# Day 2: Thinking about Relationships

Day 1 I run a HUGE physics smorgy: 11-15 demos/lab set ups with minimal directions. Students are told to play, investigate, explore, PAY ATTENTION and ask lots of questions. This is my hook into the class for the year. I’m able to observe the students, act ridiculous and ease the MASSIVE anxiety they walk into this class with.

The next four days we actually spend working with data and relationships. Specifically to build the skills necessary to analyze data on a graph and straighten it when needed. I have a reading I ask students to do ahead of time and then we go through the straightening process. These brilliant students (half of whom are in AP Calc) are completely flabbergasted by the straightening process. It just doesn’t. make. sense to them.

I decided to try something different today on the fly, and it brought about some great conversations. First I put up blank sketches of graphs depicting a linear, squared, inverse and square root function. I asked them to put the graphs on their white boards and write the relationships. The answers consisted of the following:

• “linear, squared, inverse and square root”
• y=x, y=x^2 (etc)
• y∝x y∝x^2 (etc)

This kicked off some great conversations. Are we in agreement, generally, about which is which? (yes). Are the equations really representative of the sketches? (We don’t know, there are no labels or numbers on the axes)

Next, I gave students four statements

1. “Momentum is proportional to velocity”
2. “A spring loaded gun is fired upward. The height of the bullet is proportional to the compression squared”
3. “Velocity is inversely proportional to mass”
4. “The period squared is proportional to the length of a simple pendulum”

I asked them to label the axes of their graphs with the physical quantities to match the statements. Here’s where the fun began. Students took a lot longer than I had originally anticipated completing this task. Here were the great conversations to be had:

• In science, we usually put the independent and dependent variables on the x and y axis. With these statements, is it obvious which is which?
• Since it’s not obvious, are answers where the axis are flipped wrong? (Not if they picked the appropriate shape!)
• So, we often are going to use slope to talk about relationships. Like, say, if we plotted distance on the y and time on the x what would we get? (speed…minds are blown)  The cool thing is if you plot the graph “wrong” you can look at the units,  and decide if they need to flip because you’d have seconds per meter or something. The important thing is whatever you tell me the relationship is, needs to match your graph.
• Then, of course, I let them in on the secret: we always list the y thing first. Literally all we are doing in these sentences is taking the math proportions, like y∝x^2 and saying, instead, height ∝ compression^2. It’s like the hugest lightbulb moment for students ever.

Now that they have that substitution thing in their brain, explaining how to straighten graphs is a snap. I was really pleased with the lack of frustrated and confused faces. Last year, I sadly, lost several kids during this unit. I wanted to cry so hard because we hadn’t even started physics and seriously questioned my lesson plans.

Tomorrow they finish their pendulum labs, so we’ll see how this all goes.

Meanwhile, AP Physics C is dabbling in computational physics for kinematics. More on that later.