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
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
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
• 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
COURSE ACTIVITIES/ASSIGNMENTS:
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).
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.
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.
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).
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.
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).
EVALUATION
AND GRADING:
•
•
•
Points
Group/Class Work: There will be Possible
opportunities
for students to work in
Midterm learning groups to solve problems.
150
cooperative
Work will be evaluated either
Comprehensive
Finalassignments. 150
individually
or as group
Group Work (in class)
40
There
will be a midterm during the semester
Homework
50 and a comprehensive final exam.
Portions
both the midterm
exam and the
GroupofConstruction
Project
40 final exam will be take-home.
Group Problem-Solving
Project
Construction
Project: Students
will work 70
in cooperative groups to solve
Total Possible
Pointsproblems. Members
500 of the group will be randomly
geometry
construction
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.
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
Algebra
Geometry
Measurement
Data Analysis and Probability
Problem Solving
Reasoning and Proof
Communication
Connections
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.

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.
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).
Math 3395
Koppelman
HW # 1
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.
b.
c.
d.
e.
f.
g.
Construct a triangle ABC whose sides all have different lengths.
Construct the midpoints M, N, and P of sides AB , AC , and BC respectively.
Construct line segments CM , BN , and AP .
CM , BN , and AP intersect at a point. Label the point of intersection T.
Display the lengths of segments AT and TP .
Make a conjecture about how the lengths of AT and TP are related.
Check to see if a similar conjecture holds for (i) BT and TN and (ii) CT and TM .
A
M
N
T
B
C
P
3. Review the Prior Knowledge handout and identify any questions you would like to
ask about the items on it.
Practice with GSP
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?