Discipline: Mathematics Degree Credit  [X]
Non Credit  [ ]
Nondegree Credit  [ ]
Comm Service  [ ]
 

Riverside Community College District
Integrated Course Outline of Record

Mathematics 53


COURSE DESCRIPTION
53 College Geometry Units: 3.00
 
Prerequisite(s): MAT 52: Elementary Algebra
A course covering the study of geometric figures in the Euclidean plane, including angles, triangles, quadrilaterals, circles and solids: formulas for measuring such figures, including perimeter, area and volume; proofs using postulates and theorems associated with congruent triangles, parallel and perpendicular line segments, and angle measures; construction of angles and segment measures. 54 hours lecture.
 
SHORT DESCRIPTION FOR CLASS SCHEDULE
A course in the study of Euclidian Geometry
 
ADVISORY ENTRY SKILLS
Before entering the course, students will be able to:
  1. Perform fundamental operations on real numbers.

  2. Solve linear and quadratic equations, and systems of linear equations.

  3. Recognize the language of algebra and create well formed algebraic statements from statements written in Standard American English.

  4. Apply ratios and proportions.
STUDENT LEARNING OUTCOMES
 Upon successful completion of the course, students should be able to:

1.  Differentiate between different types of angles and polygons.

2.  Explain the properties of circles, line segments, and angles.

3.  Compose proofs through the integration of definitions, axioms, and theorems.

4.  Construct geometric figures using a compass and straight edge.
 
COURSE CONTENT
  TOPICS
 

1.   Proofs
      a.  Sets
      b.  Logic
      c.  Reasoning
2.   Lines and angle relationships
      a.  Definitions, postulates, and theorems
      b.  Parallel, perpendicular, and intersecting lines
      c.   Constructions
3.   Triangles 
      a.   Congruent triangles and corresponding parts       
            congruent triangles
      b.   Special triangles and their relations
      c.   Inequalities in triangles
4.   Quadrilaterals Properties
      a.   Constructions
      b.   Perimeter and area
5.   Similar Triangles
      a.   Ratios, rates, and proportions
      b.   Similar polygons
      c.   Proofs of similar triangles and polygons
      d.   The Pythagorean Theorem and special right triangles
      e.   Segment division properties
6.   Circles
      a.   Related segments and angles
      b.   Constructions and inequalities
      c.   Circumference and area
7.   Surface and Solids
      a.   Polygons and polyhedrons
      b.   Spheres
      c.   Surface area and volume

 
 
METHODS OF INSTRUCTION
 Methods of instruction used to achieve student learning outcomes may include, but are not limited to:

  • Present class lectures/discussions/demonstrations in order to familiarize students with the elements of geometry
  • Create small group activities in order to provide an opportunity for students to the practice skills of geometry with group interaction and support.
  • Develop and assign class exercises that build mathematical and reasoning skills.
  • Design class handouts to demonstrate geometric principles for both visual and verbal learning styles.
  • Show videos/films/computer programs that demonstrate or perform geometric operations.
  • Conduct individual conferences in order to identify strengths, weaknesses, and learning styles.
  • Develop and assign web-enhanced/online/distance learning tasks such as further reading and the investigation of geometry websites to deepen understanding of mathematics.
 
METHODS OF EVALUATION
 Students will be evaluated for progress in and/or mastery of learning outcomes by methods of evaluation which may include, but are not limited to:

  • Oral reports/presentations aimed to demonstrate knowledge of geometric principles.
  • Quizzes, examinations, and written assignments designed to assess the progress and ability to define key concepts, translate statements, evaluate, and formulate solutions in algebra and geometry.
  • Group and individual projects designed to demonstrate ability to solve problems in formal reasoning cooperatively with others and to appreciate different approaches to solving such problems.
  • Final examination

 
ASSIGNMENTS

Required Reading Assignments


Required Writing Assignments


Other Outside-of-Class Assignments
 
COURSE MATERIALS
 All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include:

  • Alexander & Koeberlein. Elementary Geometry for College Students. 4th ed. Houghton Mifflin, 2006.
  • Book Kay. College Geometry: A Discovery Approach. 2nd ed. Addison Wesley Longman, 2001.
  • Musser & Trimpe. College Geometry, A Problem – Solving Approach with Applications. Prentice Hall, 1994.
  • Berele & Goldman. Geometry: Theorems and Constructions. Prentice Hall, 2001.
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