Yuba Community College District

Yuba College Course Outline

Course Information

Course Number: MATH 15
Full Course Title: Concepts and Structures of Mathematics
Short Title: Concepts of Math
Effective Term: Fall 2014

Course Standards

Lecture Hours: 54.000
Total Units: 3.000
Total Hours: 54.00
Repeatable: No
Grading Method: Letter Grade Only

Minimum Qualifications

Course Description

This course focuses on the development of quantitative reasoning skills through in-depth, integrated explorations of topics in mathematics, including real number systems and subsystems. Emphasis is on comprehension and analysis of mathematical concepts and applications of logical reasoning.

Conditions of Enrollment

Completion with a C or better in: MATH 52 or MATH 52A; MATH 101B or). Other: (Placement Exam Score)a satisfactory score on the mathematics placement test. .



Course Lecture Content
  1. Numeration systems: history, Hindu-Arabic numeration system, and place value systems
  2. Integers: structure and basic properties, computational algorithms
  3. Basic number theory: divisibility, prime and composite numbers, prime factorization, fundamental theorem of arithmetic, least common multiple and greatest common divisor
  4. Rational numbers: structure and properties, ratio and proportion
  5. Real numbers: structure and basic properties, arithmetic operations, rational and irrational numbers, decimal representation, number line representation
  6. Patterns, problem solving, communication, connections, modeling, reasoning, and representation
  7. National and state curriculum standards for elementary school math including Common Core State Standards


  1. Perform calculations with place value systems

  2. Evaluate the equivalence of numeric algorithms and explain the advantages and disadvantages of equivalent algorithms in different circumstances

  3. Apply algorithms from number theory to determine divisibility in a variety of settings

  4. Analyze least common multiples and greatest common divisors and their role in standard algorithms **Requires Critical Thinking**

  5. Explain the concept of rational numbers, using both ratio and decimal representations; analyze the arithmetic algorithms for these two representations; and justify their equivalence **Requires Critical Thinking**

  6. Analyze the structure and properties of whole, rational, and real number systems; define the concept of rational and irrational numbers, including their decimal representation; and illustrate the use of a number line representation **Requires Critical Thinking**

  7. Develop and reinforce conceptual understanding of mathematical topics through the use of patterns, problem solving, communication, connections, modeling, reasoning, and representation **Requires Critical Thinking**

  8. Develop activities implementing curriculum standards **Requires Critical Thinking**

Student Learning Outcomes

  1. Demonstrate a depth of understanding of number systems and Polya’s Method for problem solving.

Methods of Instruction


Hours per week on assignments outside of the class:

Reading Assignments
Writing Assignments

Methods of Evaluation

Course Materials

  1. Albert B. Bennett, Jr., Laurie J. Burton, L. Ted Nelson. Mathematics for Elementary Teachers: A Conceptual Approach, 9th ed. McGraw-Hill, 2012, ISBN: 9780077968830
    Equivalent text is acceptable