Elementary Theory of Arithmetic II
Revised: September, 2014 (Kathy Jaqua)
A study of mathematical topics including number theory, operations, fractions, and
proportional reasoning necessary for teaching elementary and middle grades students.
Three semester hours.
Prerequisite: Math 321.
Student Learning Goals and Objectives
MATH 322 is a C2 (Mathematics) Liberal Studies Course. The learning goals for C2 Courses
- 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.
- Students will complete a project requiring a mathematical analysis of observations,
such that a significant portion of the student project will be statistically based.
Student Learning Objectives Specific to Math 322
- Learn to use words, symbols, and techniques of mathematics with precision so as to
communicate concepts and ideas correctly and clearly.
- Experience the satisfaction of mathematics discovery, which stimulates curiosity,
initiative, confidence, and interest in mathematics.
- Develop patterns of reasoning which enable one to investigate unfamiliar situations.
- Develop understanding and appreciation of the structure of the number system, elementary
number theory, and proportional reasoning.
- Develop an ability to organize mathematics experiences as a means of discovery rather
than presentations of a fixed set of facts and procedures.
Sowder, J., Sowder, L, and Nickerson, S.
Reconceptualizing Mathematics for Elementary School Teachers, First Edition, W.H. Freeman & Co., 2010.
Grading procedures and factors influencing course grade are left to the discretion
of individual instructors, subject to general university policy.
Attendance policy is left to the discretion of individual instructors, subject to
general university policy.
Chapter 1: Reasoning about Quantities (4 days)
Sections 1-5: What is a Quantity; Quantitative Analysis; Quantitative Values.
Chapter 3: Understanding Whole Numbers Operations (7 days)
Sections 1-8: Addition and Subtraction of Whole Numbers; Multiplication and Division
of Whole Numbers; Developing Number Sense.
Chapter 2: Topics (as appropriate)
Chapter 4: Some Conventional Ways of Computing (6 days)
Sections 1-3 and some material from Chapter 2: Operating on Whole Numbers and Decimal
Numbers; Bases other than 10; Algorithms
Fractions, Ratios, and Proportions
Chapter 6: Meaning for Fractions (5 days)
Sections 1-6: Meaning of a/b; Equivalent Fractions; Relating Fractions, Decimals,
and Percents; Estimating Fractional Values.
Chapter 7: Computing with Fractions (5 days)
Sections 1-6: Adding, Subtracting, Multiplying, and Dividing Fractions.
Chapter 8: Computing with Fractions (3 days)
Sections 1-4: Multiplicative Situations; Fractions in Multiplicative Comparisons.
Chapter 9: Ratios, Rates, Proportions, and Percents (5 days)
Sections 1-5: Ratios; Percents; Proportions, and Proportional Reasoning.
Chapter 10: Expanding Our Number System (5 days)
Sections 1-6: Signed Numbers; Addition and Subtraction; Multiplication and Division;
Other Number Systems.
Chapter 11: Number Theory (4 days)
Sections 1-6: Factors; Multiples; Primes; Composites; Prime Factorization; GCF and