Mathematics
HCC Pinemont Center – Learning Hub
Math 0409: Foundations of Mathematics
CRN 12049 – Fall 2016 1st Start
North Forest campus – Room 126 – MW 10am-12pm
3 hour lecture course +0 hour lab / 64 hours per semester (16 wks)
Textbook: Introductory and Intermediate Algebra (1st Ed.)
ISBN-13: 978-1-323-15682-7
Course ID: Math 0409 – 0001(12049)
Instructor: Gustavo Jesus-Wilson
Instructor Contact Information: [email protected]
Office location and hours: Preferably by appointment via email.
Course Description
Foundations of Mathematics: Topics include real numbers, proportions, descriptive statistics, basic geometry, polynomials,
factoring, linear equations, inequalities, linear models, percentage models, order of operations, set operations, quadratic equations
and rational expressions and an introduction to other models which may include exponential, quadratic and/or rational models. A
departmental final examination must be passed with a score of 60% or more in order to pass the course. Prerequisite: MATH 0306
or equivalent test score.
Prerequisites
TSIA Reading Score above 341 or GUST 0339 with a grade of C or higher; TSIA ABE level 5 or 6; TSIA Math Score 336 – 347
with Elementary Algebra Score 5 – 15 and Intermediate Algebra Score 0 – 6; Math 0106: Pass with “C” or better
Course Goal:
This course is intended for students who have either never been exposed to algebra or who have been away from the subject for
quite some time. Particularly, this course is intended to prepare students for the study of Math 0312 or for a non−Calculus−based
College Level Math course, specifically Math 1332 or Math 1333.
Course Student Learning Outcomes (SLO):
1. Identify and apply properties of real numbers, and perform accurate arithmetic operations with numbers in various formats.
2. Demonstrate the ability to manipulate/simplify algebraic expressions, & classify/solve algebraic equations with appropriate
techniques.
3. Demonstrate the use of elementary graphing techniques.
4. Apply basic geometric theorems and formulas to rectangles, squares, parallelograms, triangles, parallelograms, triangles and
circles.
5. Apply “Proportional Reasoning” to solve related problems including ratios, rates, proportion, percent and conversions of
units.
6. Recognize, examine, and interpret the linear, quadratic, exponential, and/or rational models of equations.
Learning objectives
Students will:
1.
add, subtract, multiply and divide real numbers and manipulate certain expressions.
2.
find the perimeter and area of rectangles, squares, parallelograms, triangles and circles.
3.
solve problems using scientific notation.
4.
simplify algebraic expressions.
5.
solve problems using equations and inequalities.
6.
factor polynomials using the techniques of the greatest common factor, grouping, difference of two squares and trinomials of
the form x2 + bx + c.
7.
multiply and divide, and simplify rational expressions
8.
plot ordered pairs and graph linear equations.
9.
graph linear inequalities.
10. Find the rate of change of a line & write its equation.
11.
Model situations with linear, quadratic, or exponential functions.
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Homework: Homework will be assigned daily and required to be kept neat and organized. They will be due on the
day of every unit exam to be graded and returned. Homework must show the full work for full credit. Late
homework will only be accepted one class day late with a letter grade penalty. Adjust accordingly. HOMEWORK
WILL COUNT AS MUCH AS ONE OF YOUR EXAMS.
Make up Test Policy: There will be no make- up tests under any circumstances. If you fail to show up for an exam,
you will receive a ZERO for that exam. However, you will be allowed to replace ONE excused test absence with the
grade from your final exam score, if you anticipate a missed test day, speak to me beforehand!
Grading Scale: The final letter grade will be determined by the following ten point scale:
90 - 100
A
80 - 89
B
70 – 79
C
< 70
F (poor performance)
Stopped Attending
FX (lack of attendance)
Examinations and grading formula:
3 major exams and 1 Homework Grade….…………75%
Final comprehensive exam…………………….…….25%
*There are 3 TEST grades (not including the homework grade) of which one can be replaced with the grade from
your final exam. However, it should be utilized as an emergency in the case that you cannot make it to an exam day.
