Hagerstown Community College
OFFICIAL COURSE SYLLABUS DOCUMENT
COURSE: MAT 107 – 01 Fundamental Concepts of Mathematics I (3 credits)
TIME: MW 1:00 p.m. – 2:15 p.m.
LOCATION: LRC 121
INSTRUCTOR: Joseph C. Mason
SEMESTER/YEAR: Fall 2011
CONTACT INFORMATION:
Office phone: (301) 790 – 2800 ext 207
e-mail: jcmason@hagerstowncc.edu
Office hours: MTWR 9:00-10:00 a.m.
T 3:00 – 4:00 p.m.
COURSE DESCRIPTION: This course is required for the AAT program and includes set
theory, logic, estimation, measurement, numeration systems, operational algorithms, elementary
number theory, and problem solving. The course emphasizes constructing and expanding
mathematical knowledge using modern technologies to investigate questions and solve
mathematical problems. Total of 45 hours of lecture. Prerequisite: MAT 101 or equivalent score
on placement exam. Semesters offered: Fall, Spring 3 Credits
TEXTBOOK: A PROBLEM SOLVING APPROACH TO MATHEMATICS FOR
ELEMENTARY SCHOOL TEACHERS, 10th Edition, Billstein Libeskind Lott,Pearson Addison
Wesley, 2007, ISBN 978-0-321-67159-2 (Please note that this ISBN includes the textbook and
access code for MyMathLab)
STUDENT LEARNING OUTCOMES:
The student will:
 have the mathematical skills necessary to pass the mathematics portion of the
Praxis examination.
 have a conceptual understanding of various topics taught in mathematics.
 have a repertoire of mathematical teaching techniques and ideas to introduce to
future students.
 have an understanding of how to use manipulatives and technology in the
classroom.
 know how manipulatives and technology can enhance and facilitate mathematical
understanding.
 know when it is appropriate to use manipulatives and technology.
 have an understanding of how to incorporate and use group work in a problemsolving environment.
MAT 107 Fundamentals of Mathematics I
Fall 2011
1
COURSE CONTENT OBJECTIVES:
The student will be able to:
 represent numbers, relationships among numbers, and number systems in a
variety of ways using physical materials, drawings, and symbols.
 identify multiple interpretations of operations and describe the relationships
between operations.
 develop and use a variety of strategies to determine the results of computations
and estimations, using whole numbers, fractions, and decimals.
 represent, analyze, and generalize a variety of patterns with physical materials,
tables, graphs, words, and symbolic rules.
 use and compare different forms of representation for relationships and functions.
 model and solve problem situations using various representations such as graphs,
tables, and equations.
 identify multiple problem solving strategies and select and use the most
appropriate strategy for a given problem.
 demonstrate persistence when solving challenging problems.
 note patterns, structure, or regularities in both real-world situations and symbolic
objects.
 demonstrate a repertoire of reasoning types such as algebraic, proportional, and
deductive.
 draw, diagram, manipulate objects, verbally explain, write and use mathematical
symbols to present methods for solving problems.
 justify mathematical reasoning and procedures in a variety of ways.
 recognize and use connections among different mathematical ideas.
 select, apply, and translate among mathematical representations to solve
problems.
ASSESSMENT PROCEDURES:
Attendance (17% of grade)
Homework (17% of grade)
Exams (40% of grade - 2 exams)
Final Exam (26% of grade)
Final course grade will be calculated using the following percentage cut offs:
90% +
A
80% – 90% B
70% – 80% C
60% – 70% D
below 60% F
MAT 107 Fundamentals of Mathematics I
Fall 2011
2
COURSE POLICIES:
Attendance: Students are expected to attend all classes.
Attendance will be graded in the following manner:
each class will be awarded 2 points
arriving to class late will result in 1 point deduction
leaving class early will result in 1 point deduction
missing more than 1/2 the class will result in 2 point deduction
It is the student’s responsibility to withdraw officially from any class which
he/she ceases to attend. Students are expected to take all exams during
scheduled time. Please check the College’s attendance policy, page 60 in
catalog.
Homework: Homework will be assigned at the end of each class, is expected to be
completed by the beginning of the next class, and you will be given 3
attempts at each question. Assignments may be worked on after the due date
but any question answered correctly after the due date will receive a 5%
reduction per day late. Homework will be assigned in a variety of methods:
Handout, from text, and from course compass.
