El Camino College - Division of Mathematical Sciences

Math 110
Mathematics for Elementary School Teachers - The Real Number System
3 units; 3 hours lecture

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

Grading Method: Letter

Associate Degree Credit --- Transfers to CSU
                                           Transfer to UC is pending

Prerequisite: Mathematics 70 with a minimum grade of C or equivalent.

Catalog Description:
  This course is designed for preservice elementary school teachers. The course will examine six content areas: Numeration (historical development of numeration systems); Set Theory (descriptions of sets, operations of sets, Venn Diagrams); Number Theory (divisibility, primes and composites, greatest common divisor, least common multiple); Patterns (number and geometric patterns); Properties of Numbers (whole numbers, integers, rational numbers, and models for teaching binary operations); and Problem Solving (strategies and models to solve problems).
Note: Mathematics 110 was formerly numbered Mathematics 38.

 Course Objectives and Methods of Evaluation:

  1. Course objectives (list the major objectives stated as student outcomes in behaviorally measurable terms.)
    1.  Perform operations (union, intersection, complement) with sets and draw and interpret Venn Diagrams.
    2. Perform binary operations in a variety of numeration systems.
    3. Demonstrate models for teaching the binary operations (addition, subtraction, multiplication, and division) with whole numbers, integers, and rational numbers.
    4. Recognize the properties of the real number system.
    5. Use the rules of divisibility, prime factorization of composite numbers, find the least common multiple and greatest common divisor.
    6. Recognize numeric and geometric patterns.
    7. Use strategies (looking at simpler case, making a table, using indirect reasoning, looking for a pattern, examining a related problem) to solve application problems.
    8. Model application problems by analyzing the graphs of quadratic, cubic, exponential and rational functions.
  1. Methods of Evaluation - Associate Degree Credit Course
    1. Substantial writing assignments, including:
      1. Written homework
      2. Journal
    2. 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.
    3. Computational or non-computational problem-solving demonstrations, including:
      1. Exam
      2. Quizzes
      3. Homework problems
    4. Objective examinations , including:
      1. Completion

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Outline of Subject Matter
 

Approximate Time

Major Topic

3 hours

I. Numeration Systems

  1. Hindu-Arabic: Conversions of bases
  2. Roman: properties and binary operations
  3. Egyptian: properties and binary operations
  4. Babylonian: properties and binary operations
  5. Compare and contrast numeration systems

6 hours

II. Set Theory

  1. Definition of sets, subsets, elements, equal sets, one-to-one correspondence, null set and universal set
  2. Operations with sets and Venn Diagrams: intersection, union, complement
  3. Properties with sets: commutative, associative, distributive

6 hours

III. Number Theory

  1. Divisibility: definition, theorems and divisibility rules
  2. Prime and Composite Numbers: prime factorization, theorems of prime factorization and divisibility
  3. Greatest common divisor and least common multiple

9 hours

IV.  Patterns

  1. Arithmetic and geometric sequences
  2. Numeric and geometric patterns

18 hours

V. Properties of the Real Numbers

  1. Whole numbers, integers and rational numbers: properties and order of operations
  2. Greater than and less than relations
  3. Models of teaching binary operations for whole numbers, integers and rational numbers
  4. Decimals and scientific notation
9 hours V. Problem Solving
  1. Problem solving process: 4 step method of solving application problems
  2. Strategies to solve problems: making a table, looking for a pattern, examining a simpler case, examining a related problem, using inductive reasoning
  3. Application Problems:
    1. Growth patterns of polynomial, rational and exponential functions
    2. Graphs of functions with varying parameters

 3 hours

Examinations

Total:

54 Hours

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Planned Instructional Activities:

Lecture, discussion, individual and group work

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. Graph polynomial, rational and exponential-functions.
  2. Solve application problems at the Intermediate Algebra level.
  3. Solve polynomial and rational equations at the Intermediate Algebra level.

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Source of information: Course Outline of Record dated November, 1999



 Last Updated On: 4/20/06