Geometry Syllabus and Topics

Geometry Content Refresher for Teachers
(MTE 505 - 3 graduate semester credits)

COURSE SYLLABUS

CATALOG DESCRIPTION:

MTE 505 is designed as a thorough refresher course of the Geometry mathematical content that conforms to the National Council of Teachers of Mathematics (NCTM) standards for middle and secondary education.

It demonstrates the use of appropriate technologies and a background in Algebra is recommended. This course may not be applied to existing graduate programs at Converse College.

DVDs, TEXT and MATERIALS:

Four DVDs are provided that contain the instruction for this course and students must have access to a DVD player connected to a television or one that installed in a PC.

Geometry: Applying, Reasoning, Measuring. Larson, Boswell, Stiff, McDougal Littell.

In addition, four Practice Problem Sets are located on the course web site.

GRAPHING CALCULATOR AND SOFTWARE:

The use of a graphing calculator is required. While participants may use any graphing calculator, the instruction on the DVDs uses the TI-83. The TI-84 is very similar and can be used as well.
Knowledge and competence for use of other graphing calculators will be the sole responsibility of the participant.

The Geometer’s Sketchpad will be used as a demonstration tool throughout the course. This is an excellent opportunity for the participant to learn how to implement this interactive program in a geometry class. While you do not need this software to complete this course, you can purchase the Geometer’s Sketchpad from http://www.keypress.com/

COURSE REQUIREMENTS:

This course will be offered through Distance Education. Participating teachers will receive four DVDs to view at their convenience, taking up to nine months to complete all requirements. There are no scheduled class sessions or meetings. There is an Internet web site that contains practice problems, four quizzes - one for each DVD and a cumulative Final Examination.

1. The participant must view the four DVDs and supply a written statement that this has been accomplished. (Evaluation - Statement must be included with the End of Course packet - without it no credit is to be awarded.)

2. Participants must complete the four Practice Problem sets that are provided on the course web site. (Evaluation - The Practice Sets showing student work are submitted in the End of Course packet - without them, no credit will be awarded.)

3. Each of the four DVDs will have an accompanying quiz posted on this web site. The participant must complete each of these quizzes online and also submit printed copies of each quiz that shows their work in the end of course packet. (Evaluation - Each of the four quizzes will count 14% of the final grade.)

4. There will be a cumulative final examination. The participants will complete the final exam in the presence of a school or district administrator, have the administrator validate it, and then the participant submits it in the End of Course packet. The participants will also enter their answers to the exam online. (Evaluation – The final examination will count 46% of the final grade.)

GRADING:

Each question, whether a quiz question or a final exam question, will count as one point. There will be four quizzes consisting of six questions and one cumulative final exam consisting of twenty questions. Based on these forty-four questions, the grading scale is listed below. No other grade is given to this course. If you do not complete the course a grade of F is awarded.

A = 44-42 correct          C+ = 33-32 correct
A- = 41-40 correct         C = 31-30 correct
B+ = 39-38 correct        C- = 29-26 correct
B = 37-36 correct          F = 25 or less correct
B- = 35-34 correct

COURSE TOPICS

SESSION #1
Basics of Geometry, Reasoning and Proof, Perpendicular and Parallel Lines
1. Patterns and Inductive Reasoning
2. Points, Lines and Planes
3. Segments, Angles, Bisectors, Angle Pairs
4. Introduction to Perimeter, Circumference and Area
5. Conditional and Biconditional Statements
6. Deductive Reasoning
7. Proving Statements about Segments and Angles, Lines and Angles
8. Proof and Perpendicular Lines
9. Parallel Lines and Transversals in the Coordinate Plane
10. Proving Properties of Parallel Lines

SESSION #2
Congruent Triangles and Properties of Triangles and Quadrilaterals
1. Triangles, Angles and Congruence
2. Shortcut methods for Congruence of Triangles
3. Using Congruent Triangles
4. Isosceles, Equilateral and Right Triangles
5. Coordinate Proof and Triangles
6. Perpendiculars and Bisectors of Triangles
7. Medians and Altitudes of Triangles, Midsegment Theorem
8. Inequalities and Indirect Proof in One and Two Triangles
9. Polygons, Properties of Parallelograms, Proving Quadrilaterals are Parallelograms
10. Special Parallelograms: Rhombuses and Squares
11. Trapezoids, Kites and Special Quadrilaterals

SESSION #3
Transformational Geometry, Similarity, Right Triangles and Trigonometry, Rigid Motion in the Plane, Reflections, Rotations
1. Translations and Vectors
2. Glide Reflections and Compositions, Frieze Patterns
3. Tessellations
4. Ratio and Proportion, Problem Solving with Proportions and Similar Triangles
5. Similar Polygons, Similar Triangles and Proof
6. Dilations
7. Similar Right Triangles
8. Pythagorean Theorem and its Converse
9. Special Right Triangles, Trigonometric Ratios, Solving Right Triangles
10. Vectors