Fundamentals of Mathematics I
COURSE OUTLINE FOR MATH 0306
(REVISED APRIL 25, 2007)
Catalog Description: Topics include fundamental operations in whole numbers, fractions and
decimals, percents, ratios, proportions, descriptive statistics, and an introduction to the real
numbers. All students who enroll in this course are expected to complete MATH 0308 and
MATH 0312 in the following consecutive semesters before attempting their first college-level
mathematics course (usually MATH 1314 College Algebra). A comprehensive Departmental
Final Exam will be given in this course.
Credits: 3 credit hours (3 Lecture).
Prerequisites:
SAT:
ASSET:
COMPASS:
ACCUPLACER:
Less than 450
Scaled Score: Less than 41
Scaled Score: Less than 49
Scaled Score: Less than 49
Course Intent: This course provides students with the basic arithmetical skills enabling them to
proceed to the next level mathematics course. It is also designed to strengthen many of the skills
that an individual must demonstrate or master in order to achieve college readiness. It is also
intended for those students who are reasonably adept at performing the simple mathematical
operations needed in every day affairs, but become quite confused when confronted with the
same operations in the context of a mathematics class.
Audience: This course is for students who require state mandated remediation.
Course Objectives: Upon completion of this course, a student should be able to:
1.
2.
3.
4.
5.
6.
7.
8.
9.
add, subtract, multiply and divide whole numbers, understand the order of
operations, and solve problems involving exponential notations.
solve problems by estimating and rounding.
add, subtract, multiply and divide integers.
find the least common multiples of two or more integers.
add, subtract, multiply and divide fractions.
add, subtract, multiply and divide with decimals and percent.
simplify algebraic expressions.
solve problems involving ratio and proportion.
read and interpret data from tables, pictographs, bar graphs, line graphs, and circle
graphs.
COURSE OUTLINE — FUNDAMENTALS OF MATHEMATICS I
REVISED: April 25, 2007
PAGE 2 OF 7 PAGES
Textbook: Bittinger, Marvin L. & Ellenbogen, David J. Prealgebra and Introductory Algebra
(2nd Ed), Addison Wesley: Boston, 2008.
Course Outline: Instructors may find it preferable to cover the course topics in the order listed
below. However, the instructor may choose to organize topics in any order, but all material must
be covered.
CONTENTS
(Approximate Time)
SECTION NUMBERS
TOPICS
1
WHOLE NUMBERS
(4 hours)
This unit begins with a brief review of standard notation and the real number line. Included are
sections on the meaning of digits in standard notation; converting between standard notation and
expanded notation; converting between standard notation and word names; writing addition
sentences that correspond to a given situation; adding whole numbers; using addition in finding
perimeter; writing a subtraction sentence that corresponds to a situation involving decreasing;
writing related subtraction sentence, subtracting whole numbers; rounding to the nearest ten,
hundred, thousand; estimating sums and differences by rounding; use of ordering symbols;
multiplying whole numbers; estimating products by rounding; use of multiplication in finding
area; writing a division sentence that corresponds to a given situation; wringing related
multiplication sentences; dividing whole numbers; solving linear equations in one variable by
trial and error; solving applied problems involving addition, subtraction, multiplication or
division of whole numbers; writing and evaluation of exponential notation
1.1
Standard Notation
2
1.2
Addition
9
1.3
Subtraction
17
1.4
Rounding and Estimating; Order
25
1.5
Multiplication and Area
34
1.6
Division
45
1.7
Solving Equations
58
1.8
Applications and Problem Solving
64
1.9
Exponential Notation and Order of Operations
81
RECOMMEND EXAMINATION I: COVERS CHAPTER 1
(1 to 1.5 hours)
COURSE OUTLINE — FUNDAMENTALS OF MATHEMATICS I
REVISED: April 25, 2007
PAGE 3 OF 7 PAGES
CONTENTS
(Approximate Time)
SECTION NUMBERS
TOPICS
2
INTRODUCTION TO INTEGERS AND ALGEBRAIC EXPRESSIONS
(8 hours)
This unit provides a comprehensive coverage of comparison of two integers, absolute value of an
integer; finding integer opposites; adding, subtracting, multiplying and dividing integers without
using a number line; application problems using addition and subtraction of integers; finding the
product of three or more integers; simplifying powers of integers; using the rules for order of
operations with integers; combining like terms; determining the perimeter of a polygon; using the
addition principle to solve linear equations in single variable.
