Enrollment and Credit Options: Mathematics teachers who have completed an undergraduate major in mathematics or mathematics education or the equivalent can enroll in this module for either one-quarter unit of University of Illinois Graduate Credit or three Continuing Education Units. Within 5 working days of completion of enrollment, these teachers will be issued a log-in and password that will provide them access to the Module Working Environment (also referred to as ClassComm) where they submit required assignments and retrieve the graded results. They will also receive an 800-number for instructional and technical support.

Mathematics teachers may also enroll as MTL Guests (free). Guest registration gives teachers access to the instructional materials but no access to instructional support. including homework submission and grading or use of the MTL 800-number and e-mail help systems.

Teachers enrolled for graduate credit must complete and submit the four assignments for the module described in Steps #1 through #7 below and an approved Final Project (See Step #8 below for more details about this requirement.)

Teachers enrolled for Continuing Educations Units are not required to complete the Final Project but they are required to complete and submit the assignments for the module described in Steps #1 through #7 below. Continuing Education Units are not recorded on a University transcript; However, the University of Illinois Division of Academic Outreach provides a Letter of Completion for a teacher who completes a module for continuing education units.

Mathematics teachers may also enroll as MTL Guests (free). Guest registration gives them access to instructional materials but no access to instructional support, or to the Module Working Environment (also referred to as ClassComm).

Estimated time requirements for completion of the module: We estimate that the work for this module will take participating teachers an average of about 25 hours to complete with a range of about 20 to 30 hours. Technically, you have a 3-month enrollment period to complete the module after you enrollment is complete and you have been sent your log-in and password and 800-number Help information. However, we recommend that you have as a goal to complete the module in eight weeks or less. That should be possible even when you are teaching if you set aside three or four hours each week to work on the module.

After you have registered for Module 15 proceed as follows: Obtain a copy of the textbook Mathematics For High School Teachers by Usiskin, Peressini, Marchisotto and Stanley. Although you will be using only two chapters of this book for this module, this book is an excellent resource for your professional library or for your school library. Although there is a place on the publishers web site for requesting an examination copy, such copies are sent only to college instructors of courses for which the text may be adopted.

After you have obtained a copy of the textbook, proceed to complete the following steps:

Comments on Step #1: This part of the unit explores the concept of distance in several different contexts, some very familiar and some very unusual such as taxicab distance in the plane and the Hamming distance, which is very useful in codes and data transmission.

STEP #2: Complete Unit 1, Part 2: Minimum distance problems in plane geometry. Complete Part 2 of Assignment 1.1 according to the directions at the beginning of that assignment. Save a copy of your completed  Part 2 of Assignment 1.1 to the Module 15 Assignments folder on your hard drive. Then submit Part 2 of Assignment 1.1 by logging in to the Module Working Environment (also referred to as ClassComm) for Module 15 and use the Upload Homework button in the Homework section on the left panel of the page.

Comments on Step #2: This part of the unit discusses a number of very interesting minimum distance problems in plane geometry including Hero's Problem, which has applications to light reflection, and the Fermat and Fagnano problems. The internet-based dynamic and interactive sketches add a "hands on" aspect that make the text discussion come to life.

Note: Facility with geometric construction software such as Geometers Sketchpad is essential for creating some of the sketchs required in this part of Assignment 1.1 as well as in the remaining assignments for this module. If you do not have this prerequisite skill, you can acquire it either completing Module 4: Using the Geometer's Sketchpad for graduate or continuing education credit, or by registering as a Guest (free!) for that module and completing it on your own. If you have used Geometer's Sketchpad in the past but currently do not use it frequently, we strongly recommend that you refresh your background by completing Module 4 as an MTL Guest.

Comments on Step #3: Section 10.1.1 develops the axioms for planar area that are used to establish the area formulas for geometric figures in this and subsequent sections. The internet-based content compares the modern and classical approaches to the determination of the area of geometric formulas.

Sections 10.1.2 continues the development of area formulas for polygonal figures in the plane including Hero's formula and a variety of other formulas related to various triangle congruence tests in plane geometry.

Comments on Step #4: Archimedes applied the Method of Exhaustion to determine the exact area of a variety of geometric figures in the plane including circles and parabolic sections. Section 10.1.4 describes Archimedes' development of of the formula for the area and circumference of a circle and the determination of the value of Pi. The internet-based content explores the development of the Method of Exhaustion in calculus and also shows the very clever approach used by Archimedes to find the area of parabolic section. You will definitely learn some new and interesting things about parabolas here!

Comments on Step #5: Sections 10.2.1 develops the axioms for volume that are used to establish the volume formulas for geometric solids Section 10.2.2 applies these axioms to develop the volume formulas for all of the usual polyhedral solids. Cavalieri's principle, the main new axiom for volume, is discussed in the problems and through the internet-based resources of this unit.

Comments on Step #6: Section 10.2.3.develops the volume formulas for curvilinear solids such as cylinders, cones and spheres and Section 10.3.1 develops the corresponding formulas for surface area. The internet based materials develop related history and mathematical contents including Archimedes' famous result relating both the volume and surface area of a sphere and its circumscribing cylinder in the ratio 2:3.

If you are enrolled for Continuing Education Units, you have just completed the module. Congratulations!

You have been or will be sent feedback on your four assignments by e-mail and/or your graded assignments will be returned through the MTL Module Working Environment.

After all of these assignments have been completed, submitted and graded, the University of Illinois Division of Academic Outreach will send you an official letter of completion for the module. There is no transcript record for Continuing Education Units as there is with undergraduate or graduate credit, so this letter will serve as your proof of completion.

Those of you enrolled for graduate credit still need to complete an approved Final Project. Go to Step 7 to find out how to do that.

STEP #7: Propose and complete an approved Final Project consisting of developing a classroom unit for one of your classes based on information and techniques related to the content of this module.

Final Project Topic: You are given a great deal of latitude in the choice of topic for this unit because we want the choice to reflect your teaching situation and your interests. We require only that the unit is based on the module. Of course, this module is written for teachers and your final project is for high school students, so the level and emphasis of your final project will likely be different than what is found in the module.

Required Final Project Proposal: After you have selected the topic for your final project, compose an e-mail message describing in a paragraph or two how you want to develop your topic, and send it to us to us in an e-mail message at: geomForm@mtl.math.uiuc.edu. We will respond with suggestions or ask for further explanation. Once your final project plan is approved, you can proceed with the development of the project.

Details about the Final Classroom Project: Your final project should be a classroom unit that might require 1.5 - 2.5 class days to discuss in class. It must include a lesson plan, any necessary student worksheets or handouts and any electronic documents for classroom demonstrations that you develop for the project. The project should be documented well enough so that another teacher can use it without further explanation. If practical, we would also like you to teach and evaluate the unit as part of your report, but that is not an absolute requirement. The final project will count for at least one-fourth of your final grade in the module, so it should reflect a corresponding effort and time commitment.

When you have completed your Final Project, submit all documents electronically through the MTL Module Working Environment. Also, submit a print copy and a floppy disk copy of all Final Classroom Project materials to:

Professor Tony Peressini, Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801.

You are done! The Math Teacher Link instructional staff will review and provide feedback on your assignments and Classroom Project.