Park City Mathematics Institute
Secondary School Teacher Program

Morning Shorts

[Jim] [Cal] [Carol] [Sameer] [Carol] [Dianna] [David] [Bill] [Peg]
[Cal] [Rina] [Suzanne/Peg] [Zach] [Jet] [John] [Jesse] [Suzanne]

2010 Index Page
2010 Photos
2010 Roster
Class Notes
    Morning Shorts
Daily Schedule
Getting Started
Participant Outreach Activities
Project Abstracts

Update Contact Info
Send Note: Suzanne & Richard
Site Map
Blog List

Working Groups
Reasoning from Data and Chance
Exploring Discrete Math
Investigating Geometry
Implementing Lesson Study
Visualizing Functions
Learning the Math of Image Processing

Remote Site
E-table - New Mexico

username/password required
Contact List
E-mail Addresses
Morning Announcements
Portrait Photos

Ning: PCMI 2010


June 28 5-minute madness presentation - Jim King

Jim presented Alphabet Soup.

June 29 Ning PCMI 2010 - Cal Armstrong

Cal gave an overview of Ning PCMI 2010. Please accept your invitations!

June 30 Tour - Carol Hattan

Carol gave a brief overview of the PCMI@MathForum site using the Getting Started page.

July 1 Twitter, Blogs & Sam: Oh why?! - Sameer Shah

Three weeks ago, Sameer wore his "I only twitter with math teachers" shirt into Manhattan. He got lots of random compliments. A few were from hipsters from Williasmburg, thinking he was being ironic but he really does only twitter with math teachers. He also blogs....view more:
   download .pptx file || view as HTML
   Blogotwitterversphere: Continuous Everywhere But Differentiable Nowhere

July 1 Making Snowflakes - Carol Hattan

Carol provided step-by-step directions on how to make snowflakes based on the Hexagon Activity.

July 2 Using Webinars to Develop Learning Communities for Teachers or Students - Dianna M. Sopala

Dianna M. Sopala, an officer of the Association of Mathematics Teachers of New Jersey, will present how webinars can be used for learning communities. She will tell you about some free webinars being offered for the 2010-2011 school year. More information will be available in September 2010 at more:
   download as [MS Word] [PDF]

July 5 Competing Classroom Companies - David Metzler

Over the last year I had my two AP Calculus AB sections pretend that they were competing companies that made and sold sporks. Most of the projects we did over the course of the year were tied to this theme, as the students investigated ideas such as revenue, cost, and profit, rates of change, maximization, area, net change, and volume. I'll discuss how I set it up and show a few project descriptions.
Download a zipped file of handouts I did for my AB Calculus class.

July 6 Wolfram Alpha - Bill Thill

This is a brief introduction of ways I've used Wolfram Alpha as a tool to help students deepen their understanding of algebra and precaclulus. I will show some helpful, intriguing, and entertaining uses of this amazing computation engine.
  Find Wolfram Alpha at (and bookmark it!)
  The official Wolfram Alpha Blog:
  One teacher's experiences on her Blog:

July 7 Presidential Award - Peg Cagle

Peg presented information on the process a teacher goes through to receive National Board Certification.
   download .ppt file || view as HTML || .mov

July 8 Screencasting - Cal Armstrong

Screencasting is a tool to record what is happening on your computer (or Smartboard) to be published for later use. While they are often used for short tutorials, they can also be used to collect assessments from students. There are a number of free and easy tools that can be used in and out of the classroom, like Jing (

July 9 Virtual Manipulatives - Rina Martinez

My school is a low performance school and last year we got a grant to get laptops for our math classrooms. We use the laptops everyday. One of the things we use them for is to motivate the students to want to learn math. Another reason we use them is differentiate math instruction. Looking for computer programs/websites for tools to teach mathematics requires a lot of time.

I want to share some of the virtual manipulatives that I have found to be useful in my classroom.

Interactivate - Shodor
Explorelearning: Gizmos
National Library of Virtual Manipulatives - Utah State University
Probability Explorer - Hollylynne Stohl Lee

July 12 Quick overview of today's 4:30 program - Suzanne Alejandre and Peg Cagle

Sharing Resources - come with questions for Suzanne about what teacher resources the Math Forum offers. Come with ideas of resources you currently use to share with others.

July 13 Screencasting - Zach Korzyk


This is a website that allows a teacher to assign homework online. The website creates new problems of various types and students are expected to get a certain number of consecutive correct responses (up to teacher) to prove they know it. The website provides full solutions for each problem with explanations. There are infinite problems and the students can keep trying until they get 100%. I have only made the curriculum for Algebra 2 / Trig at this point but expect to finish Algebra 1 by the end of the summer. I invite any teacher to use the website in exchange for constructive feedback. I will also be spiffing up the visual display and simplifying the user interface.

Sign up for an independent account to test it out. Works best with Firefox (Graphics and calculator).
If you make an account I will keep you posted on updates and setting up a teacher account before the school year.

July 14 Pizza and Problems - Jet Warr


In the 2009 PCMI program, I was so excited to participate in the Pizza and Problems activity. I enjoyed the associations made while working on the problems. Because of this excitement, I decided that I had to find a way to bring it to my small 7 - 12th high school.

When I returned home I decided to have my students assist me in the writing of a grant to help our classroom, always keeping Pizza and Problems in mind. We (I say we, because my students helped with the ideas and the letter writing) were successful! My classes received a $4300 grant to purchase thirty TI-84 Silver Edition calculators and enough pizza and soda pop for two Pizza and Problem sessions.

The date was set for our first Pizza and Problems [view the invitation Jet used] to coincide with the arrival of our new calculators. Students and parents who attended the session would be the ones to Christen the brand new calculators. The problems for the evening carried the theme of Benoit Mandelbrot and fractals. I shared a brief historic story about Benoit and told students to look for that theme throughout the problem set. I created the problem set in a "Darryl and Bowen" style - appetizers, main course, and desert. I turned on the tunes, pizza was delivered, and students worked their hearts out. I was amazed at how, if I just let them, they mingled and collaborated with one another.

We ended a fantastic evening by taking pictures and participants wrote thank you letters to our "Grantors."

July 14 The Hands Project - John Mahoney

John Mahoney presented the project that his pre-calculus students do at the end of the course. It involves taking digital photos of students hands and printing them (via Sketchpad) on top of a pair of coordinate axes. Students then compute equations of the lines in their own hands. Pre-calculus students are required to use a variety of different types of functions. This project helps students review the properties of polynomials, exponential, logarithmic functions and their graphs. If this project is used with Algebra 1 students, they would use linear and quadratic functions. An article based on this Project has been accepted by the Mathematics Teacher for their Activities section.

July 15 Classroom Group Dynamics - Jesse Johnson

Jesse Johnson will do a brief introduction of classroom group dynamics through the lens of Modern Group Analysis. She will discuss the ideas of group development, role lock, supervision and some techniques for working with what's in the room. For more information, view:
A View of the Rise of Modern Group Analysis by Louis R. Ormont [requires password]

July 16 Overview of PCMI@MathForum - Suzanne Alejandre

Once you return home, start here: and click on Secondary School Teachers Program.

PCMI@MathForum Home || IAS/PCMI Home

© 2001 - 2015 Park City Mathematics Institute
IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540.
Send questions or comments to: Suzanne Alejandre and Jim King

With major funding from Math for America

With generous support from Robert and Lynn Johnston