If you miss an exam, you will receive a ZERO which may only be replaced by your final exam grade. If you do not
miss a test day, then I will replace your lowest exam grade with your final exam score if it improves your standing!
Final Exam Policy in Developmental Mathematics:
The following policy was adopted by Houston Community College regarding the system-wide Final Examinations
in developmental mathematics courses: If a student scores less than a 60 on the Final Exam, then the student
receives an F in the course. If a student scores at least a 60 on the Final Exam, then the grades will be averaged in
accordance with the grade calculation formula as stated on the student syllabus; i.e., the student earns an A, B, C, or
F in the course.
Attendance Policy: Class attendance is required, not optional, and attendance will be recorded for each class
meeting. The student is responsible for missed material covered during his absence. If some unavoidable situation
arises which causes you to miss class, then keep me advised. Otherwise, if your absences exceed 12.5 % (4 classes)
during this course, you will be encouraged to withdraw or expect to be administratively withdrawn.
Classroom etiquette: Cell phones and pagers should be on the vibrate mode or turned off completely. Cell
phones or other devices may not be out on the desk during class. If you must take a call, please step outside before
answering the call. Simply be respectful of your teacher and your colleagues!
Academic Honesty: All Houston Community College System students are required to exercise academic honesty in
completion of all tests and assignments. Penalties for academic dishonesty( cheating on a test, plagiarism, collusion
on an assignment, etc.) may include, but are not limited to, a reduced grade, or a “0” on the test or assignment, a
“W” in the course, or an “F” in that course.
Resources:
Any student enrolled in Math 0409 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.
HCC offers FREE online tutoring in a variety of subjects, including Mathematics, English and writing. Students can get free
assistance, 24 hours a day, 7 days a week, in Math, English and other subjects, at www.hccs.askonline.net. Typically, posted
questions are answered by an HCC tutor or faculty within 24 hours (usually under 6 hours). There are also several online math
resources that you can find with an internet search. You may also find information on the Learning Web site accessible through your
specific HCCS campus website.
Familiarize yourself with the website www.kahnacademy.org for a free resource that offers tutorials on many different subjects!
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TOPICS CALENDAR
TOPIC
INTRO. TO REAL NUMBERS & ALGEBRAIC EXPRESSIONS (Unit I)
Approximate Time
(8 hours)
This unit presents an introduction to algebra and the real number system. The instructor should emphasize addition,
subtraction, multiplication and division of real numbers and the properties of real numbers. This unit concludes with
simplifying expressions and the order of operations. Listed below are the subtopics covered in this unit:
1.1
Introduction to Algebra
1.3
Addition of Real Numbers
1.2
1.4
1.5
1.6
1.7
1.8
The Real Numbers
Subtraction of Real Numbers
Multiplication of Real Numbers
Division of Real Numbers
Properties of Real Numbers
Simplifying Expressions; Order of Operations
GEOMETRY and SET OPERATIONS (Unit II)
(6 hours)
This unit presents the basic geometric figures, their relations, and basic set operations. The instructor should
emphasize the perimeter and area of triangles, quadrilaterals, and circles and set operations including union,
intersection, and complement. Listed below are the subtopics covered in this unit:
8.2
Perimeter
8.4
Circles
8.3
Area
Appendix D. Introduction to Set Operations
RECOMMEND EXAMINATION I: COVERS UNITS I & II
SOLVING EQUATIONS AND INEQUALITIES (Unit III)
(1.5 to 2 hours)
(8 hours)
The major emphasis of this chapter is to teach solving linear equations. A mastery of this chapter requires that the
