
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 5minute madness presentation  Jim King
Summary:
Jim presented Alphabet Soup.
July 3 Tour  Carol Hattan
Summary:
Carol gave a brief overview of the PCMI@MathForum site using the Getting Started page.
July 5 UW Credit  Jim King
Summary:
Jim explained the UW credit and referred to this UW Credit FAQ.
July 5 Lessons Using Google Earth  Richard Stewart
Summary: 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
Summary: Texas Instruments has funded the writing of high school level
mathematical activities to accompany the CBSTV 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: http://www.cbs.com/primetime/numb3rs/ti/. 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: town_math@yahoo.com
July 9 Parade Songs
Let's sing:
July 9 Kitchen Table  Steve Phelps
Summary:
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 bestknown 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 http://www.chartwellyorke.com/cabri3d/demo.html in order to manipulate the sketches in the powerpoint presentation, as well as the Cabri3D files.
files to download:
HaroldScottMacDonaldCoxeter.ppt
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 popup 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
 Show participnts how to access the Exeter problem sets.
 Do a lightning demo of the free geometry program, in particular, the nonEuclidean program.
July 12 Stella  Ralph Polley
You can purchase or download a trail copy of Stella at: http://www.iseesystems.com/
Apparently Vensim is no longer free but you can purchase or download a trial copy: http://www.vensim.com/download.html
July 12 Sharing Math Songs  Joyce Frost
Sharing math songs with students can be a nice icebreaker 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 trichairs of the 46th Northwest Mathematics Conference in Bellevue, Washington, October 1113, 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 MathGrad.com 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  PodcastPeople.com
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 K12 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 http://www.unitedstreaming.com/home/aboutus.cfm.
July 17 Truncated 120cell  Brian Hopkins
The giant Zome model living on Table 3 is a "truncated 120 cell." A
120cell 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 120cell 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, 6fold 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,
http://www.georgehart.com/zomebook/zomebook.html). 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 http://www.zometool.com/modelofmonth_407.html (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 webbased.
July 18 Presentation  Craig Morgan
Craig introduced the group to
[view PowerPoint in html] [download PowerPoint file]
July 19 CarBoat Problem  Gail Burrill
Gail will present a question about the CarBoat Problem using TINspire.
July 20 Uganda  Richard Opaka Awichi
Richard presented Pedagogy in Uganda [view PowerPoint in html] [download PowerPoint file].
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 program support provided by Math for America
This material is based upon work supported by the National Science Foundation under DMS0940733 and DMS1441467. 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.
