Download Topics: Right Triangles

Towson University
MTED 615: Geometry for Middle School Teachers
Summer 2012
The mission of teacher preparation at Towson University is to inspire, educate, and prepare
facilitators of active learning for diverse and inclusive communities of learners in environments
that are technologically advanced.
Professor
Dr. Maureen Yarnevich
Office: 7800 York Road, Room 318
Phone: 410-704-2988 (office)
Email: [email protected]
Office Hours
Available by email or call 410-992-8561
It is alright to call!!
COURSE DESCRIPTION AND RELATED OBJECTIVES
Important information about the online course format:
This course is being offered in a fully online format. That means that we will not meet on
campus at any point and everything required for the course will be done at your own computer.
You will have flexibility to complete course activities at any time or location you like, as long as
you complete the activities by each date and time indicated on assignment. You will not be
required to be at your computer at any specific times. Since this is a shorter 10 week course, you
should expect to spend 8-12 hours on course activities each week (this includes the time you
would otherwise spend “in class” as well as time you would otherwise spend on “homework”).
Finally, one additional requirement for this section of the course is that you must buy a
copy of the Geometer’s Sketchpad, Version 5.
This is an educational software package that was designed for students learning geometry from
the elementary to college level, and the majority of our course assignments will be completed via
Sketchpad. You do not need to purchase a textbook for the course, and the cost of the software
is reasonable. It can be ordered and downloaded at the following website:
http://www.keymath.com/x18112.xml
It is your choice of whether you would like to buy a permanent license for $29.95 (in which case
you can use the software indefinitely) or a 1-year expiring license for $9.95. However, I would
encourage you to buy the permanent license since I believe this software can be extremely
valuable to elementary teachers. Instructions for purchasing the software can be found in the
Course Information folder on Blackboard.
MTED 615 Online Geometry Course Syllabus
General Course Description:
Geometric vocabulary, relationships, concepts and skills in two and three dimensions
using techniques of synthetic, coordinate and transformational geometries, measurement,
and use of appropriate technology.
Objectives:
Upon successful completion of this course, students will be able to:

Apply problem-solving heuristics to solve a variety of geometric problems.

Use software to construct geometric patterns and figures, explore their properties, and
make/test conjectures.

Analyze and present convincing justifications of geometric relationships.

