Park City Mathematics Institute
Secondary School Teacher Program

Morning Shorts

[Jim] [Carol] [Jim2] [Richard] [John] [JimT] [Parade Songs] [Steve] [Judith] [Philip] [Ralph] [Joyce] [Lars] [Kymberly] [Brian] [Suzanne] [Craig] [Gail] [RichardA]

July 2 5-minute madness presentation - Jim King

Jim presented Alphabet Soup.

July 3 Tour - Carol Hattan

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

July 5 UW Credit - Jim King

Jim explained the UW credit and referred to this UW Credit FAQ.

July 5 Lessons Using Google Earth - Richard Stewart

Richard explained a couple of lesson on circles he created using Google Earth. One lesson deals with inscribed angles (download: GoogleEarthInscribedAnglesCentralAngles.doc) and one lesson deals with arc length and area of a sector (download: GoogleEarthArcsAndSectors.doc). Along with the worksheets students were handed a printed picture from Google Earth. These lessons were adapted from various lessons and should not be taken as final products.

July 6 An introduction to NUMB3RS activities - John F. Mahoney

Texas Instruments has funded the writing of high school level mathematical activities to accompany the CBS-TV series NUMB3RS for the last three seasons. Johnny Lott helped write activities for season 2 and John Mahoney wrote them for season 3. Gail Burrill has been a math advisor for the writing teams for the past two years. The activities can be accessed through the site: There are usually at least three activities for each episode. Many are also available in Spanish. Each activity contains a Teacher Page, Student Pages, and a page of Extensions. John concluded by showing a 1 minute clip from the Season 2 Episode "Bettor or Worse" which featured Farey sequences - the topic which was introduced in Thursday's 8:30 class.

July 6 Random Straws - Jim Town

Problem statement:
Four externally tangent cylinders are arranged with no gaps (each cup is externally tangent to at least two others - we'll represent this using cups). If you drop a straw from a height of 2 feet above the cups (bottom of straw to top of cup equals 2 feet), how often does the straw land in the empty space in the middle?

Please send a sketch for the arrangement of the cups and data for trials and successes to Jim Town at:

July 9 Parade Songs

Let's sing:

July 9 Kitchen Table - Steve Phelps

Harold Scott MacDonald Coxeter (1907 - 2003), is known as the "man who saved geometry." Many areas of Coxeter's work involved the study of symmetry. Perhaps his best-known legacy is his work on the mathematics of kaleidoscopes, including those operating in higher dimensions. These Cabri3D sketches illustrate some of the solid polyhedron that can be constructed using a 3D kaleidoscope. You should download an evaluation version of Cabri3D from in order to manipulate the sketches in the powerpoint presentation, as well as the Cabri3D files.

files to download:
The following four files are Cabri3D files. If you just click on the link, the page will probably just display "garbage" text. Instead, right click if you're using a PC or if you're using a Macintosh hold down the CONTROL key as you click. A window will pop-up and you will be given the option to Save Linked File to the Desktop. Once saved, the file can be opened if you have a copy (or evaluation version) of Cabri3D.
      Kaleidoscope using the Fundamental Chamber in a Tetrahedron
      Fundamental Chamber in a Cube
      Kaleidoscope using the Fundamental Chamber in a Dodecahedron
      Kaleidoscope using the Fundamental Chamber in an Octahedron

July 10 MegaMan - Judith Carlin

This is a simulation for problem 13 from Day 3 (MegaMan). Fathom was used to simulate the number of boxes a child needs to purchase before getting all 10 different Mega Men.
  • MegaMan.ftm [Fathom file] NOTE: If you have issues when you download it, try saving it the way I described above for the Cabri3D files.

July 11 Exeter Resources - Philip Mallinson

  1. Show participnts how to access the Exeter problem sets.
  2. Do a lightning demo of the free geometry program, in particular, the non-Euclidean program.

