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Master Syllabus

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Administrative Unit: Computer and Mathematical Sciences Department
Course Prefix and Number: MATH 155
Course Title: Algebraic Reasoning for Elementary and Middle School Teachers
Number of:
Credit Hours 3
Lecture Hours 3
Lab Hours 0
Catalog Description:

This course introduces some basic concepts of number theory and modern algebra that underlie elementary and middle grade arithmetic and algebra, with a focus on collaborative learning and technology. Prerequisites: MATH 102 and MATH 150 (or higher).

Prerequisite(s) / Corequisite(s):

MATH 102 and MATH 150 (or higher).

Course Rotation for Day Program:

Offered odd Fall.

Text(s): Most current editions of the following:

A TI-84 calculator is required for this course. This calculator will be allowed on most assessment opportunities in this course.

Algebra Connections
By Papick, I.J. (Pearson)
Course Objectives
  • To progress from a procedural/computational understanding of mathematics to a broad understanding encompassing logical reasoning, generalization, abstratction, and formal proof.
  • To use technology (calculator and computer) as a learning and teaching tool for mathematics.
  • To learn the algorithmic approach to problem solving.
  • To display an understanding of the nature of rigorous proof.
  • To write elementary proofs, especially proofs by induction and basic number theory proofs.
Measurable Learning
  • Know the basic properties of integers such as divisibility, primes, and congruence.
  • Know the basic properties of the real numbers including commutativity, associativity, identity, distributivity.
  • Apply the Euclidean Algorithm to find the greatest common denominator.
  • Determine whether or not a set of three numbers is a Pythagorean Triple and it is primitive.
  • Apply the algorithm to generate Primitive Pythagorean Triples.
  • Represent patterns algebraically.
  • Recognize and generate arithmetic and geometric sequences and find the sums of a finite number of terms of the sequence.
  • Calculate numbers of possible outcomes of elementary combinatorial process using the sum and product rules, permutations, and combinations.
  • Apply the method of mathematical induction to prove basic mathematical statements.
  • Apply the binomial theorem to expand a binomial raised to a given power.
  • Use the Fibonnacci sequence to other mathematical problems.
  • Use the Fibonacci sequence in combination with the binomial theorem.
Topical Outline:
  • Properties of numbers
  • Divisibility, greatest common divisor, andlLeast common multiple
  • Prime numbers
  • Pythagorean Triples and Primitive Pythagorean Triples
  • The division algorithm and modulus
  • Representing patterns
  • Arithmetic sequences
  • Geometric sequences
  • Mathematical induction
  • Counting tools
  • The Binomial Theorem
  • The Fibonacci Sequence

Recommended maximum class size for this course: 20

Library Resources:

Online databases are available at You may access them from off-campus using your CougarTrack login and password when prompted.

Prepared by: Ann Schlemper Date: November 6, 2013
NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this course for Columbia College are expected to facilitate learning pursuant to the course objectives and cover the subjects listed in the topical outline. However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.

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