student have a thorough understanding of combining like terms and properties of equality. The skills necessary for
solving equations is extended to include working with the equality of two fractions and solving inequalities in a
single variable. Listed below are the subtopics covered in this unit:
2.1
Solving Equations: The Addition Principle
2.3
Using the Principles Together
2.2
2.4
2.5
Solving Equations: The Multiplication Principle
Formulas
Applications of Percent
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2.6
Applications and Problem Solving
2.8
Applications and Problem Solving with Inequalities
2.7
Solving Inequalities
TOPIC
Approximate Time
GRAPHS OF LINEAR EQUATIONS AND INEQUALITIES (Unit IV)
(6 hours)
This unit introduces plotting ordered pairs, rates of change (slopes), and sketching linear equations of the form y =
mx + b and linear inequalities. Listed below are the subtopics covered in this unit:
3.1
Graphs Linear Equations
3.3
Slope and Applications
3.2
3.5
3.7
More with Graphing and Intercepts
Graphing Using the Slope and the y-Intercept
Graph Linear Inequalities in Two Variables
RECOMMEND EXAMINATION 2: COVERS UNITS III, IV
POLYNOMIALS: OPERATIONS (Unit V)
(1.5-2 HOURS)
(12 hours)
This unit begins with integer exponents and scientific notation. The topics include the techniques to recognize a
polynomial and find the degree of a polynomial; perform addition, subtraction, multiplication and division of
polynomials. Listed below are the subtopics covered in this unit:
3.1
Integers as Exponents
3.3
Introduction to Polynomials
3.2
3.4
3.5
3.6
3.7
3.8
Exponents and Scientific Notation
Addition and Subtraction of Polynomials
Multiplication of Polynomials
Special Products
Operations with Polynomials in Several Variables
Division of Polynomials (Monomials Divisors Only)
POLYNOMIALS: FACTORING (Unit VI)
(6 hours)
This unit covers factorization of polynomials. Listed below are the subtopics covered in this unit:
4.1
Introduction to Factoring (GCF and Grouping)
4.5
Factoring Trinomial Squares and Differences of Squares
4.2
4.6
Factoring Trinomials (of the type x2 + bx + c only)
Factoring : A General Strategy (Omit ax2 + bx + c, a1)
RECOMMEND EXAMINATION 3: COVERS UNITS V, VI
(1.5-2 HOURS)
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TOPIC
Approximate Time
RATIONAL EXPRESSIONS AND EQUATIONS (Unit VII)
(4 hours)
This unit begins with multiplying and simplifying rational expressions. The topics include the techniques to reduce
or build–up fractions; perform addition, subtraction, multiplication and division of fractions. Listed below are the
subtopics covered in this unit:
6.1
Multiplication and Simplifying Rational Expressions (Omit ax2 + bx + c, a1)
6.7
Rational Equations and applications (Proportions only)
6.2
Division and Reciprocals (Omit ax2 + bx + c, a1)
RADICAL EXPRESSIONS AND EQUATIONS (Unit VIII)
(2 hours)
This unit covers finding the principal square roots, identifying radicands of radical expressions, identifying whether
a radical expression represents a real number and simplifying radical expressions with a perfect-square radicand.
Listed below is the subtopic covered in this unit:
8.1
Introduction to Radical Expressions (Include Perfect Square Radicands Only)
LINEAR, QUADRATIC, AND EXPONENTIAL MODELING (Unit IX)
(4 hours)
This unit covers includes matching scatter plots with tables of values and simple equations, knowing that a linear
equation has a straight line, quadratic is U-shaped, and exponential either increases or decreases without bound in
one direction and levels out in the other direction (without mentioning the term "asymptote.") Listed below are the
subtopics covered in this unit: The material for Unit IX can be found in the Eagle Online Model Course.
Linear modeling
Quadratic modeling
Exponential modeling
RECOMMEND EXAMINATION 4: COVERS UNITS VII, VIII & IX
(1.5-2 HOURS)
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Math 0409 – Foundations of Mathematics
Mr. Gustavo Jesus-Wilson [email protected]
(Please put your Course Number and your name in the subject heading of any email!)