Classify figures in terms of congruence and similarities; describe and use conditions that
produce congruence or similarity of figures.
RESPONSIBILITIES AND ASSIGNMENTS
The following is a list and brief description of responsibilities and assignments that will help you
meet the goals of this course.
Lesson Notes (Power Point): Each topic of the course will have its own power point
presentation highlighting important concepts of the topic. Be sure to watch carefully and send
me questions about material you do not understand. Homework and quizzes will be based off the
material
Video: For each topic I have tried to include video for each topic. Videos are there for you to
watch when you need additional resources for the material.
Homework Assignments: Each topic will have a homework assignment that is required as part
of the individual topic. Homework Assignment
Quizzes: Online quizzes will be based on Power Point Lesson. They will be short quizzes that
you will be required to complete in a fixed amount of time (usually 30 minutes). You are
required to complete a quiz in one sitting so if you start a quiz you must finish it so prepare
accordingly.
Exams: Three exams will be given. You will be responsible for completing each exam during a
specified period of time and will be bound by the honor code to complete it individually
and without outside help.
Dr. Maureen Yarnevich
Towson University
2 of 8
MTED 615 Online Geometry Course Syllabus
SketchPad Activities: You will be required to use The Geometer’s Sketchpad to complete
activities. The goals of these activities are to reinforce ideas form the lecture material.
Set Puzzles: You will have a weekly set Sets Puzzle that you will be responsible. I have
included sample example puzzle in blackboard for you to look at plus you can check out the
SETS Daily Puzzle website http://www.setgame.com/set/puzzle_frame.htm
Problem of the Week: Problem of the week problems assignments will be due on Saturday of
each week. You can use the Problem of the Week discussion board thread to check your weekly
answer with classmates. I will not comment on answers in the discussion board, only your
classmates can comment on each other solutions.
Geometry Math Game: You will be required to post one geometry game that can be used by
other teachers in a geometry classroom. The game should have thorough instruction and any
class materials should be provided. If you have used the game in our own classroom you can
share any insight in how it worked for you.
EVALUATION
Your final grade will be based on your success in meeting the goal and objectives of this course
as demonstrated throughout the semester and in the course assignments and examinations. The
assignments and examinations will make up your grade according to the following percentages:
Note:
All your material must be submitted through Blackboard. It is
too hard for me to keep all of the assignments organized if they are not
submitted in blackboard. In case of emergency you can email me the
assignment but you will still be required to submit the assignment in
blackboard as well.
3 Exams (Including Final)
45%
Homework Assignments/Geometry Game
15%
Sketchpad Assignments
20%
Quizzes
10%
Set Puzzle (Always Due Friday at 11:00PM)
Problem of the Week ((Always Due Saturday
at 11:00PM)
TOTAL
5%
5%
100%
Grading Scale
94 < A < 100%
83 < B < 87%
70 < C < 77%
Dr. Maureen Yarnevich
Towson University
90 < A- < 94%
80 < B- < 83%
55 < D < 70%
87 < B+ < 90%
77 < C+ < 80%
0 < F < 55%
3 of 8
MTED 615 Online Geometry Course Syllabus
REQUIRED EQUIPMENT (NO TEXTBOOK IS REQUIRED)
Geometer’s Sketchpad, Version 5. Available for purchase online at
http://www.keymath.com/x18112.xml Please see document titled “Purchasing
Geometer’s Sketchpad” available in the Week 1 Materials folder of Blackboard.
Note: It is also important for this class that you be able to open and work with Microsoft
Word 2007 documents (those using the .docx file extension). If you have a copy
of Word 2007 or higher, this will be fine. If your version of Word is earlier, you
will need to download and install the free compatibility pack in order to access all
the course documents. You can download the compatibility pack here: Word
2007 Compatibility Pack
TENTATIVE SCHEDULE
Test 1 Material
Test 2 Material
Test 3 Material
Note
Topics Explored (may be subject to change)
Fundamental of Geometry, Introduction to Sketchpad,
Lines and Polygons,
Triangle Congruency & Similarity, Introductions to
Proofs, Right Triangles
Quadrilaterals, Circles, Tessellations
There is NOT cumulative final only 3 Individual Test
LEARNING OUTCOME FOR SPECIFIC TOPICS
INTASC PRINCIPLES
1.
2.
3.
4.
The teacher understands how learners grow and develop, recognizing that patterns of
learning and development vary individually within and across the cognitive, linguistic,
social, emotional, and physical areas, and designs and implements developmentally
appropriate and challenging learning experiences.
The teacher uses understanding of individual differences and diverse cultures and
communities to ensure inclusive learning environments that enable each learner to meet
high standards.
The teacher works with others (learners, families, colleagues) to create effective learning
environments that support individual and collaborative learning, and that encourage
positive social interaction, active engagement in learning, and self-motivation.
The teacher understands the central concepts, tools of inquiry, and structures of the
discipline(s) he or she teaches and creates learning experiences that make these aspects of
the discipline accessible and meaningful for learners to assure mastery of the content.
Dr. Maureen Yarnevich
Towson University
4 of 8
MTED 615 Online Geometry Course Syllabus
5.
The teacher understands how to connect concepts and use differing perspectives to
engage learners in critical thinking, creativity, and collaborative problem solving related
to authentic local and global issues.
The teacher understands and uses multiple methods of formative and summative
assessment to engage learners in their own growth, to monitor learner progress, and to
guide the teacher’s and learner’s decision making.
The teacher plans instruction that supports every student in meeting rigorous learning
goals by drawing upon knowledge of content, curriculum, cross-disciplinary skills, and
pedagogy, as well as knowledge of learners and the community context.
The teacher understands and uses a variety of instructional strategies to encourage
learners to develop deep understanding of content areas and their connections, and to
build skills to apply knowledge in meaningful ways.
The teacher engages in ongoing professional learning and uses evidence to continually
evaluate his/her practice, particularly the effects of his/her choices and actions on others
(learners, families, other professionals, and the community), and adapts practice to meet
the needs of each learner.
The teacher seeks appropriate leadership roles and opportunities to take responsibility for
student learning, to collaborate with learners, families, colleagues, other school
professionals (including resource personnel), and community members to ensure learner
growth, and to advance the profession.
6.
7.
8.
9.
10.
11.
The teacher views technology not as an end in itself, but as a tool for learning and
communication, integrating its use in all facets of professional practice, and for adapting
instruction to meet the needs of each learner.
NCTM PROCESS AND PEDAGOGY PROGRAM STANDARDS
1.
2.
3.
4.
5.
6.
7.
8.
Knowledge of Mathematical Problem Solving
Knowledge of Reasoning and Proof
Knowledge of Mathematical Communication
Knowledge of Mathematical Connections
Knowledge of Mathematical Representations
Knowledge of Technology
Dispositions
Knowledge of Mathematics Pedagogy
COURSE CONTENT TOPICS
Fundamental of Geometry