2.1
Integers and the Number Line Operations
2.2
Addition of Integers Operations
103
2.3
Subtraction of Integers Operations
109
2.4
Multiplication of Integers
117
2.5
Division of Integers and Order of Operations
123
2.6
Introduction to Algebra and Expressions Operations
129
2.7
Like Terms and Perimeter Operations
137
2.8
Solving Equations
145
RECOMMEND EXAMINATION II: COVERS CHAPTER 2
3
FRACTIONAL NOTATION: MULTIPLICATION AND DIVISION
96
(1 to 1.5 hours)
(4 hours)
This unit addresses multiples of a number, divisibility tests for 2,3,5,6,9,10; factoring an integer;
identifying prime numbers from 1 to 100; prime factorization of composite numbers;
identification of numerator and denominator; simplifying fractions; problem solving using
fractional multiplication; determining whether two fractions are equivalent; working with the
reciprocal of a number; addition, subtraction, multiplication and division of fractions and mixed
numbers; solving linear equations using the multiplication and division principles; an
introduction to problem solving related to linear equations in a single variable.
3.1
3.2
3.3
3.4
3.5
Multiples and Divisibility
Factorizations
Fractions and Fraction Notation
Multiplication of Fractions
Simplifying
160
167
173
184
191
COURSE OUTLINE — FUNDAMENTALS OF MATHEMATICS I
REVISED: April 25, 2007
3.6
3.7
3.8
Multiplying, Simplifying, and More with Area
Reciprocals and Division
Solving Equations: The Multiplication Principle
RECOMMEND EXAMINATION III: COVERS CHAPTER 3
4
PAGE 4 OF 7 PAGES
198
208
213
(1 to 1.5 hours)
FRACTIONAL NOTATION: ADDITION AND SUBTRACTION
(6 hours)
This unit consists of finding the LCM of two or more numbers; converting from mixed numerals
to fraction notation; converting from fractional notation to mixed numbers; addition and
subtraction of fractions; evaluating expressions using mixed numerals; solving linear equations
in a single variable containing fractions; addition, subtraction, multiplication and division of
mixed numerals; using fractions in problem solving situations.
4.1
4.2
4.3
4.4
4.5
4.6
4.7
Least Common Multiples
Addition, Order and Applications
Subtraction, Equations, and Applications
Solving Equations: Using the Principles Together
Mixed Numerals
Addition and Subtraction Using Mixed Numerals: Applications
Multiplication and Division Using Mixed Numerals: Applications
RECOMMEND EXAMINATION IV: COVERS CHAPTER 4
5
DECIMAL NOTATION
228
236
246
256
263
269
282
(1 to 1.5 hours)
(4 hours)
This unit provides coverage of writing word names for decimal notation; converting between
fractions and decimals; comparing decimal numbers; rounding and estimating decimals; addition,
subtraction, multiplication and division of decimals, solving linear equations in a single variable
that contain decimals. The unit concludes with by problem solving that requires an application
of decimals.
5.1
5.2
5.3
5.4
5.5
5.6
5.7
Decimal Notation
Addition and Subtraction of Decimals
Multiplication of Decimals
Division of Decimals
More with Fractional Notation and Decimal Notation
Estimating
Solving Equations
304
314
322
331
341
351
357
COURSE OUTLINE — FUNDAMENTALS OF MATHEMATICS I
REVISED: April 25, 2007
5.8
PAGE 5 OF 7 PAGES
Applications and Problem Solving
363
CONTENTS
(Approximate Time)
SECTION NUMBERS
TOPICS
6
PERCENT NOTATION
(6 hours)
This unit covers finding fraction notation for ratios; giving the ratio of two different measures as
a rate; determining whether two pairs of numbers are proportional; solving proportions; solving
application exercises involving ratios; writing three kinds of notation for a percent; converting
between percent notation and decimal notation; converting from fraction notation to percent
notation; converting from percent notation to fraction notation; translating percent problems to
percent equations; solving basic percent problems; translating percent problems to proportions;
solving basic percent problems; solving applied problems involving percent; solving applied
problems involving percent of increase or decrease; solving applied problems involving sales tax,
percent, commission, discount, simple interest, compound interest; interest rates on credit cards
and loans.
