations were still great anyway! I am not sure I would change it in the next version, but I would think more about it.

I would also think more about whether to include all of the numbers on the other graphs. When is it helpful to include them? When is it better to show just the shape? Observing my students in this task, I think it would have been too difficult if I had removed many more of the numbers. They needed a place to start and get their heads wrapped around it before they even understood what was happening.

Summer Workshop!

If you like these card sorts, you might also be interested in my week-long summer workshop in NYC. Among many other activities, it will include exploring card sort activities as well as time and feedback for developing new ones. All of the information to register is here: Designing for Discourse and Sense-making in Physics Class


6 thoughts on “Multiple Representations of Momentum Transfer — The Card Sort

  1. One thing that jumps out is that your graph of F vs t doesn’t match the velocity and momentum graphs. If the impulse is a triangle (half increasing linearly & half of decreasing linearly), you would not generate a linear change in velocity nor momentum. To get the momentum and velocity graphs you (and Brian) depicted, you would need a constant force in the “during” segment. Thus the force graph should be a horizontal line at zero, a discontinuous jump to some non-zero horizontal line at the beginning of the “during” segment. Then another discontinuous jump to a horizontal line at zero at the end of the “during” segment.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s