Download Math 154 – Geometry for Elementary Teachers – Course Goals and

SOUTHWESTERN MICHIGAN COLLEGE
Division of Arts and Science
Dowagiac, Michigan
Winter Semester, 2006
Course Title:
Mathematics for Elementary Teachers II
Course Number:
Math 154
Section Number:
Section 3943
Instructor:
Mrs. Deborah Arent
Office: 713G Daugherty
Phone: 269-782-1253
Office Hours: M,T,W,Th,F - 9:20 to 10:15 and I will be in the ERC
Mondays from 1:00 to 2:00.
Email: [email protected]
Prerequisite:
Math 153 with grade of “C” or higher.
Course Description: This course is devoted to an analysis of geometric figures in the
plane and space, including investigations into their transformation and symmetries.
Fundamental concepts in measurement and construction are also considered. Emphasis
will be on the active participation of the student in discovering and communicating
mathematical ideas.
Distribution Requirements: This course may be used to meet a SMC Natural Science
and Mathematics requirement.
Required Textbooks:
Mathematics for the Elementary Teacher, A Contemporary_Approach, sixth
edition, by Musser, Burger, and Peterson: John Wiley & Sons, publishers.
Intro. To Geometry, Math Grades 5-8, by Vivian, Bohn-Voepel and Thomas:
McGraw Hill Children’s Publishing
Math 154 – Geometry for Elementary Teachers – Course Goals and Objectives:
Goal A: Use shape as an analytic and descriptive tool, identify characteristics and
define shapes, identify properties and describe relationships among shapes.
1. Distinguish among shapes and differentiate between examples and non-examples
of shapes based on their properties.
2. Generalize the characteristics of shapes and apply their generalizations to classes
of shapes.
3. Combine, dissect and transform shapes and study transformations of shapes using
isometries.
4. Generalize about the common properties of similarity, congruence, parallelism
and perpendicularity of shapes.
5. Describe translations, reflections, and rotations using the language of
transformations and employ transformations to verify congruence of figures.
Goal B: Collect, explore and organize data into a useful form and develop skill in
representing and reading data displayed in different formats.
6. Select and use appropriate tools; measure objects using standard units in both
metric and common systems and measure angles in degrees.
7. Make and apply measurements of length, mass (weight), time, temperature, area,
volume, and angle; and classify objects according to their dimensions.
8. Use accepted mathematical formulas to calculate area, surface area, and volume
for geometric shapes.
9. Identify specific types of angles including (but not restricted to) acute, obtuse,
supplementary, complementary, right, interior, exterior, alternate interior,
adjacent and corresponding angles.
10. Identify what data are needed to answer a particular question or solve a given
problem and design and implement strategies to obtain, organize and present
those data.
Goal C: Investigate relationships such as equality, inequality, inverses, factors and
multiples, and represent and compare very large and very small numbers.
11. Develop an understanding of integers and rational numbers and represent rational
numbers in both fractions and decimal forms.
12. Extend their understanding of numeration systems to include decimal
numeration, scientific notation and non-decimal numeration systems.
13. Recognize equivalent representations of a number, especially fractions, decimals
and percents and translate (convert using a conversion factor) freely among
representations.
14. Explain the meaning of powers and roots of numbers and use calculators to
compute powers and square roots.
15. Extend relationships of primes, factors, multiples and divisibility in an algebraic
setting.
Goal D: Use a compass and protractor to construct the basic Euclidean
Constructions.
Method of Instruction:
Evaluation:
Evaluation Method:
Lecture/Discussion/Group Work
Evaluation will consist of three chapter exams and 5 quizzes, a
comprehensive final exam, class projects and assignments,
community service (tutoring), and a class
presentation with lesson plan.
3 Exams @ 100 points each
Tutoring and Tutoring Journal
3 Math Projects @ 50 points each
5 Quizzes @ 10 points each
One Class Presentation @ 50 pts.
1 Final Exam @ 100 pts.
Total
=
=
=
=
=
=
=
300 pts.
100 pts.
150 pts.
50 pts.
50 pts.
100 pts.
750 pts.
