PCTM 2022 Resources


Visual Patterns (thanks Fawn Nguyen!):

Investigating T-Shirt Offers Desmos Activity:

Shared Work and Cocoa Puffs: Cocoa Puffs and Shared Work


Introverts and Signatures:

Luke Wilcox / StatsMedic – Does Beyonce Write Her Own Lyrics?:

Doug Tyson – Grabbing Starbursts:


Chessboards for Jack

“Mr. Lochel – we have a check to send to you. Please provide us an address.”

What a fantastic e-mail I received this past year. It combines two wonderful things – money, and people wanting to send money to me. But this money was coming from a very special place.

In 2017, a talented, driven group of students at my high school participated in the Moody’s Mega-Math Challenge. In this annual math modeling contest students are provided a prompt and 14 hours to develop a framework for a solution. The contest is now sponsored by MathWorks, and you can learn about the contest and resources for getting your students involved at the contest website. The team earned an honorable mention award for their solution – and a $1,000 prize to be split amongst the team members. Not a bad way to close out their math careers in our district, and on to bigger and better things!

The 2017 Math Challenge Team: Principal Dennis Williams with Quinn, Jack, Mathew, Jason and Dmity.

Jack enrolled at Dartmouth University in the fall of 2017. Like most students who move on to college, I had limited contact with Jack after he left high school. And similar to many of my colleagues here who were part of Jack’s life, I was gutted when I learned of his passing in 2019.

Fast-forward to last spring, when the nice folks at the Society for Industrial and Applied Mathematics informed me that 2 years after winning his prize for the modeling contest, Jack hadn’t cashed the prize check. After contacting his family, the funds were donated to the high school math club. A wonderful gesture, but math club really doesn’t require much funding….so what to do with found money? How best to honor Jack’s legacy at our school?


Red and Black week chess tournament. Jack is seated at the center table, in black.

I’m not sure what percentage of Jack’s down time at our high school was spent playing chess, or even how much time was spent playing chess when he was supposed to be working on something else, but it was a solid amount. But if you observed Jack playing chess you quickly realized the game was secondary. Having a conversation, thinking deeply, learning about someone new – these were the important residuals of a chess board.

I used the donated money to purchase as many nice-ish chess boards as possible and worked with our HS guidance department to generate a list of teachers Jack worked with during his time in our district. This past week I organized 8 boards including a note about Jack encouraging players to make a new friend and enjoy a conversation through chess. Four of Jack’s former teachers received chessboard gifts, and classrooms all the way down to 4th grade will have a new set to enjoy. I hope the wonderful culture of caring about others and getting to know someone new through chess which Jack embraced will live on through these boards.

Getting the boards ready for delivery.

I hope you find these resources helpful for learning more about Jack and helping individuals and families in your own community who struggle with mental illness.

Jack Duffy 5K Run

NAMI – Montgomery County PA

Liv Associates

Thanks Jack.


You Have an Awesome Math Lesson – Share It!

Do you have an awesome math lesson? Do you like handsome cash prizes? The Rosenthal Prize for Innovation and Inspiration in Math Teaching offers a top prize of $25,000…and the 2019 winners have just been announced by the National Museum of Mathematics! Congratulations to Nat Banting, this years winner and a fun and inspiring twitter follow. I’m really looking forward to hearing more about dice outcomes auction somewhere down the road. On the link above you can read about past winners and learn about how to apply for 2020.

I applied for the Rosenthal Prize back in the spring. At that time I looked back at old blog posts for lessons which seemed to be of interest and use to teachers, and chose one which has generated many positive comments: the 35 Game. The original post describes the game and how to leverage the results to build need for compound inequalities:

I was thrilled to find out later in the year that my lesson was chosen as a Finalist for the award, but then the hard work begins. There is quite a lot to submit for this prize including:

  • A complete lesson plan
  • A video of the lesson in action
  • 3 recommendation letters

Every year the “35 Game” seems to get many blog hits and comments from teachers who use it. I am hoping that sharing my lesson plan write-up with the math community will provide guidance and usefulness to those teachers who enjoy this lesson. Any feedback you have is appreciated!

Thanks to my friends and colleagues Dennis Williams, DJ Fromal and David Weber for their willingness to provide recommendation letters. I work with inspiring and wonderful educators!