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
TOP Code:
1701.00  Mathematics, General
Effective Term:
Fall 2014
Course Standards
Course Type:
Credit  Degree Applicable
Units: 3.0
Total class hours: 162.0
Total contact hours in class: 54.0
Lecture hours: 54.0
Hours outside of class: 108.0
Repeatable:
No
Grading Method:
Letter Grade Only
Minimum Qualifications for Instructors
 Mathematics (Masters Required)
Course Description
This course focuses on the development of quantitative reasoning skills through indepth, 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
Satisfactory completion of: MATH 52 or MATH 52A; MATH 101B or) (Placement Exam Score)a satisfactory score on the mathematics placement test.
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Advisories

Language  recommended eligibility for English 1A
Content
Course Lecture Content
 Numeration systems: history, HinduArabic numeration system, and place value systems
 Integers: structure and basic properties, computational algorithms
 Basic number theory: divisibility, prime and composite numbers, prime factorization, fundamental theorem of arithmetic, least common multiple and greatest common divisor
 Rational numbers: structure and properties, ratio and proportion
 Real numbers: structure and basic properties, arithmetic operations, rational and irrational numbers, decimal representation, number line representation
 Patterns, problem solving, communication, connections, modeling, reasoning, and representation
 National and state curriculum standards for elementary school math including Common Core State Standards
Objectives

Perform calculations with place value systems

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

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

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

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**

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**

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

Develop activities implementing curriculum standards
**Requires Critical Thinking**
Student Learning Outcomes
 Demonstrate a depth of understanding of number systems and Polya’s Method for problem solving.
Methods of Instruction

Lecture/Discussion
Assignments
Reading Assignments
Writing Assignments
Methods of Evaluation
 Essay/Paper
 Exams
 Homework
 Portfolio
 Problem Solving Exercises
 Quizzes
 Research Project
Course Materials
Textbooks:

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