Introductory and Intermediate Algebra, by Marvin Bittinger, Margaret Lial, et al, Pearson
Education, Inc. for HCC Developmental Math Courses 0409/0312
ISBN 10: 1-323-15682-8
ISBN 13: 978-1-323-15682-7
EXERCISES: Complete all of the ODD problems assigned, unless otherwise specified.
Week
Section
1/2
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
3
8.2
8.3
8.4
Apx D
4
2.1
2.2
2.3
2.4
2.5
2.6
2.7
5
2.8
6
3.1
3.2
3.3
3.5
3.7
Topic
EXERCISE SET
Introduction to Algebra
The real numbers
Addition of real numbers
Subtraction of real numbers
Multiplication of real numbers
Division of real numbers
Properties of Real Numbers
Simplifying Expressions; Order of Operations
1-17, 37-51, 61, 63
7-25, 39-67
25-43, 49-65, 77, 78
25-39, 65-77, 87-93
25-41, 63-73, 81, 84, 86
13-35, 53-65, 73, 75, 82
7-25, 55-71, 93-107
19-35, 45-55, 75-81, 93
Perimeter
Area
Circles
Set & Set Notation
Ch 8 & 9 Summary and review
Pg 760 1-19 ALL
Pg 768 5-15, 21-27, 41, 45
Pg 778 1-13, 21-27
Pg 748 2-30 ALL
EXAM 1
Solving Equations: The Addition Principle
Solving Equations: The Multiplication Principle
Using the Principles Together
Formulas
Applications of Percent
Applications and Problem Solving
Solving Inequalities
Applications and Problem Solving with
Inequalities
Graphs and Applications of Linear Equations
More with Graphing and Intercepts
Slope and Applications
Graphing Using the Slope and the Y-Intercept
Graphing Inequalities in Two Variables
Ch 2 & 3 Summary & Review
1-27, 29-51
11-39
9-27, 41-47, 59-73
5-21, 29-39
1-18 ALL, 37-43 ALL
1-12 ALL, 29-34 ALL
1-43, 61-71
1-12 ALL, 21-26 ALL
1-61
1-11,13-41, 43-59
1-8 ALL, 9-55 Odds
1-29
1-27
EXAM 2
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Week
Section
Topic
7
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
Integers as Exponents
Exponents and Scientific Notation
Introduction to Polynomials
Addition and Subtraction of Polynomials
Multiplication of Polynomials
Special Products
Operations with Polynomials in Several Variables
Division of Polynomials
27-61, 71-101
13-69
1-13,29-57,63-79
1-19, 27-55, 83
9- 49, 61-71
1-33, 43-59, 75-85
1-7, 17-47,63-79
5-41
5.1
5.2
5.5
Introduction to Factoring
Factoring Trinomials of the Type x 2  bx  c
Factoring Trinomial Squares and Differences of
Squares
Factoring: A General Strategy (Review of all
factoring techniques)
Ch 4 & 5 Summary & Review
5-27, 35-45
1-33, 45-59
1-35, 45-71
8
9
10
5.6
11
6.1
6.2
*6.6*
6.7
8.1
EXAM 3
Multiplying and Simplifying Rational Expressions
Division and Reciprocals
Solving Rational Equations
Applications Using Rational Equations and
Proportions
Introduction to Radical Expressions (Include Perfect
Square Radicands Only)
EXERCISE SET
1-27, 45-55, 69-73
1-11, 21-45, 55-65
1-35
1-35
23-35, 43-55
1-35, 51-63
Linear Modeling
Quadratic Modeling
Exponential Modeling
Ch14 & 16 & Auxiliary Summary & Review
12
COMPREHENSIVE DEPARTMENTAL FINAL
EXAM
Buy a Scantron at the
bookstore
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