July 12 Stella - Ralph Polley

You can purchase or download a trail copy of Stella at:

Apparently Vensim is no longer free but you can purchase or download a trial copy:

July 12 Sharing Math Songs - Joyce Frost

Sharing math songs with students can be a nice ice-breaker in your classes. Here are a few of my favorites that have made the rounds with math educators. Art Mabbott, Joe Frost, and Joyce Frost are the tri-chairs of the 46th Northwest Mathematics Conference in Bellevue, Washington, October 11-13, 2007. You will recognize several of the speakers from PCMI including: Kelley Butler, Gail Burrill, Peg Cagle, Nicole Davis, Carol Hattan, Lani Horn, Jim King, and Connie Savoie. We expect around 2500 participants with over 200 speakers including the famous artist Dick Termes (1 - 6 point perspective) and Mary Kay Stein (remember her name from Cognitive Demand?). Visit the website if you would like to attend.

July 13 Podcasts - Lars Nordfelt

Podcasting is another way we can reach our students. See the presentation "What is Podcasting" [html version or download the PPT file] to see how podcasting works, why teachers should podcast, ideas for using podcasting in the classroom, and suggestions to create effective podcasts for education (podagogy). See and Lars Nordfelt's Podcast for examples.

Here are some other websites that might be helpful as you start podcasting:

  • free download to subscribe to and organize podcasts - iTunes
  • free download to record and edit your own audio files - Audacity
  • free online podcast provider -

July 16 United Streaming - Kymberly Riggins

The morning short will involve a tour of United Streaming. United Streaming is a website that streams segments of instructional videos in all areas K-12 learning for both students and teachers. In this short we'll look at searching for and incorporating united streaming resources into a lesson fibonacci sequences and pascal's triangles. We will also look at professional development opportunities available through united streaming. For more information about United Streaming see

July 17 Truncated 120-cell - Brian Hopkins

The giant Zome model living on Table 3 is a "truncated 120 cell." A 120-cell is a four dimensional polytope related to the dodecahedron. In the same way a polyhedron has polygon faces, a 4d polytope has polyhedra "hyperfaces" -- here, 120 dodecahedra. In the first week we made a projection ("shadow") of a 120-cell in just white & warm colors. The new object is what happens when each of the 330 nodes is replaced by a tetrahedron. Shaving down a polyhedron node gives a new polygon face; truncating a polytope node gives a new polyhedron.

There are beautiful symmetries to be seen from various points of the room: 2, 3, 4, 6-fold symmetries, 'tunnels,' and much more. Enjoy looking at this until we're done Friday, but please don't touch it!

Construction notes: 1260 nodes, 780 B1 struts, 800 Y1, 480 R1, and 600 RO (projects like this prompted Zome to make these shorter reds). It helps to have a 120 cell as a guide (see the book Zome Geometry, Study the nodes from the center outward, which partitions them as 330 = 20 + 20 + 30 + 60 + 60 + 60 + 20 + 60. Each node will be replaced by one of eight types of tetrahedra, detailed in step #3 of (for a different project). Make the tetrahedra first -- this will use all the nodes, so that everything else is connecting these with struts. Conveniently, the tetrahedra types are numbered 1 through 8 corresponding to their order from center to boundary. Build from the inside out. We succeeded with only a few missteps; the wonderfully engineered Zome system forces many of the decisions.

July 18 The Math Forum @ Drexel - Suzanne Alejandre

Suzanne originally made this page to help visitors new to the Math Forum be able to find resources: Making Effective Use of Math Forum Resources. One exciting new feature of the Math Forum's Problems of the Week subscription service is that starting in the fall email access for students will no longer be required for online submissions. All of the interaction will be web-based.

July 18 Presentation - Craig Morgan

Craig introduced the group to

[view PowerPoint in html] [download PowerPoint file]

July 19 Car-Boat Problem - Gail Burrill

Gail will present a question about the Car-Boat Problem using TI-Nspire.

July 20 Uganda - Richard Opaka Awichi

Richard presented Pedagogy in Uganda [view PowerPoint in html] [download PowerPoint file].

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© 2001 - 2018 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 program support provided by Math for America

This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.