How I Develop the Model of Balance

Alert: first unit of the school year!

Where do you start your physics classes? The cannon suggests we have to start in one particular place (kinematics!), but my experience suggests there are many entry points. I’ve tried a wide variety of first units, from qualitative energy to waves.

Everyone in the room has something to contribute, not only those with a certain type of prior experience.

What makes a good opening topic? What features do you look for in your first unit? I’m generally looking for establishing the model development cycle, helping students build an experiment to test a claim, and to do it all via content students haven’t seen before. The last one is critical, as it sets our earliest whiteboard discussions on near-equal footing. I want to establish from early on that everyone in the room has something to contribute, not only those with certain type of prior experience.

That’s why this year, I opened 9th grade physics with Balance. The unit itself is not my creation, credit goes to Vol 2 of Physics By Inquiry written by Lillian McDermott and to my colleagues who developed our local version about 10 years ago. I’d like to walk you through how I teach Balance, especially as a first unit, and show off my favorite features of opening with it.

What is Balance?

(as a unit of study in secondary physics)

Investigations center around a pegboard hung on a ringstand. Students hang large washers from paper clips hooked through the holes in the pegboard. The goal is to achieve balance (i.e. the board is horizontal and not moving).

We measure quantities in “number of washers” and “distance from the fulcrum.” Later on, when we get to off-center problems where the mass of the pegboard matters, we talk about the pegboard’s mass measured in equivalent number of washers. I don’t say torque. By the end of the unit, I’m stretching them to solve problems with masses in grams and distances in centimeters.

How is Experimentation Structured?

Day 1

(30 minute class) Set up a hard problem and ask students to predict the number of washers needed to balance the board. Something like this works great:

After everyone’s guessed at the number of washers and each table has tested to find the actual value, shift conversation to “What is a model?” My main idea is that models are predictors of future behavior.

Days 2-4

(60 or 90 minute class) “I’m going to walk y’all through building your first model, which will be useful for predicting future outcomes. My job is in setting up the experiments to thoughtfully move you toward a complete understanding. Your job is to engage thoughtfully while making notes to document your work.”

Set up three different experiments during class that are projected on the board. I pre-assign random groups of 2-3 that shift daily. Each table has their own materials.

Experiment 1

Center-pivot, balancing one mass on each side of the pivot. Let them experiment for 10 minutes. Give them 5 min to prepare their models (aka “prediction tools”) on a whiteboard.

For the teacher, make sure students see the full range of single-mass balancing possibility. As I circulate while they’re experimenting, I ask “can you solve this (gestures to their setup) a different way?” Early on, they’re going to gravitate toward mirroring the setup on the right. Hopefully, they eventually realize that any two numbers with the same product will balance.

When writing their models on whiteboards, most will start by writing a descriptive model. I push them to translate the description into an equation

Discuss as a whole class with the purpose of arriving at a shared understanding. I spend a lot of time here on norming whiteboard discussions

After Experiment 1, I hope to arrive at

Experiment 2

Center-pivot, balancing multiple masses on either side of the pivot

As with Experiment 1, make sure students take a wide variety of data — this is when I generally introduce the experimental design principle of spreading independent variables as wide as possible

Bring students back together in a board meeting to revisit the equation developed after Experiment 1. Is Experiment 2 similar to Experiment 1 or fundamentally different? If the former, can the equation of center-pivot, single-mass balance be modified to include Experiment 2? The goal is to arrive at

Experiment 3

Off-center pivot, balancing one mass
I encourage students to get the board balanced with all the washers hanging on the shorter side of the board (as in the example above). It highlights for them that the board must be providing some balancing effect on its own. I have to encourage my students to be thorough in gathering values so they might see a pattern.
Come together to discuss a third time. Modify the equation again. We’re hoping to arrive at

Finally, I always encourage students to break the model after they’ve created it. The idea is to come up with a scenario that can’t be solved with the equation built built during the experiments.

The full model takes several days of experimentation and discussion to develop. I have two problem sets that can go out as homework in the interim. The first problem set includes several questions from the PBI book, so I can’t share it here. Those problems feature exclusively center-pivot balances with questions about where to place washers to bring a given board into balance. After Experiment 3, my problem set is useful.

References and Resources

I learned pretty much all I know from these sources about leading whiteboard discussions in STEM classrooms:

• Whiteboarding (2012) by O’Shea
• Best practices for whiteboarding in the physics classroom (2017) by McKagan and McPadden
• Facilitating Discourse in the Physics Classroom (2004) by Schmitt and Lattery
• Whiteboard Training Camp (2013) by Abud

This is my Balance Problem Set: