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Charles Koppelman

Math 3395 - GEOMETRY. 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.

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Charles Koppelman

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  1. Math 3395 - GEOMETRY 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

  2. 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.

  3. 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

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

  5. 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 • Compass, straightedge • Flash drive (or other method for saving your files) • 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

  6. COURSE ACTIVITIES/ASSIGNMENTS:

  7. 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).

  8. 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.

  9. 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.

  10. 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).

  11. 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.

  12. EVALUATION AND GRADING: Possible Points Midterm 150 Comprehensive Final 150 Group Work (in class) 40 Homework 50 Group Construction Project 40 Group Problem-Solving Project 70 Total Possible Points 500 • 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 (www.science.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.

  13. 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.

  14. 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 Solving Algebra Reasoning and Proof Geometry Communication Measurement Connections Data Analysis and Probability Representation

  15. 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. 

  16. 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. 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.

  17. 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. 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).

  18. Practice with GSP • Construct a line segment and label its endpoints A and B. • Construct a line perpendicular to • segmentAB at point A. • Construct a point somewhere on the • line and label it point P. • Construct line segment PB. • Construct the midpoint of segment PB and • label it point M. • Construct segment AM. • Display the lengths of AM and PB and • make a conjecture about how the lengths • are related. • Move point P along the line. Is your • conjecture still valid?

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