MATH 2008This is an archive of the Common Course Outlines prior to fall 2011. The current Common Course Outlines can be found at http://www.gpc.edu/programs/Common-Course-Outlines.
Credit Hours 3
Course Title Foundations Of Numbers And Operations
Prerequisite(s) EDUC 2110 with a "C" or better and successful completion of any college-level mathematics course
Corequisite(s) None Specified
This course is an Area F introductory mathematics course for early childhood education majors. This course will emphasize the understanding and use of the major concepts of numbers and operations. As a general theme, strategies of problem solving will be used and discussed in the context of various topics.
Expected Educational Results
Upon completion of this course, students will be able to do the following:General Education Outcomes
- Understand numbers, ways of representing numbers, relationships among numbers, and number systems
- Understand meanings of operations and how they relate to one another
- Compute fluently and make reasonable estimates
- Apply multiple problem solving strategies and understand how approaches to solutions relate to one another
- Use Venn diagrams to illustrate the set operations union, intersection, and complement
- Represent and interpret functions verbally, numerically, graphically and symbolically
- Distinguish between deductive and inductive reasoning and valid and invalid arguments
- Understand the role of place value and notation in various numeration systems
- Use mental arithmetic to perform basic calculations
- Use tests for divisibility and determine prime factorization, GCF and LCM
- Use integers and rational numbers to demonstrate concepts of order and equivalence
- Use rational and irrational numbers in problem-solving settings
I. This course addresses the general education outcome related to effective individual and group problem-solving and critical-thinking skills as follows:Course Content
II. This course addresses the general education outcome related to use of mathematical concepts to interpret, understand, and communicate quantitative data as follows:
- Students develop their problem-solving skills individually in homework assignments, assigned group problem-solving activities, and group quizzes or project assignments.
- Students develop their critical-thinking skills specifically in the unit on problem solving as well as in application problems throughout the course.
- Students understand and use the major concepts of numbers and operations in mathematics for grades P-5.
- Students solve problems using multiple strategies, manipulatives, and technological tools; interpret solutions; and determine the reasonableness of answers and efficiency of methods.
- Students communicate using precise mathematical terminology
- Students construct and justify arguments as well as interpret solutions; and determine the reasonableness of answers and efficiency of methods
- Students learn and apply problem-solving skills in each unit, especially in applications of decimals, fractions, and percents.
A. Problem SolvingAssessment of Outcome Objectives
B. Sets, Functions, and Reasoning
- Introduction to Problem Solving
- Patterns and Problem Solving
- Technology in Problem Solving
C. Whole Numbers
- Sets, Operations and Counting (Natural & Whole)
- Order Relationships
- Functions and Graphs
- Introduction to Deductive, Inductive, and Proportional Reasoning
D. Number Theory
- Estimation, Approximation, & Computation
- Place Value & Other Bases
- Numeration Systems
- Addition and Subtraction
- Multiplication & Exponents
E. Integers and Fractions
- Prime & Composite
- Factors and Multiples
- Even & Odd
- Divisibility Rules
- Greatest Common Factor and Least Common Multiple
F. Decimals: Rational and Irrational Numbers
- Introduction to Fractions
- Operations with Fractions
G. Statistics (optional)
- Decimals and Rational Numbers
- Operations with Decimals
- Ratio, Percent, and Scientific Notation
- Irrational and Real Numbers
- Describing and Analyzing Data
- Graphing Data and Making Predictions
- Systems of Measurement
- Area and Perimeter
- Volume and Surface Area
A. COURSE GRADE
The course grade will be determined by the individual instructor using a variety of evaluation methods. A portion of the course grade will be determined through the use of frequent assessment using such means as tests, quizzes, projects, or homework as developed by the instructor. Some of these methods will require the student to demonstrate ability in problem solving and critical thinking as evidenced by explaining and interpreting solutions. A comprehensive final examination is required which must count at least one-fifth and no more than one-third of the course grade.
B. DEPARTMENTAL ASSESSMENT
This course will be regularly assessed in accordance with the GPC policies. An appropriate assessment instrument will be determined by the Math 2008 course committee.
C. USE OF ASSESSMENT FINDINGS
The Math 2008 committee, or a special assessment committee appointed by the Academic Group, will analyze the results of the assessment and determine implications for curriculum changes. The committee will prepare a report for the Academic Group summarizing its finding.