Academic integrity: As in all courses you take at Hagerstown Community College, you
are always expected to turn in only your own work on each
examination and graded assignment. Cheating in any form will not
be tolerated and any instances that are uncovered will result in a
"zero" grade being recorded for that work in the course. (College’s
honor code, page 59 in catalog)
Cell phones: All cell phones should be turned off and out of sight during class time
unless previous arrangements are made with the instructor. Once, shame on
you, after that, 1 point deduction in attendance for class.
Food and Drink: All food should be consumed before or after class, NOT DURING
CLASS. You may have a drink in class as long as it is not distracting
to other students or the instructor.
SERVICES FOR STUDENTS WITH SPECIAL NEEDS: Hagerstown Community College
is committed to providing support services for students who have special needs. Students are
encouraged to identify themselves to the coordinator of special student services as early as
possible. Reasonable accommodations based on current documentation are provided to qualified
students. Jamie Bachtell is the advisor and contact person in The Office of Students with
Disabilities. She may be reached at 301-790-2800 ext. 273 or via e-mail at
bachtellj@hagerstowncc.edu.
Total Hours of Coursework: To earn one academic credit at HCC, students are required to
complete a minimum of 37.5 clock hours (45 fifty-minute “academic” hours) of coursework per
semester. Those hours of coursework may be completed through a combination of hours within
the classroom and hours outside the classroom. Certain courses may require more than the 37.5
MAT 107 Fundamentals of Mathematics I
Fall 2011
3
minimum hours of coursework per credit. For most classes, students should expect to do at least
2 hours of coursework outside of class for each hour of in-class coursework.
Course content: The instructor reserves the right to modify course content or
exam schedule as he deems necessary or beneficial to students throughout the
course.
MAT 107 Fundamental Concepts of Mathematics I
Lecture Outline
Lecture 1
 Intro to course, expectations, and grading policy.
 Problem Solving Activity
Lecture 2 (section 1.1)
 Discuss results of Problem Solving Activity
 Go over goal of math education in Elementary School
 Why so many Students Dislike Math
 Discussion of pros and cons of present math education
 Polya's four-step problem solving process
 Problem solving strategies
 Guess and Check
 Make a Diagram
 Make a Table
 Work Backwards
Lecture 3 (section 1.2)
 Problem solving strategies
 Look for a Pattern
 Examine a Related Problem
 Examine a Simpler Case
 Using Algebra
 Arithmetic Sequences
 Fibonacci Sequence
 Geometric Sequences
Lecture 4 (section 1.3)
 Introduction to Reasoning and Logic
 Statements
 Negation and Quantifiers
 Truth Tables
 Conjunction
 Disjunction
 Logically Equivalent
 Conditional or Implications
 Converse statement
 inverse statement
MAT 107 Fundamentals of Mathematics I
Fall 2011
4


Contra positive statement
Tautology
Lecture 5 (section 2.1)
 Numeration Systems
 Numeration Systems using Additive Property
 Tally Numeration System
 Egyptian Numeration System
 Roman Numeration System
 Numeration Systems using Additive Property and Place Value
 Babylonian Numeration System
 Mayan Numeration System
 Hindu-Arabic Numeration System
Lecture 6 (section 2.1)
 Hindu-Arabic Numeration System
 Place Value
 Reading
 Writing
 Rounding
 Other Number Base Numeration Systems
 Place Value
 Counting
 Expressing as a base 10 numeral
 Expressing a base 10 numeral in a different base
Lecture 7 (section 2.2)
 Definition of a Set
 Elements of a Set
 Set Notation
 Equal Sets
 One-to-one Correspondence
 Fundamental Counting Principle
 Equivalent Sets
 Cardinal Number of a Set
 Venn Diagrams
 Compliment of a Set
 Subsets
Lecture 8 (section 2.3)
 Set Intersection
 Set Union
 Set Difference
 Cartesian Product
 Using Set theory to Problem Solve
MAT 107 Fundamentals of Mathematics I
Fall 2011
5
Lecture 9 (section 3.1 & 3.2)
 Addition of Whole Numbers in Base 10
 Teaching Basic Addition Facts using the Traditional Methods
