Course Outline for Mathematics 41
Number Systems

Effective: Fall 2022
SLO Rev: 10/27/2021
Catalog Description:

MTH 41 - Number Systems

3.00 Units

Development of mathematical thinking through exploration of the number system. Topics include structure of numeration systems including the real number system and its subsystems, number theory, and computational algorithms. Supports Number Sense Domain in the elementary subject matter preparation standards of the California Commission on Teacher Credentialing.
Prerequisite: MTH 53 or MTH 55 or an appropriate skill level demonstrated through the Mathematics Assessment process.
1701.00 - Mathematics, General
Letter Grade Only
Type Units Inside of Class Hours Outside of Class Hours Total Student Learning Hours
Lecture 3.00 54.00 108.00 162.00
Laboratory 0.00 18.00 0.00 18.00
Total 3.00 72.00 108.00 180.00
Measurable Objectives:
Upon completion of this course, the student should be able to:
  1. perform calculations with place value systems;
  2. evaluate the equivalence of numeric algorithims;
  3. explain the advantages and disadvantages of equivalent algorithms in different circumstances.;
  4. apply algorithms from number theory to determine divisibility;
  5. compare and contrast least common multiple and greatest common divisor;
  6. analyze the roles least common multiple and greatest common divisor have in standard algorithms;
  7. explain the concept or rational numbers using ratio and decimal representations;
  8. analyze, determine and justify the equivalency of arithmetic algorithms of the ratio and decimal representations of rational numbers;
  9. analyze the structure and properties of different number systems including real numbers and its subsystems;
  10. define the concept of rational and irrational numbers, including their decimal representation;
  11. develop and reinforce conceptual understanding of mathematical topics through the use of patterns, problem solving, communication, connections, modeling, reasoning, and representation;
  12. illustrate the use of a number line representation; and
  13. develop math activities based on the state and national curriculum standards.
Course Content:
  1. Numeration systems
    1. Historical
    2. Hindu-Arabic
    3. Place-value
  2. Basic number theory
    1. Divisibility
    2. Prime and composite numbers
    3. Prime factorization
    4. Fundamental Theorem of Arithmetic
    5. Least Common Multiple
    6. Greatest Common Divisor
  3. Integers
    1. Structure
    2. Properties
    3. Computational algorithms
  4. Rational numbers
    1. Structure
    2. Properties
    3. Ratio
    4. Proportions
  5. Real numbers
    1. Structure
    2. Operations
    3. Properties
    4. Rational and irrational numbers
    5. Decimal representations
    6. Number line representation
  6. Equivalency of computational algorithms
  7. Developing conceptual understanding
    1. Patterns
    2. Problem Solving
    3. Communication
    4. Connections
    5. Modeling
    6. Reasoning
    7. Representation
  8. National and state standards for elementary school mathematics
Methods of Instruction:
  1. Demonstration/Exercise
  2. Group Activities
  3. Lecture/Discussion
  4. Textbook reading assignments
  5. Problem Solving
  6. Presentation of audio-visual materials
  7. Computer-based interactive curriculum
  8. Hands-on Activities
  9. Diagnostic Quizzes
  10. Verbal explanation and demonstration.
  11. Handouts and rule interpretations.
  12. Distance Education
Assignments and Methods of Evaluating Student Progress:
  1. The NCTM Standards state "All students should solve simple problems involving rates and derived measurements for such attributes as velocity and density." Provide two examples that satisfy this statement and justify your choices.
  2. What is the largest three-digit prime all of whose digits are prime?
  3. An iPod is on sale for $159.20 and its normal price is $199. A student says that the percent discount is 39.8%. Is the student correct? If not, where did the student go wrong?
  1. Class Work
  2. Homework
  3. Quizzes
  4. Group Projects
  5. Online Assignments
  6. Class Participation
  7. Exams/Tests
  8. Final Examination
Upon the completion of this course, the student should be able to:
  1. critically analyze mathematical problems using a logical methodology;
  2. communicate mathematical ideas, understand definitions, and interpret concepts;
  3. increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.
Textbooks (Typical):
  1. Billstein, R. Libeskind, S. Lott, J. W (2019). A Problem Solving Approch to Mathematics for Elementary School Teachers (13th). Pearson.
  2. Long, C, T. De Temple, D. W. Millman, R. S (2019). Mathematical Reasoninig for Elementary Teachers (7th). Pearson.
  • Scientific calculator
Abbreviated Class Schedule Description:
Serving future elementary school teachers, this course develops mathematical thinking by exploring in depth the number system we now use.
Prerequisite: MTH 53 or MTH 55 or an appropriate skill level demonstrated through the Mathematics Assessment process.
Discipline:
Mathematics*