Informal Geometry
Revised: September 2020
Course Description
Points, lines, planes, constructions; axiomatic structure of geometry and the nature
of proof. Prerequisite: Math 321. Three semester hours
Liberal Studies Objectives
This course can satisfy the C2 (Mathematics) portion of the Liberal Studies Program.
The learning goals of the Liberal Studies Program are for students to:
- Demonstrate the ability to locate, analyze, synthesize, and evaluate information;
- Demonstrate the ability to interpret and use numerical, written, oral and visual data;
- Demonstrate the ability to read with comprehension, and to write and speak clearly,
coherently, and effectively as well as to adapt modes of communication appropriate
to an audience;
- Demonstrate the ability to critically analyze arguments; demonstrate the ability to
recognize behaviors and define choices that affect lifelong well-being;
- Demonstrate an understanding of
o Past human experiences and ability to relate them to the present;
o Different contemporary cultures and their interrelationships;
o Issues involving social institutions, interpersonal and group dynamics,
human development and behavior, and cultural diversity; scientific concepts and methods
as well as contemporary issues in science and technology; cultural heritage through
its expressions of wisdom, literature and art and their roles in the process of self
and social understanding.
C2: Mathematics Objectives (pending approval)
- Students will be introduced to applications of mathematics in daily experience.
- Student learning will be focused on the development of conceptual understanding rather
than computational drill.
- An assignment in which students display an application of mathematics will be required.
This assignment will address an application of mathematics, which may include statistics,
optimization, linear regression, the mathematics of motion, or the mathematics of
population growth.
Student Learning Objectives
In this course you will be asked to:
- Utilize information methods such as dot paper constructions, folding, and tracing
to determine facts and relationships;
- Study and develop fundamental ideas of Euclidean geometry based on measurement, parallelness
and congruence;
- Perform basic Euclidean constructions using traditional tools and the MiraTM;
- Develop a system of facts and relationships concerning triangles, quadrilaterals,
and other polygons;
- Develop a system of facts and relationships concerning circles and circle parts;
- Study and develop a system of facts and relationships concerning the measurement of
length, area, surface area, and the Pythagorean Theorem;
- Perform standard geometric constructions using geometry software such as GeogebraTM,
GeosketchpadTM, or DesmosTM;
- Develop an appreciation of formal deductive reasoning through pattern description,
inductive reasoning, and the formulation of conjectures.
Text
Serra, M. Discovering Geometry, An Investigative Approach, Fourth Edition, 2008
Grading Procedure
Grading procedures and factors influencing course grade are left to the discretion
of individual instructors, subject to general university policy.
Attendance Policy
Attendance policy is left to the discretion of individual instructors, subject to
general university policy.
Course Outline
- Chapter 1&2: 2 weeks
Introducing and Reasoning in Geometry – work on definitions
- Chapter 3: 2 weeks
Using tools of Geometry
- Chapter 4: 1 week
Discovering and Proving Triangle properties
- Chapter 5: 1 week
Discovering and Proving Polygon Properties
- Chapter 7: 3 weeks
Transformations and Tessellations
- Chapter 8-9: 2 weeks
Area + Pythagorean Theorem
- Chapter 9-10: 1 week
Volume + Pythagorean Theorem
- Chapter 11: 2 weeks
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