
Park City Mathematics Institute
High School Teacher Program
Morning Shorts

[David K]
[Troy]
[Cal]
[David H]
[John]
[Nicole]
[Nancy]
[James]
[Peg]
[Joyce]
July 8 Cabri Junior  David Kapolka
Summary: I demonstrated the features of Cabri Jr. to the HSTP group. I compared the features to those of Geometer's Sketchpad and Cabri for computer. I demonstrated several sketches that I had prepared and showed participants the pull down menus similar to the computer software. They found the use of Cabri for TI83+ Silver Edition a very inexpensive alternative to a computer and computer lab.
Download Cabri Junior App and the Cabri Junior GuideBook [PDF].
July 9 Digital Pictures and Dynamic Functions in Geometer's Sketchpad  Troy Jones
Summary: I did a short demonstration on taking digital pictures and importing them into Geometer's Sketchpad and then fitting a dynamic function to the picture. We took a picture of a standing sine wave and a water fountain.
Several participants requested an evening session to learn the basics of creating a dynamic function and importing digital pictures into Sketchpad.
July 10 MT Maple  Cal Armstrong
Summary: Maple TA is an online mathematics assessment tool (web based) that allows you to program random variables so that each student's assignment is unique. Proper mathematical notation can be written and the program evaluates it either numerically (within an error interval, if necessary) or algebraically (so x^2 + 5x + 6 is equivalent to (x+2)(x+3) )Sketchpad sketches, image maps and Java applets can also be introduced into the questions. If you would like to trial MapleTA, please email me! You can find more info at http://www.maplesoft.com/mapleta
I also mentioned the Smartboard, an interactive whiteboard that interfaces with your laptop & projector. Grants are available at http://www.smarterkids.org/
July 11 Fathom  David Hernandez
Summary:
The Fathom demonstration focused on an activity from the Data in Depth workbook, entitled "Area and Perimeter: A Study in Limits", p. 111113. It is an excellent one because it explores the relationship between area and perimeter of 200 randomly generated rectangles. The results will astound anyone who performs this activity! It is also a good to use to demonstrate the power of Fathom to first time users.
July 14 ONMath  John Mahoney
Summary:
Online Journal of School Mathematics
NCTM's new onlineonly school journal presents ideas for teaching and learning mathematics at all grade levels.
July 15 Communicator  Nicole Benevento
Summary:
Nicole presented an idea for using what she calls a "communicator" made from a plastic sheet cover.
July 16 short presentation  Nancy Wilson
Summary:
This short discussed a project related to volume and surface area. The introduction activity included finding the volume of a "Mystery Vessel". The project itself requires students to determine the volume and surface area of some irregular solid. The purpose is to help studnets build the accucumlation idea that is a major component of calculus.
(password required to download three MS Word documents)
Volume Project
Grade Sheet for Volume Project
A Mysterious Vessel
July 16 Helping Students Understand Proof  James Stallworth
Summary:
To help students understand proof, I have used two videos to allow students to become detectives. View this page for more details.
July 17 Volume of a Cone Activity  Peg Cagle
Summary:
The maximum cone is an extension of the old classic open box problem. In that scenario, students are asked to determine the square that should be cut from each corner of a rectangular sheet of paper to yield the box with the maximum volume. With the cone, they are all given a circle of equal radius and are asked to generate the cone with the maximum value by deciding what size sector to remove. The students made predictions, took capacity measurements (in M & M's), wrote equations and analyzed their results using regressions to arrive at the answer.
July 16 Hot Air Balloon  Joyce Frost
Summary:
Robin Washam did a presentation on creating hot air balloons from tissue paper at a Northwest Mathematics Interaction workshop a few years ago in Bellevue, Washington. This is a project that she uses with her AP Calculus students. These documents are ones that I have prepared to use with my Math Analysis classes and include the information sheet and chart for students to fill in, an assessment piece, and pictures of student balloons.
Students start by choosing a function which has roughly the shape of half of the cross section of a hot air balloon over the interval from x = 0 to 11 or 12. The students then calculate the corresponding y values at one inch intervals in order to compute the circumference at each of these points and determine the width of the eight panels. They also compute the distance between y values using the distance formula to approximate the curve between these points. This allows them to determine the length of the panels between each of the key points. Students then create a pattern piece which has the linear dimensions tripled. Their balloons are created using tissue paper and glue. The balloons are then flown using hot air generated from a small portable barbeque.
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IAS/Park City Mathematics Institute is an outreach program of the School of Mathematics at the Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540
Send questions or comments to: Suzanne Alejandre and Jim King

This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
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