Free Fall: A Satisfying Board Meeting

Finally! A satisfying board meeting with students! It’s been a long fall with awkward board presentations around my room. Silence, constantly looking to me for affirmation, and boards that are total messes have been the hallmarks of the past few months.

I’m here today to say that with persistence, it’s possible to have a great discussion. First, a few whiteboards post-meeting:

Thursday: Free Fall Day 1

My rough outline of class goes as follows: Introduce that the topic today is free fall. Explain it’s a subset of the uniform acceleration model we’ve been studying. Drop a few objects and suggest which ones I think could probably be modeled with a free fall model and which can’t. Ask what they think free fall means, what it implies as far as a model.

Then I asked students to film a falling ball and perform video analysis. First time with this particular tool, so I taught it to them.

They then took the two graphs they got directly from Logger Pro (position-time and velocity-time) and used them to generate semi-quantitative versions of the other representations they know (acceleration-time graph, motion map, verbal description, and mathematical models).

No board meeting at the end of Thursday’s class. Instead, I wrapped with a definition along the lines of “an object in free fall experiences no air resistance, only the force due to gravity” and sent them on their way.

Friday: Free Fall Day 2

On Friday, a student and I launched a ball straight up (using a projectile launcher). From that observation, the students were asked to produce whiteboard models. I gave students 12-15 minutes working in pairs and brought them together for a board meeting after.

The first questions I got included:

  • But we don’t know any values, how are we supposed to create a data table or equation?
  • Should this be a qualitative or quantitative model?
  • Where is x = 0m?

Most boards came in with impeccable kinematics graphs.

When the graphs had mistakes, it was almost always on the velocity-time graph. Here are the two variations.

When confronted with these graphs, students had detailed discussions about how long the ball is at rest at the top of the motion. Does the ball pause for more than a moment? How do we know? Someone pointed to the acceleration graph at a constant a = -9.8 m/s/s as their proof — velocity must change by that amount every second.

This was my first board meeting where other students were able to explain the exact ways in which these are not a representation of the ball launched up. Kids were out there changing their whiteboards in the moment.

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Look at the data table in the center — this pair of students, bothered by not knowing v0, opted to make up a value and go from there.

models.001

Group 2 here got their graphs right. But if you look closely at their motion map, they believe the acceleration changes direction with the object. Also, they switched to thinking initial velocity is 0 m/s on the more concrete models in the second picture.

But We Still Need More Time

So, after the boards were correct, I had 5 minutes remaining in my last section of Physics 1, so I asked them “An object in free fall’s time in the air is represented by time, t. At what time would it reach the apex?” Though this kind of algebraic representation is new to my 9th graders, most said “1/2t” with confidence.

Yay! They get it! So I followed up with:

“For the launched ball you just modeled, does the ball spend more time going up or more time falling down?”

A variety of answers, no consensus, not a soul says “the times are equal.” I point out how it’s the same question I just asked them mathematically. They push back with all sorts of considerations. Very few students truly believe “the times are equal.”

Then the bell rang.

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