Math 409 (Topics in Geometry for Secondary and Middle School Teachers)
Spring 2013

General Information | Homework Assignments | Midterm and Final Exam Information | Links

Now available: Final Exam review sheet.

Pre-final exam office hours:

• Friday 5/10 (Stop Day): 2-4 PM
• Monday 5/13 (Exam day): 10 AM-noon

The Basics

• Meeting times: Tue/Thu, 1:00-1:50 PM, 301 Snow
• KU course line number: 53481
• Instructor: Prof. Jeremy Martin
  
  623 Snow, 864-7114
  (The best way to contact me: send me e-mail!)
• Office hours: Tue/Wed, 2-3 PM or by appointment
  
• Syllabus (1/18/13)
• Prerequisites: Math 122. Students in 409 should enroll simultaneously in Math 410 (Mathematics History for Secondary and Middle School Teachers).

Important Dates

• Monday 1/28: Last day to add/change sections
• Monday 2/11: First Period Drop ends
• Thursday 3/14: Pi Day; Midterm exam
• Monday 3/18-Friday 3/22: Spring Break
• Monday 4/22: Second Period Drop ends
• Friday 5/10: Stop Day
• Monday 5/13: Final Exam (1:30-4:00, 301 Snow)

Required Materials

• Bring a ruler and compass to class.
• All students should purchase a copy of the software Geometer's Sketchpad. The cost is $60 for the full version, or $10 for a one-year license.
• If possible, install Sketchpad on your laptop or tablet and bring it to class every day.

Here is the master problem list, which I will update frequently (last update: (May 1). I'll assign some of these as homework, and you'll work on some of them in groups in class. You can use the other ones for review. I will be adding problems to the list as the semester progresses.

Homework is due every Tuesday at 5:00 PM. No late homework will be accepted. If you have a conflict which prevents you from turning the homework in on time, let me know before the deadline.

Written assignments should be submitted to me in class, left in my mailbox in the Math Department office (405 Snow) or brought to my office (623 Snow). When you write proofs, you should refer to the master list of axioms, definitions and theorems (last updated 2/12/13), and cite (by number) every fact or definition that you use. Here is a short list with the same numbering, but no proofs --- just axioms and theorems.

Sketchpad assignments should be e-mailed to me as attachments. If you submit them early, I will try to respond as quickly as possible so that you can fix mistakes. You can keep re-submitting sketches until the weekly deadline of Tuesday at 5 PM. Here is the grading scale for Sketchpad assignments:

• 5/5: Construction works, and I can't mess it up no matter how hard I try
• 4/5: Construction works in most cases, but after some effort, I found a way to mess it up
• 3/5: Construction works in some cases, but I found an easy way to mess it up
• 2/5: Construction doesn't work, but I think you've made partial progress toward a solution
• 1/5: Construction doesn't work, and I don't see any partial progress
• 0/5: No construction submitted

Re-submitting a sketch (before the deadline) can only increase your grade on it.

Homework #1 (due Tuesday, January 29):

• Purchase and install Geometer's Sketchpad. Work through the introduction handout to become familiar with what the software does. (You don't need to turn anything in.)
• Ruler/compass constructions: RC 3, RC 9, RC 10. Each construction should be accompanied by an explanation of the steps you have taken and why the construction works.
• Sketchpad problems: SA 2, SA 3, SA 4. For SA 2 and SA 3, use only the Point, Circle and Line tools---do not use any of the shortcuts from the Construct or other menus.

Homework #2 (due Tuesday, February 5):

• Read these notes on axiom systems.
• Ruler/compass constructions: RC 6, RC 7, RC 8. Each construction should be accompanied by an explanation of the steps you have taken and why the construction works.
• Sketchpad problems: SA 6, SA 7, SA 8. Do not use any of the circle or arc constructions from the Construct menu.

Homework #3 (due Tuesday, February 12):

• Euclidean geometry proofs: EG 6, EG 11. When you write proofs, you should refer to the master list of axioms, definitions and theorems, and cite (by number) every fact or definition that you use.
• Sketchpad constructions: SA 10, SA 11, SA 12. It is now officially OK to use the Construct menu.

Homework #4 (due Tuesday, February 19):

• Euclidean geometry proofs: EG 8, EG 14. Again, you should refer to the master list of axioms, definitions and theorems, and cite (by number) every fact or definition that you use.
• Sketchpad constructions: SA 18, SA 20.
  Note on SA18 (2/17/13)

Homework #5 (due Tuesday, February 26):

• Euclidean geometry proofs: EG 19, EG 20. (Postponed until 3/5)
  
• Sketchpad constructions: SA 21, SA 24.

Homework #6 (due Tuesday, March 5):

• Euclidean geometry proofs: EG 19, EG 20.
  (Be sure to obtain the new versions of the axioms and homework problems, updated 2/18/13.)

Homework #7 (due Tuesday, March 12):

• Euclidean geometry proofs: EG 21, EG 22, EG 23. (This last one should look familiar! This is the promised redo --- if you write a careful proof with all steps justified and earn full credit, then you'll also get retroactive full credit on SA11.)
• Sketchpad construction: SA 22. (This doesn't have much to do with things we've been talking about --- but it is really neat.)

Homework #8 (due Tuesday, April 2):

• Written problems: TG 1, TG 2, TG 3, TG 4, TG 5. Be sure to obtain the latest revision of the master problem list. The notes on transformational geometry will be helpful. For TG 3 and TG 4, your answer should use the standard notation for transformations.
  Clarification on TG 1 and TG 2: You only have to list transformations that are isometries.

Homework #9 (due Tuesday, April 9):

• Written problems: TG 6, TG 8, TG 9.

Homework #10 (due Thursday, April 18):

• Written problems: TG 11, TG 12, TG 13.

Homework #11 (due Tuesday, April 30):

• Written problems: TG 20, PH 1, PH 2. Extra credit: TG 17. You may want to consult the notes on polyhedra.

Homework #12 (due Thursday, May 9):

• Written problems: TG 21, PH 3, PH 4. (Note that PH4 has been updated as of May 1.)

The midterm exam took place in class on Thursday, March 14. Here is midterm review information and the short list of axioms and theorems.

The final exam will take place on Monday, May 13, from 1:30-4:00 PM in Snow 301. Here is exam review information.

Course materials

• Introduction to Geometer's Sketchpad
• Notes on axiom systems
• Axioms, definitions and theorems for Euclidean geometry (with proofs and comments)
• Axioms and theorems (no proofs, just statements)
• Notes on transformational geometry (3/25/13)
• Quick reference: Notation for transformations
• Notes on polyhedra

KU links

• Math 410
• Jeremy Martin's home page
• KU Mathematics Department
• UKanTeach
• KU Registrar
• KU policies on academic honesty
• Academic Achievement and Access Center (resources for students with disabilities)