El Camino College - Division of Mathematical Sciences

Math 60
Elementary Geometry
4 units; 4 hours lecture

Catalog Description Course Objectives and Methods of Evaluation
Outline of Subject Matter Planned Instructional Activities

Grading Method: Letter

Associate Degree Credit --- Does not transfers to CSU and
                                           Does not transfers to UC

Prerequisite: Mathematics 40 or Mathematics 41B with a minimum grade of C in prerequisite or qualification by testing (El Camino College Mathematics Placement Test) and assessment.

Catalog Description:
  This is an introductory course in geometry. Topics include: properties of geometric figures including circles, triangles and other polygons, congruence and similarity, and elementary logical reasoning. Formal proof is introduced and used throughout the course.

Note: This course is equivalent to one year of high school geometry.
Note: Mathematics 60 was formerly numbered Mathematics B.

Course Objectives and Methods of Evaluation:

  1. Course objectives (list the major objectives stated as student outcomes in behaviorally measurable terms.)
    1.  Identify and apply properties of basic geometric figures.
    2. Perform constructions using a compass and straightedge.
    3. Use inductive reasoning to formulate conjectures.
    4. Make and justify deductive conclusions and arguments using direct and indirect proofs.
    5. Determine the validity of arguments in elementary logic.
    6. Apply properties of right triangles: the Pythagorean Theorem and simple trigonometric rations.
    7. Determine perimeter and area for common two-dimensional figures and surface area and volume for common three dimensional figures.
    8. Use proportional reasoning, congruence and similarity in problem solving.
    9. Solve problems involving triangles and other polygons inscribed within and circumscribed about circles.
  1. Methods of Evaluation - Associate Degree Credit Course
    1. Substantial writing assignments are inappropriate for this degree applicable course because:
      1. The course is primarily computational in nature
      2. The course primarily involves skill demonstrations or problem solving.
    2. Computational or non-computational problem-solving demonstrations, including:
      1. Exam
    3. Skill demonstrations, including:
      1. Geometrical constructions using straight-edge and compass
Return to the top of the page.

Outline of Subject Matter
 

Approximate Time

Major Topic

8 hours

I. Fundamental Concepts

  1. Inductive and deductive reasoning
  2. Undefined terms and basic definitions
  3. Angles
  4. Geometric constructions
  5. Introduction to proof  (including indirect proof)
  6. Theorems involving supplementary, complementary, and vertical angles

8 hours

II. Congruent Triangles and Basic Theorems

  1. Congruent triangles
  2. Proofs using corresponding parts of congruent triangles
  3. Theorems involving isosceles triangles

12 hours

III. Parallel Lines, Parallelograms, Trapezoids and Other Polygons

  1. Parallel Lines
  2. The sum of the angles in a triangle
  3. The sum of the angles of a polygon
  4. Parallelograms
  5. Rectangles and rhombi
  6. Trapezoids
  7. Areas of polygons and volumes of solids
  8. The Pythagorean Theorem

4 hours

IV.  Polygons Inscribed within and Circumscribed about Circles
8 hours

IV.  Ratios, Proportions and Similarity

  1. Ratio and Proportion
  2. Similar Triangles
  3. Introduction to the trigonometric ratios
8 hours

IV.  Circles

  1. Areas of circles
  2. Theorems involving chords, tangents and secants of circles
4 hours

IV.  Inequalities

  1. Fundamental  properties of inequalities
  2. Inequalities involving triangles and circles
  3. Inequalities involving chords of circles
4 hours

IV.  Geometric Loci

  1. Basic locus theorems
  2. Concurrency theorems

4 hours

V. Mathematical Logic

  1. Simple and compound statements
  2. Longer statement forms
  3. Tautologies
  4. Valid arguments
8 hours

IV.  Analytic Geometry

  1. The Cartesian Coordinate System
  2. The straight line
  3. Points of intersection of lines

 4 hours

Examinations

Total:

72 Hours

Return to the top of the page.


Planned Instructional Activities:

Lecture, class discussion, demonstration, calculator instruction, individual assistance

Entrance Skills and Knowledge:

List the required skills and/or knowledge without which a student would be highly unlikely to receive a grade of A, B, C, or Credit (or for Health and Safety, would endanger self or others) in the Target Course.
  1. Manipulate algebraic expressions including expressions with fractions and radicals
  2. Solve quadratic equations and systems of linear equations
  3. Graph systems of linear equations
  4. Solve application problems using linear and quadratic equations
Return to the top of the page.
 
Source of information: Course Outline of Record dated November, 2001


 Last Updated On: 4/20/06