Variation and Measurement Labs

I have been Modeling – teaching physics using the Modeling Method for about 14 years now.  I took my first training in the summer of 2000 with a very dynamic teacher from Michigan, Mark Davids, who had been modeling then for at least 10 years, having received his training in 1997 and 1998.  I mention the lineage because the modeling materials have changed over time and something that I think is so important has been lost.

That is serious practice in graphing and analysis.

When I first took the class the facilitator had us to between 8 and 10 labs where we took data, graphed it (using some automatic graphing program or calculator) and analyzing the graphs - writing equations, describing the relationships, etc..  I thought that this is the way that all modelers do it.  But when I got to Arizona State (where I studied modeling for the next couple of years) I found out that no one did it this way.  They all used the script from the modeling materials that suggested doing just the pendulum lab.  

I was like, "What?  None of those are even a linear relationship!"  

How are kids going to experience all of the relationships by only doing a pendulum?  In my experience there were myriad labs with almost all of the standard relationships represented.  Here is my list of all of the labs that I have the kids do in the first week.

Linear Relationship

Circles #1: Circumference vs. Diameter

The participants measure the circumference of various cans, lids and bottles with a string and the diameter with a meter stick.

Rods: Mass vs. Length

The participants measure the length of a bunch wooden dowels cut from the same long dowel with a meter stick and the mass with a triple beam balance.

Tiles: Mass vs. Area

The participants measure the area of pieces of white board with 1 cm x 1 cm grid paper and the mass with a triple beam balance.  I cut a white board into small pieces of various sizes and shapes between 50 cmxcm and 500 cmxcm.

Spheres: Mass vs. Volume

The particpants measure the volume of 5 differnt steel ball bearings by dropping them into a graduated cylinder and the mass with a triple beam balance.

Cups and Dice:  Mass vs. Number of Dice

The participants count the number of dice in a cup and measure the total mass with a triple beam balance.  This one is particularly interesting!

Parabolic or Quadratic or Squared Relationship

Circles #2: Area vs. Diameter

The participants measure the area of circles with 1 cm x 1 cm grid paper and measure the diameter with a meter stick.

Square Root Relationship

Pendulum #1: Period vs. Length

The participants measure the period of the pendulum with a stop watch and the length using a meter stick.

No Relationship or No Variation

Pendulum #2: Period vs. Mass 

The participants measure the period of the pendulum with a stop watch and the mass by reading the mass on some "physics class masses".

Pendulum #3: Period vs. Angle

The participants measure the period of the pendulum with a stop watch and the angle by using a protractor or other "angle-o-meter".

Inverse Variation

Baseball Balance: Distance to Center vs. Mass

The participants vary the mass on one end of a meter stick and change the distance from the center by sliding it toward or away getting it to balance.   

There isn't an inverse square relationship here but that doesn't mean I can't do one.  

I am tired of teachers who say, "these kids don't have any skills."  I am like, "then just teach them what you want them to know!"  

With in these labs I teach my kids how to measure with meter sticks, stop watches and balances.  They learn to make white boards, to graph with the computer and to analyze their graphs; all of the skills they will need for the whole year!  And I am in the room coaching and watching and hinting.  I get to know the kids and their skill level.  

I have been running Modeling Workshops in Michigan for 5 years now and have done these with my participants and I bet if you ask any of them they will support my claim that these are valuable parts of their classes.