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COURSE SYLLABUS Mathematics Content Refresher

MPD505 — GEOMETRY Course Number MPD505 Course Credits 60 recertification units / certificate Course Description: This course is designed for participants who need a refresher course in Geometry, or for

new teachers who need insights, additional resources or a different perspective into the content taught in Geometry.

Text: Geometry: Applying, Reasoning, Measuring. Larson, Bosweil, Stiff. McDougal Littell. 2003

Participants, however, may use any other Geometry text. Course Videos that contain approximately 20 hours of instruction are provided for the student. Also, four corresponding Practice Problem Sets are provided to each student on the course homepage in Moodle, the learning management system for all TeacherStep® courses.

Graphing Calculator: Participants are expected to use a graphing calculator. While participants may choose

any graphing calculator, instruction and the suggested text will use the TI-83 or equivalent. Knowledge and competence for use of other graphing calculators will be the sole responsibility of participants.

Course Goals, Objectives & Outcomes 1. To refresh the participant’s content knowledge in Geometry. 2. To initiate or revitalize participating teachers’ interest in Geometry.

Course Requirements

This course is delivered online via Moodle, though participants receive four Videos to view offline as well. Moodle provides the practice problems, a short quiz for each of the course sections and a cumulative Final Exam.

1. The participant must view the four Videos before taking the quiz. 2. Participants must also complete the four Practice Problem Sets that are provided, scan (or take a

photo of) and submit their work in Moodle. Answer keys are provided, and professors are available for feedback as well.

3. Each of the four Videos / problem sets has an accompanying quiz posted, and the participant must complete each of these quizzes for grading in Moodle.

4. Participants will then complete a cumulative Final Exam in Moodle.

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Course Topics Section 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

Section 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

Section 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

Section 4 Circles, Area of Polygons and Circles, Surface Area and Volume

1. Tangents to circles, arcs chords, inscribed angles

2. Other angle relationships in circles 3. Segment lengths in circles 4. Equations of circles and locus

5. Angle measurement in polygons, area of regular polygons

6. Perimeters and areas of similar figures

7. Circumference and arc length 8. Areas of circles and sectors

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The Videos, the Practice Problem Sets and the Quizzes Begin the course by viewing Video #1, and then find Practice Problem Set #1 in Moodle, which covers the

information presented in this video. The Practice Problem Set should then be printed and completed; you are encouraged to use your graphing

calculator. Use additional sheets of paper as needed to show your work. Scan the practice sets and your work for these problems, and submit these in Moodle as a PDF, JPG or PNG.

Answers to these questions are provided in Moodle for you to check afterwards. After completing Practice Problem Set #1, complete the Quiz #1 in Moodle. Repeat this process for the remaining three Videos, Practice Problem Sets and Quizzes.

The Final Examination After completing the four quizzes, complete the Final Exam in Moodle in the presence of a library, school or

university official or administrator. If you are unable to have one of these persons proctor your exam, contact the Course Instructor to explain your situation, and an alternative person will be identified.

The Final Exam is a timed test, and you have 90 minutes to complete it. Please print, complete, and sign the Validation Statement that is located in Moodle. Students must submit an electronic copy of the completed form within the online course immediately after the student has completed the examination. The submission link for this form is located in the Final Exam bucket.

After completing your course successfully, you will receive your certificate by email and will be asked to complete a course evaluation.

Instructor Contact and Support

At any time during the course you may contact the Course Instructor via email. Contact information is provided in Moodle on your course’s homepage. The TeacherStep® Student Advisor Office is available during business hours at (864) 308–1322 or anytime at http://www.teacherstep.com/help/.

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