We are finally here! Thank you to everyone who has embarked on this journey of reflection with me. If you missed the first few posts check out the introduction to the entire series here. This is part 3 of a 3 part series on momentum. You can read how I introduce the unit with impulse and check out some of the follow up activities I do before we move into collision.
Today we are going to talk about momentum conservation. I find that most novice-style teaching approaches look something like this:
- Momentum is conserved. That means initial = final
- Write an mv term for each object in the collision before and after the collision
- Solve for the unknown variable.
- An even more novice approach is to use MVP charts to help students organize the information.
I’ll start with this: I hate charts almost as much as I hate formula triangles. Why? Because if students exclusively use charts to exclusively calculate values with no other expectations the “learning” is “I multiply these boxes” and “I divide these boxes”. This is not demonstrating much of anything except that the student could probably play sudoku (I’m also not a fan). I do however incorporate the charts for those “easy wins” with my regular level students as an option…but only after we’ve done some of the heavy lifting first.
Say what you will about AP as a program, it has made my teaching more thoughtful and as a result, way better than before I taught AP.
Recall that in the early days of impulse, students were asked to sort of consider conservation without outright stating it. We now go through this process formally. I begin with the following prompts:
From here we collectively work our way to the final statement that -Dmv1 = Dmv2…. and THAT is conservation. It is a transfer of momentum from one object to another such that the total of the system remains constant.
At this point it’s all about application for my AP students. They get thrown into the lab for a few days so they can collect data for the various collision types and determine whether or not momentum was conserved. (Lab handout)
After the lab students are given one collision type they are responsible for in a board meeting. Rather than having a class conversation I let students circulate and provide written feedback. (The prompts for the boards are at the bottom of the image below, feedback prompts at the top)
Board meetings are always opportunities for students to check their work, collaborate, and ensure they can submit the best possible product. While I took the idea from here, I do make modifications depending on the activity because some students… no matter what… will never speak in a whole group setting, but they will offer written feedback. Some students (myself included!) freeze “on the spot” but when given time to reflect, have amazing things to offer! I think too often we create classrooms that are driven by extroversion but never take the time to consider what learning looks like for introverts, and write it off as “shyness” or “refusal to participate”. I also like to have students circulate when we have a significant amount of information on the boards, so it doesn’t lend itself to a traditional board meeting.
We do some conceptual practice (which has a bigger Force? a ball that bounces or one that lands?) and we discuss how we could know if there were an external impulse acting on the cars during a collision. I love using this graph from AP and asking students to determine if there is an external impulse
Oh! But let’s not forget all of the richness we learned earlier in the unit! I need to make sure to weave in the first half of our learning with this second half! I assign students what I call “special problems“. This problem set is a few problems that are neither perfectly elastic nor perfectly inelastic, but something in between or there’s an extra nuance added. For each problem I ask students to sketch the force vs time graphs, solve the question, and then answer an additional conceptual item about the problem.
When we review these problems here’s what I do: I randomly select 6 students to put up the graph or mathematical solution to each problem. Then I select 6 more students and their task is to either explain the answer on the board if they agree, or write a different solution on the board if they disagree. When there is a disagreement we open the floor to a class discussion about the two different answers to decide which is correct.
What about 2D Collisions?
2D isn’t really a major emphasis in APP1. We discuss it briefly in terms of the vector nature of momentum so momentum must be conserved in each direction
Regular Level Physics
In my regular physics class have to scale back just a bit and shift my focus. I give students opportunities for “wins” so they can feel like they “understand” and then I start layering some of the more complex problem solving tasks.
We begin with a marble activity. Students use the grove between their desks and run collisions with marbles (kind of like a Newton’s Cradle). They are asked to record observations about the velocity, and therefore the momentum of the objects. After this activity we have the same conservation discussion as my regular students.
The other major difference between regular and AP is that I present and have students practice each of the collision types one day at a time. When I present these I will show them the chart method first, explaining that it is an option, but not my personal favorite.
I also explain WHY it’s not my favorite. The reason is that you have to remember the important physics idea in the MIDDLE of your work… that initial momentum is the same as final. If, however, they do it in the algebraic way, they start with the physics idea and then they can forget about it. I generally have a 50-50 split in my room who does which method. The other important part about how I teach this lesson is I want to make it super clear that we get all of the same numbers both ways. For this reason I will copy the chart over to the next slide and solve the same problem in the algebraic way
The collision lab is also different. I give students one lab at a time and students collect the data in pre-made tables. Since students need to determine initial AND final AND keep track of signage, there’s just a lot going on to also add the layer of “do this without a guide”. It’s not my finest moment, but, again, my students need some wins.
Problem Solving Skill Building
Another layer I add to momentum is that since the equation and relationships are simple, I introduce proportional reasoning with students (what happens if we double the mass, half the velocity, do both?). Many of my regular level students really struggle with thinking in this way (so does AP!) but I feel it’s important that they get some exposure to this. We talk about how you could choose to make up numbers and see what you get, but it’s also more efficient to shove the changes into the equation and see what comes out
I’ve also started incorporating more ranking task type items that are conceptual in our classroom practice to push their problem solving skills. I intro with the following
Students then solved tasks like the ones below in groups on whiteboards. Notice that the tasks chosen are ultimately fairly simple. I did the colliding carts first because it provided numbers and allowed students to calculate in order to come to a conclusion
However in this final problem we did, there are nearly no numbers at all! This was a good place to really discuss the relationships within momentum, and in this case focus on what is the same, greater and less in order to come up with an answer. Student groups ended up being highly successful. We did about 4 of these tasks in the 50 minute class period.
I suppose I should discuss what assessments look like in my classroom at some point, especially for the non-AP students. Another day, another post! (Spoiler: it’s changed quite a bit since I first started teaching!)