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6.
Minimum hours per week of independent work done
outside of class: 6
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Course
Preparation – (Supplemental form B
required) |
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7a.
Prerequisite(s):
(Course and/or other preparation/experience that
is REQUIRED
to be completed previous to enrollment in this
course.) |
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Completion of Math. A with
a grade of "C" or better, or placement by
matriculation assessment process
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7b.
Co-requisite(s): (Courses
and/or other preparation that is REQUIRED to be
taken concurrently with this
course.) |
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7c.
Advisory:
(Minimum preparation RECOMMENDED
in order to be successful in this
course. Also known as “Course
Advisory”.) |
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Catalog
Description And Other Catalog Information
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8.
Repeatability: |
Not Repeatable
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9a.
Grading Option: |
Standard Grade
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9b.
Catalog Description: |
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Study of points, lines,
angles, polygons, triangles, similarity,
congruence, geometric proofs, area, volume,
perimeter, the circle, right triangle
trigonometry.
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Course
Outline Information |
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10.
Student Performance Outcomes:
(Outcomes for all credit courses must
indicate that students will learn critical
thinking and will be able to apply concepts at
college level. Outcomes must be
related to items listed in Section 11.)
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1. Name, identify,
reproduce and differentiate between definitions,
postulates/axioms and theorems;
2. create
deductively valid proofs verifying mathematical
statements concerning lines, angles, polygons
and circles by using appropriate definitions,
axioms or theorems, as necessary then identify,
recall and demonstrate the method of indirect
and direct proof;
3. cite, list and identify
definitions and axioms/postulates about parallel
lines; analyze properties of transversals of
parallel lines and corresponding angles;
4.
demonstrate the use of construction tools,
particularly a compass and straight edge, to
create various geometric figures (parallel
lines, angle bisectors, congruent segments,
equilateral triangles, perpendicular bisectors,
etc);
5. verify congruency and similarity of
two dimensional geometric figures by using
congruence or similarity to solve for missing
lengths;
6. calculate the perimeter and area
of standard two dimensional figures; identify
properties specific to two dimensional geometric
figures;
7. apply properties of the chords,
tangent lines and secants of a circle; find the
area, circumference and arc length of a sector
of a circle; determine relationships between
angles found in a circle;
8. determine the
lateral area, surface area and volume of
standard three dimensional figures; and
9.
apply the sine, cosine and tangent ratios of a
right triangle; find the measure of an angle
given the values of unknown sides using a
calculator; solve right triangles and evaluate
trigonometric values of special angles
30*,45*,60*.
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11.
Course Content Outline:
(Provides a comprehensive, sequential outline of
the course content, including all major subject
matter and the specific body of knowledge
covered.) |
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I. Terminology Needed for
Proofs
A. Definitions
B.
Axioms/Postulates
C. Theorems
II.
Geometric Proofs and Logic
A. Direct Proof
B. Indirect Proof
III. Parallel
Lines
A. Definition
B. Postulates
C.
Transversals and Corresponding Angle
Properties
IV. Construction
A. Parallel
Lines
B. Angle Bisectors
C. Perpendicular
Bisectors
D. Congruent Segments and Angles
E. Applications
V. Triangles
A. Sum of
angles
B. Area
C. Congruence,
Corresponding Parts
D. Isosceles, Equilateral
E. Similar
F. Ratio, Proportion
G.
Pythagorean Theorem
VI. Polygons
A.
Properties of Polygons
B. Properties of
Quadrilaterals
C. Perimeter
D.
Area
VII. Circles
A. Angles
B.
Circumference
C. Area
D. Arcs, Sectors,
Chords, Secants and Tangents.
VIII. Three
Dimensional Figures
A. Lateral Area
B.
Surface Area
C. Volume
IX. Right Triangle
Trigonometry
A. Sine, Cosine, Tangent
Ratios
B. Special Angles:
C. Solving
Right Triangles
D.
Applications
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12.
Typical Out-of-Class Assignments:
(Credit
courses require two hours of independent
work outside of class per unit of credit for
each lecture hour, less for lab/activity
classes. List types of assignments,
including library assignments.)
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a.
Reading Assignments:
(Submit at least 2 examples)
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1. Read selected topics
throughout the course from the textbook. For
example, how geometric proofs should be written
without leaving out logical steps.
2. Read
supplementary handouts on topics such as various
construction methods to demonstrate the
Pythagorean Theorem or Greek
history.
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b.
Writing, Problem Solving or
Performance:
(Submit at least 2 examples)
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1. Complete homework
problems from the textbook on topics throughout
the course such as geometrical calculations
involving triangles, area, and
constructions.
2. Work in pairs or groups to
hone skills in doing geometrical proofs, both
direct and indirect.
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c.
Other
(Term projects, research papers, portfolios,
etc.) |
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Use geometric software to
investigate theorems and
postulates.