 Why Students Struggle with Basic Addition Facts
 Teaching Basic Addition Facts using a Conceptual Method
 Traditional Method for Addition
 Lattice Addition
 Scratch Addition
Lecture 10
 Exam 1 covering Lecture 1 through Lecture 8 material
Lecture 11 (section 3.1 & 3.2)
 Addition of Whole Numbers in Other Number Bases
 Teaching Basic Addition Facts using a Conceptual Method
 Addition in other Number Bases
 Scratch Addition in other Number Bases
Lecture 12 (section 3.1 & 3.2)
 Subtraction of Whole Numbers in Base 10
 Teaching Basic Subtraction Facts using the Traditional Methods
 Why Students Struggle with Basic Subtraction Facts
 Teaching Basic Subtraction Facts using a Conceptual Method
 Traditional Method for Subtraction
 United Kingdom Method of Subtraction
Lecture 13 (section 3.1 & 3.2)
 Subtraction of Whole Numbers in Other Number Bases
 Teaching Basic Subtraction Facts using a Conceptual Method
 Subtraction in other Number Bases
 United Kingdom Method of Subtraction
Lecture 14 (section 3.3 & 3.4)
 Multiplication of Whole Numbers in Base 10
 Teaching Basic Multiplication Facts
 Traditional Method for Multiplication
 Modification to Traditional Method
 Lattice Multiplication Method
 Mental Multiplication Method
 Russian Peasant Multiplication Method
Lecture 15 (section 3.3 & 3.4)
 Division of Whole Numbers in Base 10
 Long Division
MAT 107 Fundamentals of Mathematics I
Fall 2011
6


Short Division
Division by a Two or Three Digit Number
Lecture 16 (section 5.1)
 Meaning of Integers
 Absolute Value
 Addition of Integers using the Traditional Methods
 Definition of or Rules for Addition
 Chip Model
 Charged Field
 Number Line
 Addition of Integers using a Non-Traditional Method
Lecture 17
 Exam 2 covering Lecture 9 through Lecture 15 material
Lecture 18 (section 5.2)
 Multiplication of Integers using the Traditional Methods
 Definition of or Rules for Multiplication
 Chip Model
 Charged Field
 Number Line
 Division of Integers using Traditional Method
 Definition of or Rules for Division

Lecture 19 (section 5.1)
 Subtraction of Integers using the Traditional Methods
 Definition of or Rules for Subtraction
 Chip Model
 Charged Field
 Number Line
 Subtraction of Integers using a Non-Traditional Method
Lecture 20 (section 4.2)
 Fact Families
 Solving Simple One Step Equations
 Traditional Method
 Non-Traditional Conceptual Method
 Solving more complex Multi-Step Equations
 Traditional Method
 Non-Traditional Conceptual Method
Lecture 21 (section 5.3 & 5.4)
 Definition of Divides
 Divisibility Rules
 Two
 Three
MAT 107 Fundamentals of Mathematics I
Fall 2011
7




 Four
 Five
 Six
 Eight
 Nine
 Ten
 Fifteen
Prime Number
Composite Number
Prime Factorization of a Composite Number
 Using a Factor Tree
 Using Compact Division
Fundamental Theorem of Arithmetic
Lecture 22 (section 5.5)
 Finding Greatest Common Divisor
 Listing Method
 Prime Factorization Method
 Euclidean Algorithm Method
 Finding Least Common Multiple
 Listing Method
 Prime Factorization Method
 Box Method
Lecture 23
 Administer a Practice Praxis Exam
Lecture 24
 Go over and Discuss Practice Praxis
Lecture 25 (section 6.1)
 Why Students Struggle with Fractions
 Introduction to Fractions
 Meaning of
 Parts of
 Types of
 Proper
 Improper
 Mixed
 Simplifying Fractions
 Equivalent Fractions
Lecture 26 (section 6.2)
 Traditional Methods for Addition of Fraction
 With Common Denominator
 With Unlike Denominators
 Commonly used Fractions
 Other Fractions
MAT 107 Fundamentals of Mathematics I
8
Fall 2011
 Non-Traditional Method for Addition of Fractions
 Addition of Mixed Fractions
Lecture 27 (section 6.2)
 Traditional Methods for Subtraction of Fraction
 With Common Denominator
 With Unlike Denominators
 Commonly used Fractions
 Other Fractions
 Non-Traditional Method for Subtraction of Fractions
 Subtraction of Mixed Fractions
Lecture 28 (section 6.3)
 Multiplication of Fractions
Lecture 29 (section 6.3)
 Division of Fractions
Lecture 30
 Using Technology While Computing With Fractions
Final Exam will cover Lecture 16 through Lecture 30 (counts as two exams)
MAT 107 Fundamentals of Mathematics I
Fall 2011
9