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
Ratio and Proportion Operations
Percent Notation Operations
Percent and Fraction Notation Operations
Solving Percent Problems Using Percent Equations Operations
Solving Percent Problems Using Proportions Operations
Applications of Percent Operations
Sales Tax, Commissions, Discount, and Interest Operations
Interest Rates on Credit Cards and Loans (Optional) Operations
7
DATA, GRAPHS, AND STATISTICS
384
400
407
416
423
429
443
457
(3 hours)
This unit covers finding the average of a set of numbers; problem solving using averages; finding
the median of a set of numbers; solving applications involving medians; finding the mode of a set
of numbers; solving problems using modes; comparing two sets of data using their means;
extracting and interpreting data from tables; extraction and interpreting data from pictographs;
extracting and interpreting data from bar graphs; drawing bar graphs; extracting and interpreting
data from bar graphs; drawing bar graphs; extracting and interpreting data from line graphs;
drawing line graphs; extracting and interpreting data from circle graphs; drawing circle graphs;
7.1
7.2
7.3
7.4
Averages, Medians and Modes
Tables and Pictographs
Bar Graphs and Line Graphs
Circle Graphs
474
485
494
505
COURSE OUTLINE — FUNDAMENTALS OF MATHEMATICS I
REVISED: April 25, 2007
PAGE 6 OF 7 PAGES
RECOMMEND EXAMINATION V: COVERS CHAPTERS 5, 6, 7
(1 to 1.5 hours)
REFVIEW FOR FINAL EXAMINATION: COVERS CHAPTERS 1-7
(1 to 1.5 hours)
COMPREHENSIVE FINAL EXAMINATION: COVERS CHAPTERS 1-7
(1 to 1.5 hours)
System-Wide Policies:
1. Each instructor must cover all course topics by the end of the semester. The
final exam is comprehensive and questions on it can deal with any of the
course objectives.
2. Each student should receive a copy of the instructor’s course syllabus during
the first week of class.
3. A minimum of three in class tests and a comprehensive final departmental
examination must be given. All students must take the final examination.
4. All major tests should be announced at least one week or the equivalent in
advance.
5. The final exam must count for at least 25 to 40 percent of the final grade.
6. The final exam course average will be computed using a ten point scale
(90–100 "A", 80–89 "B", 70–79 "C", 69 or below "F or IP").
7. Neither an open book nor a take home major test may be given at the
discretion of the instructor.
8. Any review sheet(s) should be comprehensive and the student should not feel
that classroom notes, homework, and tests might be ignored in favor of the
review sheet for any examination.
9. No calculators are to be used on graded course work and in particular all
examinations.
Resource Materials: The student textbook is supplemented by MyMathLab. Students should
be encouraged to access MyMathLab to review problems, work interactive exercises, view
video presentations related to specific topics and use the tutoring component. Any student
enrolled in Math 0306 at HCC has access to the Learning Resource Center (LRC) where they
may get additional help in understanding the theory or in improving their skills. The LRC is
staffed with mathematics faculty and student assistants, and offers tutorial help, videotapes and
computer assisted drills. Also available is a student solutions manual that may be obtained from
the bookstore.
Suggested Methods: It is helpful to begin each class with questions related to previous material
discussed and assigned homework problems. It is recommended that allowing the students to
work on examples in class follow lectures and new material. Students should be encouraged to
COURSE OUTLINE — FUNDAMENTALS OF MATHEMATICS I
REVISED: April 25, 2007
PAGE 7 OF 7 PAGES
work the review exercises at the end of each chapter and prompted to use the Learning Resource
Center at their respective college.
Final Examination: The final examination is departmental and consists of 50 multiple-choice
problems. The problems cover only the material required in this course.
Americans with Disabilities Act (ADA): Persons needing accommodations due to a
documented disability should contact the ADA counselor for their college as soon as possible.
Identify all documented disabled students and insure them that your class will be structured to
comply with their disabilities. It is recommended that you put a clause in you course syllabus
that addresses the disabled student.