Elementary Theory of Arithmetic II

Revised: July 2009 (Ralph Willis)

Course Description

Number Theory, Whole Number Operations and Properties, Algorithms for Whole Numbers, Integer Operations and Properties, Rational Number Operations and Properties, Ratio and Proportion, The Real Number System, Percent, Interest.

Prerequisite: Math 321.

Liberal Studies Objectives This course can satisfy the C2 (Mathematics) portion of the Liberal Studies Program. The learning goals of the Liberal Studies Program are for students to:

• Demonstrate the ability to locate, analyze, synthesize, and evaluate information;
• Demonstrate the ability to interpret and use numerical, written, oral and visual data;
• Demonstrate the ability to read with comprehension, and to write and speak clearly, coherently, and effectively as well as to adapt modes of communication appropriate to an audience;
• Demonstrate the ability to critically analyze arguments; demonstrate the ability to recognize behaviors and define choices that affect lifelong well-being;
• Demonstrate an understanding of
• Past human experiences and ability to relate them to the present;
• Different contemporary cultures and their interrelationships;
• Issues involving social institutions, interpersonal and group dynamics, human development and behavior, and cultural diversity; scientific concepts and methods as well as contemporary issues in science and technology;

Cultural heritage through its expressions of wisdom, literature and art and their roles in the process of self and social understanding.

C2: Mathematics Objectives (pending approval)

• Students will be introduced to applications of mathematics in daily experience.
• Student learning will be focused on the development of conceptual understanding rather than computational drill.
• An assignment in which students display an application of mathematics will be required. This assignment will address an application of mathematics, which may include statistics, optimization, linear regression, the mathematics of motion, or the mathematics of population growth.

Course Specific Objectives

1. Learn to use words, symbols, and techniques of mathematics with precision so as to communicate concepts and ideas correctly and clearly.
2. Experience the satisfaction of mathematics discovery which stimulates curiosity, initiative, confidence, and interest in mathematics.
3. Develop patterns of reasoning which enable one to investigate unfamiliar situations.
4. Develop understanding and appreciation of the structure of the number system, elementary number theory, and the use of algebra and geometry.
5. Develop an ability to organize mathematics experiences as a means of discovery rather than presentations of a fixed set of facts and procedures.

Text

Billstein, Libeskind and Lott. A Problem Solving Approach to Mathematics for Elementary School Teachers, Tenth Edition, Pearson/Addison-Wesley, 2010.

Grading Procedure

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Course Outline

• Chapter 5: Integers and Number Theory (6 days)
  Sections 3-5:Divisibility; Prime and Composite Numbers; Greatest Common Divisor and Least Common Multiple.
• Chapter 3: Whole Numbers and their Operations (8 days)
  Sections 1-5: 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.
• Chapter 5: Integers and Number Theory (7 days)
  Sections 1-2: Integers and the Operations of Addition and Subtraction; Multiplication and Division of Integers.
• Chapter 6: Rational Numbers as Fractions (8 days)
  Sections 1-3: The Set of Rational Numbers; Addition, Subtraction, and Estimation with Rational Numbers; Multiplication and Division of Rational Numbers.
• Chapter 7: Decimals and Real Numbers (10 days)
  Sections 1-4: Introduction to Decimals; Operations on Decimals; Nonterminating Decimals; Real Numbers.
• Chapter 8: Proportional Reasoning, Percents and Applications (4 days)
  Sections 1-2: Ratios; Proportions, and Proportional Reasoning; Percents.