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13.
Required Materials: |
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a.
All Textbooks, resources and other materials
used in this course are College
Level? |
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 Yes
 No
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b.
Representative college-level textbooks (for
degree-applicable courses) or other print
materials.
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Book
1: |
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Author:
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Alexander/Koeberlein |
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Title:
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Elementary
Geometry for College
Students |
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Publisher:
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Houghton
Mifflin |
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Date
of Publication: |
2007 |
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Edition:
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Fourth |
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Book
2: |
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Author:
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Title:
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Publisher:
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Date
of Publication: |
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Edition:
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Book
3: |
|
Author:
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Title:
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Publisher:
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Date
of Publication: |
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Edition:
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Book
4: |
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Author:
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Title:
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Publisher:
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Date
of Publication: |
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Edition:
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Book
5: |
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Author:
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Title:
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Publisher:
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Date
of Publication: |
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Edition:
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c.
Other materials and/or supplies required of
students: |
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Methods
of Instruction |
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14.
Check all instructional methods used to present
course content. |
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Lecture
|
Activity |
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Discussion
Seminar |
Distance
Ed (requires supplemental form) |
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Lab
|
Work
Experience |
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Directed
Study |
Tutoring
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Other:
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Give
detailed examples of teaching methodology that
relate to the course outcomes: |
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Critical
Thinking: In class collaborative learning
activity - students will name, identify,
reproduce and differentiate between definitions,
postulates/axioms and theorems; and create
deductively valid proofs verifying mathematical
statements concerning lines, angles, polygons
and circles by using appropriate definitions,
axioms or theorems, as necessary then identify,
recall and demonstrate the method of indirect
and direct proof;
Critical Thinking:
Instructor will use an interactive lecture
style, requesting participation from all
students in developing the concepts from the
course content (similar to the Socratic
Method).
Reading: After reading about the
Pythagorean theorem, students will integrate a
geometric model with an algebraic model to prove
that the square of the legs of a right triangle
is equal to the square of the hypotenuse.
Reading: Students will read the
explanations and examples to apply the sine,
cosine and tangent ratios of a right triangle;
find the measure of an angle given the values of
unknown sides using a calculator; solve right
triangles and evaluate trigonometric values of
special angles 30*,45*,60*.
Writing:
After an in-class discussion, students will
write a paragraph proving the diagonals of a
rhombus are perpendicular
bisectors.
Writing: Students are expected
to take written notes in class for use while
working on assignments.
Reading and
Writing: After reading the appropriate sections
from the text or computer software, students
will write an explanation of how to distinguish
between the median of a triangle and the
altitude of a triangle.
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15.
Methods of Assessing Student
Learning
15a. Methods
of Evaluation:
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Essay
Exam |
Reports |
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Objective
Exam |
Problem
Solving Exam |
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Projects |
Skill
Demonstration |
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Classroom
Discussion |
Other |
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15b.
(All courses must provide for measurement of
student performance in terms of stated student
performance objectives, Area 10, and culminate
in a formal recorded grade based on uniform
standards. Submit at least 2
examples.) |
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Example 1. With appropriate
"Givens," prove that if a ray is on the interior
of an angle, the sum of the two smaller angles
is equivalent to the largest angle.
Example
2. Using only a straight-edge and a compass,
construct a rectangle of a given size, i.e.,
length and width.
Example 3. With
appropriate "Givens," complete a proof that two
triangles are congruent using the method of
Side-Angle-Side.
Example 4. Find the arc
length on a given circle when the measure of the
swept out angle is known.
Example 5. Find the
missing lengths of the legs in a 30-60-90 degree
triangle when the length of one leg is
known.
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Program title - TOPS Code: |
Mathematics,
General- 170100
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SECTION
D |
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General
Education Information: |
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1. College
Associate Degree GE
Applicability: |
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Math
Competency
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2. CSU
GE Applicability (Recommended-requires CSU
approval): |
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3. IGETC
Applicability (Recommended-requires CSU/UC
approval): |
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4.
CAN: |
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SECTION
E |
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Articulation
Information: (Required
for Transferable courses only)
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1. |
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CSU
Transferable. |
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UC
Transferable. |
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CSU/UC
major requirement. |
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If
CSU/UC major requirement, list campus and major.
(Note: Must be lower division) |
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2.
|
List
at least one community college and its
comparable course. If requesting CSU
and/or UC transferability also list a CSU/UC
campus and comparable lower division
course. |
|
|
American River College -
Math 110 5 units
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SECTION
F |
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|
Resources: |
|
Please
consider the identified concerns below:
1.
Library: Please
identify the implications to the
library
None
2.
Computer Support Services: Please
identify the implications to Computer Support
Services:
None
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SECTION
G |
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1. Maximum
Class Size (recommended): 35
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2. If
recommended class size is not standard, then
provide rationale: |
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