math 235:Structure and Application of the Number System (3)


Course Prerequisites/Corequisites: MATH 133 and a passing score on the mathematics portion of the ASSET Examination.

Course Description:
Sets, functions, logic, numeration theory, advanced definition perspectives, arithmetic operations (properties and algorithms), rational numbers, system of real numbers, and mathematical applications. Problem solving emphasized.

Required Reading/Textbook: A Problem Solving Approach to Mathematics for Elementary School Teachers, 11th Edition by Billstein, Rick | Libeskind, Shlomo | Lott, Johnny; Publisher: Pearson Math & Statistics.

Major Assignments/Exams

  • Homework
  • Quizzes
  • Exams
  • Final Exam

List of Discussion/Lecture Topics

  1. An Introduction to Problem Solving (weeks 1, 2 & 3)
    • Mathematics and Problem-solving
    • Explorations with Patterns
    • Reasoning and Logic: An Introduction
  1. Numeration Systems and Sets (weeks 4, 5 & 6)
    • Numeration Systems
    • Describing Sets
    • Other Set Operations and Their Properties
  1. Whole Numbers and Their Operations (weeks 7 & 8)
    • Addition and Subtraction of Whole Numbers
    • Algorithms for Whole-number Addition and Subtraction
    • Multiplication and Division of Whole Numbers
    • Algorithms for Whole-number Multiplication and Division
    • Mental Mathematics and Estimation for Whole-number operations
  1. Number Theory (weeks 9, 10)
    • Divisibility
    • Prime and Composite Numbers
    • Greatest Common Divisor and Least Common Multiple
  1. Integers (week 11)
    • Integers and the Operations of Addition and Subtraction
    • Multiplication and Division of Integers
  1. Rational Numbers and Proportional Reasoning (week 12)
    • The Set of Rational Numbers
    • Addition, Subtraction, and Estimation with Rational Number
    • Multiplication and Division of Rational Numbers
    • Ratios, Proportions, and Proportional Reasoning
  1. Decimals: Rational Numbers and Percent (weeks 13 & 14)
    • Introduction to Decimals
    • Operations on Decimals
    • Nonterminating Decimals
    • Percent and Interests
  1. Real Numbers and Algebraic Thinking (weeks 14, 15)
    • Real Numbers
    • Variables
    • Equations
    • Functions

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