Part One: Take Home

Midterm Exam 
Part One: Take Home
(given October 3rd --- due October 10th)

Part A: Reaction Paper

Reaction Paper Preparation

Read over the reaction papers you have already written this semester in both EMAT 4680 and your discussions in EMAT 3500
Go to NCTM's site: http://standards.nctm.org to see the E-Standards
Select the full-text of the Principles and Standards
Select the Standards for Grades 9-12
Select the Geometry Standard

Since you have already read this standard, take a minute to skim over it and refresh your memory. I would then like you to focus in on the paragraph at the bottom of page 311. It begins "One of the most important challenges in mathematics teaching..."
Continue reading through the "hypothetical situation" that the authors pose to support their writings
Make sure to click on the icon out to the left to investigate with the E-example

Reaction Paper
Write a 3 - 5 page typed paper (double spaced with font size of twelve) in which you reflect on the above reading, the portion of the Geometry Standard it represents, the Technology Principle, the Reasoning and Proof Standard, the deVilliers reading on functions of proof, any other readings you feel apply, and your experiences in this course so far.
Cite your references!!

Note: This Paper is due at the beginning of class on October 10, 2000...no late papers will be accepted. Please have a hard copy ready to give to your instructor at the beginning of class and place a copy of the file in your class folder.

Part B: Mathematical Investigation

Below you will see a table in which you are assigned a new triangle center to investigate.
You may work with all four people in your team and turn in one write-up (one for the entire team),
or you may pair up and thus turn in two write-ups (one for each pair),
or you may work individually and turn in your own write-up...Get the idea?

Your write-up should include, but is not limited to:

Definition and construction of your triangle center
Link to the GSP Construction
Explorations of the relationships in the triangle with respect to your center
Several conjectures about these relationships
The proof of one of your conjectures
Brief history of the problem or information about the person your center is named
Link to more information about your center
Extension(s) of this investigation that you might like to explore

Triangle Center	Team
NINE-POINT CENTER The center of the nine-point circle.	Lindsay Allen Lee Nguyen Katie Gerker Kelly Samuelson
FEUERBACH POINT The point of tangency of the nine-point circle and the incircle.	Megan Barnett Raju Patel Corrie Collier Kristen Robinson
NAPOLEON POINTS Suppose ABC is a triangle. Let points D,E,F be points for which the threetriangles DBC, CAE, ABF are equilateral. Let G = center of triangle DBC, H = center of triangle CAE, I = center of triangle ABF. The lines AG, BH, CI meet in the first Napoleon point.	Doris Daniel Rebecca Parker Matt Fiedler Niki Satchwell
SCHIFFLER POINT Write I for the incenter; the Euler lines of the four triangles IBC, ICA, IAB, and ABC concur in the Schiffler Point	Ava Antone Natalie Smith Elizabeth Jones Amy Terry
FERMAT POINT In the plane of any triangle ABC, let A'BC = the equilateral triangle constructed on side BC, AB'C = the equilateral triangle constructed on side CA, ABC' = the equilateral triangle constructed on side AB. The lines AA', BB', CC' meet in the Fermat point	Mary Beth Miles Julie Terry Matthew Moon Kristen Thomas

Note: Please post this assignment to your web page by Tuesday, October 10th at 8:00am! Make sure that all the names of the people you worked with are documented on your write-up. Thanks!!

HAVE FUN!!

I CAN'T WAIT TO SEE YOUR WORK!!

I KNOW IT IS GOING TO BE REFLECTIVE, THOROUGH, CREATIVE, MATHEMATICALLY RICH, AND VERY INTERESTING :)

Triangle Center

Team