A Unit on Units, Two Ways

I always think it’s interesting to see how similar classes at different levels and grades learn the same topics.  This year I’m teaching both freshmen physics and regular level upperclassmen physics.  In both classes we began the year with a unit on units, measurements, and conversions.  Each class learned the basic concepts but had the opportunity to apply the concepts in two very different ways.

Freshmen Physics – Make Your Own Unit

All freshmen at Pomfret School take the same level introductory physics course.  This is great because they all share in a common experience, even if they have a different teacher.  Fellow teacher, Josh Lake, and I work closely to create each unit and keep our classes paced together.  This year, students worked on a lab where they were tasked to create their own unit.


A student measuring his tie using his unit, a AA battery.

Students embark on a several day lab where they measure common objects in the classroom, find conversion factors, and standardize their unit to the metric system.  In years past the lab ended there, but this year, Josh and I decided to have the students create an art installation with their own units.  It turned out really well, students transformed a drab white walled stairwell into a pretty cool hanging art display.


Upperclass Physics – Scaling Our Solar System

In the upperclassmen physics class I decided to up the difficulty a bit and provide the students with a bit of an open ended project based experience.  The goal of the project was to create an installation along a long hallway leading to our classroom.


Our hallway just before installation.

On the first day of class I presented the students with a properly scaled model of the Earth and the Moon and then had each of them select a random sphere from a box.  They then used that sphere as a starting point for their own individual model.  Students chose a celestial body in our solar system to represent their sphere and then picked a second body to create their model.  They had to determine their scale and then use that scale to determine the proper size of their other object and the


Each class makes peer feedback norms.

distance between the two.  Along with the physical model, they create a one page description of the model and we go through two rough drafts and peer editing before they are ready to hang everything on the wall.  In the end there were more than 40 objects on the wall, connected by pink string, each with a description mounted on foam core.  One student said after hanging her model, “At first I wasn’t sure what you had in mind, but now I love it!”




The final product of their work on display.

Putting Student Work on Display

Although I loved my physics major in college I got just as much joy and sense of accomplishment from my art minor.  I was constantly creating things and putting them on display for critique and public viewing.  It made me take a little more pride in my work when I knew it was going to be hung with my name near it.  For many of our students this was the first time they had to create an art style display for their scientific work and many of them struggled to move forward with it.


Students painting their spheres before hanging them on the wall.

Now, especially with the upperclass project, when the students walk by they always check on their display, making sure it’s still hanging straight and looking good.


A completed model.

There’s never much physics content learned in the process of putting their work on display but I have felt that the extra pride they take in their work translates into a better final product and more learning along the way.


Students working on their units display.

They ask more questions about things they are unsure of because hanging something out on display with an error for all their friends to see is sometimes more scary then getting a bad grade.  In my eyes, taking the time to put student work on display is time well spent.





Students working on their display.  Fellow teacher, Josh Lake, in the background.


From Slide Rules to Mathematica

It’s hard to believe that we use to carry out complicated computations on something that required no batteries to operate, had no screen, and no buttons; it was called a slide rule.  I have no idea how it even worked, just take a look at the photo below…


These things were complicated, yet they powered the analysis of complex mathematical systems and provided a quick way to perform calculations.  According to the website, The Museum of HP Calculators, the slide rule reigned supreme for about 300 years.  You can even take a look at the instructions for its operation here, it’s not very intuitive at first glance.

We’re almost 400 years post slide rule invention, credited to William Oughtred in 1622, and technology has brought us a long way.  At Pomfret School we provide all students with a Wolfram account and the science department requires all students to download, install, and use Mathematica to perform a whole host of operations.  Students are first introduced to the program in our freshmen physics class where we work to provide them with all of the skills and know how to use Mathematica (MMA) confidently.


We begin the year with a simple lab where students use Mathematica to calculate percent error, a value that we end up using frequently


Student write-up submitted for grading.

throughout the year to inform students of their own lab/data collection skills.  The lab centers on the Vitruvian Man and the students
use the ideal proportions and their own measurements to calculate percent error.  They then write-up the lab in Mathematica and submit it for grading.  This is definitely not second nature for most of our students and many struggle with the programming nature of the input and formatting nuances of the program.

With some practice and after many failed outputs, about 90% of the students are ready to move on, and to begin tackling harder material on their path to unlock the power of such a robust program.  We move into units, measurements, and conversions next and present the students with a lab where they make their own unit and learn how to convert measurements using Mathematica.


All lab handouts are made using Mathematica so students are interacting with the software on many different levels.

At this point we are just two weeks into class, and we begin to show students


Notes can be easily formatted and images inserted in MMA.

how Mathematica can be used to take notes as well.  It’s interesting to note that although we have spent time teaching the students how to use Mathematica we have also been able to move through typical freshmen year content at a reasonable pace.  This lab, unlike the last, incorporates the use of more complex mathematical skills and reasoning.  Mathematica allows students to see the format of the conversions, much like on paper, but are less intimidated by the process of solving the equation.  As the students begin to see the merit in


Student generated conversion practice.

learning the Mathematica input language we begin to see them embracing the fact that they don’t have to worry about inputing their work on paper into their calculator.  What was once a two step process on paper and with a calculator has now become one step in Mathematica.


We’re almost three weeks into the school year now and I’m 100% behind the use Mathematica in the classroom.  It has allowed students to solve mathematical problems, take notes in class, and learn how to do some basic programming.  It makes me wonder what it would be like trying to teach these students how to use a slide rule…

I have to also give a huge amount of credit to my fellow teacher, Josh Lake, as much of this content was generated initially by him.