40.0%
13.0%
20.0%
7.0%
7.0%
13.0%
Grading Scale: 100 - 94% = A
93 - 90% = A89 - 87% = B+
86 - 84% = B
83 - 80% = B79 - 77 % = C+
76 - 74% = C
73 - 70% = C69 - 67% = D+
66 - 64% = D
63 - 60% = D59 - 0% = F
Attendance Policy: Attendance is required at all class sessions unless an emergency or
an SMC approved event arises. Written notes from SMC sponsors,
doctors, etc. will be required to make up missed exams,
assignments, or projects. It is the student’s responsibility to notify
the instructor when an absence is unavoidable. The student is
expected to take responsibility for making up any assignments.
Tentative Schedule
( All chapter homework assignments are due at the time that we have the exam for that
chapter. Please do not feel that you need not attempt any of the other questions for these
chapters, however, those that I list in class are the ones that you are expected to complete
and turn in.)
Week #1
Chapter #12 - Recognizing Geometric Shapes; The Van Hiele Theory;
Defining Geometric Shapes; Points, Lines and Planes
Week #2
Chapter #12 - Common Geometric Shapes con’t; Classifying Triangles;
Classifying Triangles by Angles; Symmetry and Symmetry using a Mira;
Perpendicular and Parallel Line Segments
Week #3
Chapter #12 - Geometric Shapes -con’t. – Regular Polygons; Properties
Of Geometric Shapes; Points Lines and Angles; Regular Polygons and
Tesselations ; Corresponding Angles; Angles formed by parallel lines.
Special pairs of Angles- Supplementary, Complementary and Vertical.
Quiz #1
Week #4
Chapter #12 - Describing Three-Dimensional Shapes; Polyhedra; Curved
Shapes in Three Dimensions; Parts of a Circle, and Secants and Tangents;
Arcs and Angles.
Project #1 is due!
Week #5
Chapter #12- con’t. and Begin Chapter # 13 – Measurement
Nonstandard Units; Standard Units; Dimensional Analysis; Length and
Area – Quiz #2
Week #6
Chapter #13 - Measurement - con’t.
Length and Area con’t.; Surface Area; Volume, Perimeter
Exam #1
Week #7
Chapter #14 - Geometry Using Triangle Congruence and Similarity
Congruence of Triangles; Similar Triangles – Quiz #3
Project #2 is due!
Week #8
Chapter #14 - Triangular Congruence Con’t.
Fractals and Self Similarity; Basic Euclidean Constructions
Week #9
Chapter #14 – Basic Euclidean Constructions Con’t.
Additional Euclidean Constructions – Circumscribed and Inscribed Circles
And Constructing Regular Polygons – Quiz #4
Week #10
Chapter #14 -Pythagorean Theorem
Project #3 is due!
Week #11
Chapter #15 – Geometry Using Coordinates
Distance and Slope, Coordinate Distance Formula, Collinear Test
Exam #2
Week #12
Chapter #15 – Geometry Using Coordinates - Midpoint Formula,
Slope of a Line, Slopes of Parallel Lines, Slopes of Perpendicular Lines
Week #13
Chapter #15 – Geometry Using Coordinates – Slope Intercept
Equation of a Line, Graphing Lines, Solving Simultaneous Equations
Quiz #5
Chapter #16 – Transformations – Isometries, Translation, Rotation
and Reflections.
Exam #3
Week #14
Week #15
Class Presentations – (Remember your lesson plan!)
Tutoring Journal is due this week!
Week #16
Final Exams – Date and Time to be announced.
Notice: Information in this syllabus was, to the best knowledge of the instructor,
considered correct and complete when distributed for use at the beginning of the
semester. The instructor, however, reserves the right, acting within the policies and
procedures of Southwestern Michigan College to make changes in course content or
instructional techniques without notice or obligation.
Honesty Policy
Cheating or plagiarizing will absolutely not be tolerated at Southwestern Michigan
College. Any student found cheating or plagiarizing material in any manner may be
assigned a failing semester/session grade in this course. A second such incident while at
SMC could result in suspension or expulsion from the institution. A student found in
violation of this section of the syllabus will not be allowed to drop this course.
Additional detail regarding cheating and/or plagiarism may be found elsewhere in this
syllabus.