Charles Koppelman Office:Math and Statistics, 018 Phone:470-578-2051 Email:ckoppelm@kennesaw.edu...

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Charles Koppelman

Office: Math and Statistics, 018

Phone: 470-578-2051 Email: ckoppelm@kennesaw.edu

Website: http://math.kennesaw.edu/~ckoppelm

Office Hours: Monday & Wednesday 12:00 - 1:30 Other times by appointment

Math 3395 - GEOMETRY

Be sure to go on D2L or on my website (http://math.kennesaw.edu/~ckoppelm)

and download and print a copy of the syllabus.

We have been asked to keep copying to a minimum and have been told not to print syllabi.

Required Materials

• Geometer’s Sketchpad (Version 5) computer software, student edition, published by McGraw-Hill (previously Key Curriculum Press). A single-user license is available to purchase from the bookstore for $43.70.

Or you can purchase it on line at

https://www.mheonline.com/program/view/2/16/2647

Required Materials

• Geometer’s Sketchpad (Version 5) computer software, student edition, published by McGraw-Hill (previously Key Curriculum Press). A single-user license is available to purchase from the bookstore for $43.70.

Or you can purchase it on line at

https://www.mheonline.com/program/view/2/16/2647

Recommended Materials

• Essentials of Geometry for College Students by Margaret Lial, et al 2nd edition; ISBN 978-0201748826

• Scientific calculator, preferably a TI-84 Plus graphing calculator

• Compass, straightedge

• Flash drive (or other method for saving your files)

COURSE ACTIVITIES/ASSIGNMENTS:

• Homework will be assigned most days. Assignments will be collected and returned the next class meeting. Most HW assignments have a Geometer’s Sketchpad component that must be sent to me electronically. All homework handouts and full solutions will be posted on D2L and on my website (math.kennesaw.edu/~ckoppelm).

• Group/Class Work: There will be opportunities for students to work in cooperative learning groups to solve problems. Work will be evaluated either individually or as group assignments.

• There will be a midterm during the semester and a comprehensive final exam. Portions of both the midterm exam and the final exam will be take-home.

• Construction Project: Students will work in cooperative groups to solve geometry construction problems. Members of the group will be randomly selected to demonstrate the group’s solution in an interview with me and to provide an oral proof that the solution is valid (Details will be provided).

• Group Problem-Solving Project: Students will use Geometer’s Sketchpad to form conjectures about the answers to various non-standard geometry problems representing the major areas of study in the course. Students will work cooperatively to present written and computer generated solutions verifying their conjectures.

• Homework will be assigned most days. Assignments will be collected and returned the next class meeting. Most HW assignments have a Geometer’s Sketchpad component that must be sent to me electronically. All homework handouts and full solutions will be posted on D2L and on my website (www.science.kennesaw.edu/~ckoppelm).

• Group Problem-Solving Project: Students will use Geometer’s Sketchpad to form conjectures about the answers to various non-standard geometry problems representing the major areas of study in the course. Students will work cooperatively to present written and computer generated solutions verifying their conjectures.

EVALUATION AND GRADING: Possible Points

Midterm 150Comprehensive Final 150Group Work (in class) 40Homework 50Group Construction Project 40 Group Problem-Solving Project 70Total Possible Points 500

No Class (Labor Day) Monday, September 2

Deadline for construction project Monday, September 30

Midterm Wednesday, October 7

Last day to withdraw without penalty Friday, October 11

No Class (Thanksgiving) Wednesday, November 27

Group Problem Solving Project due Monday, December 2

Last day of class Wednesday, December 4

Final Exam Wed. December 11, 1:00–3:00

PURPOSE/RATIONALE:

One purpose of this course is to prepare prospective 5-8 teachers and 7-12 teachers to become effective facilitators in the teaching of geometry.

National Council of Teachers of Mathematics (NCTM)

Principles and Standards for School Mathematics

http://standards.nctm.org/document/chapter1/index.htm

Content Standards: Process Standards:

Number and Operations Problem SolvingAlgebra Reasoning and ProofGeometry CommunicationMeasurement ConnectionsData Analysis and Probability Representation

The Burning House Problem

A man is walking in an open field some distance from his house. It’s a beautiful day and he is carrying an empty bucket with him to collect berries.

A man is walking in an open field some distance from his house. It’s a beautiful day and he is carrying an empty bucket with him to collect berries. Before long, he turns around and, to his horror, sees that his house in on fire. Without wasting a moment, he runs to a nearby river (which runs in a straight line from east to west) to fill the bucket with water so that he can run to his house to throw water on the fire. Naturally, he wants to do this as quickly as possible.

A man is walking in an open field some distance from his house. It’s a beautiful day and he is carrying an empty bucket with him to collect berries. Before long, he turns around and, to his horror, sees that his house in on fire. Without wasting a moment, he runs to a nearby river (which runs in a straight line from east to west) to fill the bucket with water so that he can run to his house to throw water on the fire. Naturally, he wants to do this as quickly as possible. Describe how to locate the point on the river bank to which he should run in order to minimize his total running distance (and time).

1. Conduct a Burning House simulation using Geometer’s Sketchpad in which the man is further from the river than the house. Locate the optimum point on the river. Either verify a conjecture that was discussed in class, or formulate a new conjecture about where the optimum point is located. 2. Perform the following construction using Geometer’s Sketchpad. When you finish,

your construction should look like the one below (but with measurements displayed). Please email your construction as an attachment to ckoppelm@kennesaw.edu by noon on the day of our next class. Please include your name in your email message.

a. Construct a triangle ABC whose sides all have different lengths.

b. Construct the midpoints M, N, and P of sides AB , AC , and BC respectively.

c. Construct line segments CM , BN , and AP .

d. CM , BN , and AP intersect at a point. Label the point of intersection T.

e. Display the lengths of segments AT and TP . f. Make a conjecture about how the lengths of AT and TP are related.

g. Check to see if a similar conjecture holds for (i) BT and TN and (ii) CT and TM .

3. Review the Prior Knowledge handout and identify any questions you would like to ask about the items on it.

Math 3395 HW # 1 Koppelman

1. Construct a line segment and label its endpoints A and B.

2. Construct a line perpendicular to segment AB at point A.

3. Construct a point somewhere on the line and label it point P.

4. Construct line segment PB.

5. Construct the midpoint of segment PB and label it point M.

6. Construct segment AM.

7. Display the lengths of AM and PB and make a conjecture about how the lengths are related.

8. Move point P along the line. Is your conjecture still valid?

Practice with GSP

Charles Koppelman Office:Math and Statistics, 018 Phone:470-578-2051 Email:ckoppelm@kennesaw.edu...

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