The student will be able to make and describe fundamental sketches. The student will also be able
to understand basic concepts such as intersect, horizontal, vertical, collinear and coplanar.
 The student will be able to define segment, ray, opposite rays, congruent, midpoint, bisect, length
and postulate. The "Ruler Postulate" and "Segment Addition Postulate" will be introduced.
Dr. Maureen Yarnevich
Towson University
5 of 8
MTED 615 Online Geometry Course Syllabus
 The students will be able to define four types of angles (acute, right, obtuse, and straight) and will
solve algebraic problems associated with them. In addition, the student will sketch these angles
using computer software and/or a protractor. The students will be able to define "angle bisector"
and solve problems using the "Angle Addition Postulate".
 The student will solve practical problems involving complementary, supplementary, and congruent
angles that include vertical angles
Lines
 The student will solve practical problems involving complementary, supplementary, and congruent
angles that include vertical angles.
 The student will be able to determine if pair of lines are parallel, perpendicular, skew or oblique.
 The student will be able to determine the measures of angles formed by parallel lines and a
transversal.
 The student will use the relationships between angles formed by two lines cut by a transversal to
determine if two lines are parallel and verify, using algebraic and coordinate methods as well as
deductive proofs.
Triangles / Polygons
 The student will be able to describe triangles based on their angles and sides. The student will also
be able to determine the measures of interior and exterior angles of triangles.
 The student will be able to apply the Isosceles Triangle Theorem in determining angle and side
measurements.
 The student, given information concerning the lengths of sides and/or measures of angles, will
apply the triangle inequality properties to determine whether a triangle exists and to order sides
and angles. These concepts will be considered in the context of practical situations.
 The student will use measures of interior and exterior angles of polygons to solve problems. Tiling
problems will be used to make connections to art, construction, and nature.
Triangle Congruency and Introductions to Proofs




Proving Triangles Congruent (SSS, SAS, ASA)
Proving Triangles Congruent (AAS, HL)
The student will be able to use algebraic properties to explain a series of logical statements
Congruent Triangles
Topics: Similarity
 The student will use proportional reasoning to solve practical problems, given similar geometric
objects.
 The student will investigate and identify similarity relationships between triangles; and prove two
triangles are similar given information in the form of a figure or statement.
Dr. Maureen Yarnevich
Towson University
6 of 8
MTED 615 Online Geometry Course Syllabus
 The student will be able to use proportional reasoning in determining segment lengths when
parallel lines are intersected by more than one transversal, and an angle bisector of a triangle
intersects the opposite side of the triangle.
Topics: Right Triangles
 The student will solve practical problems involving right triangles by using the Pythagorean
Theorem.
 The student will solve practical problems involving right triangles by using properties of special
right triangles.
Topics: Quadrilaterals
 The student will investigate and identify properties of parallelograms involving opposite sides and
angles, consecutive sides and angles, and diagonals.
 The student will be able to determine if a quadrilateral is a parallelogram
 The student will investigate and identify properties of rectangles involving opposite sides and
angles, consecutive sides and angles, and diagonals.
 The student will investigate and identify properties of rhombi and squares involving opposite sides
and angles, consecutive sides and angles, and diagonals.
 The student will investigate and identify properties of trapezoids and kites involving opposite sides
and angles, consecutive sides and angles, and diagonals.
Topics: Right Triangles
 The student will solve practical problems involving right triangles by using the Pythagorean
Theorem.
 The student will solve practical problems involving right triangles by using properties of special
right triangles.
Topics: Circles:


The student will be able to define and sketch the following circle related objects: circle, radius,
chord, diameter, secant, tangent, point of tangency, common tangents, congruent circles,
concentric circles, inscribed/circumscribed objects, arc, minor arc, semicircle, major arc,
arc length, circumference, sphere, and great circle.
The student will use angles, arcs, chords, tangents, and secants to find arc lengths and
areas of sectors in circles.
Topics: Tessellations
Dr. Maureen Yarnevich
Towson University
7 of 8
MTED 615 Online Geometry Course Syllabus


The students will learn which polygons will tessellate and which will not.
The Students will learn to create tessellation patterns.
ACADEMIC INTEGRITY
All students are expected to adhere to the Towson University Student Academic Integrity Policy,
which can be accessed at http://www.towson.edu/provost/resources/studentacademic.asp
Students are responsible for reading, understanding, and following this policy. Cheating or plagiarism
in any form is unacceptable and failure to abide by the Student Academic Integrity Policy may
result in penalties up to and including the grade of F for the course.
ACADEMIC ACCOMMODATION
If you have a documented disability and wish to discuss academic accommodations, please
contact me as soon as possible.
Dr. Maureen Yarnevich
Towson University
8 of 8