1. COURSE DESCRIPTION.Mathematical modeling uses graphical, numerical,
symbolic, and verbal
techniques to describe and explore real-world data and phenomena. Emphasis is on
the use of elementary
functions to investigate and analyze applied problems and questions , on the use
of appropriate supporting
technology, and on the effective communication of quantitative concepts and
results. THIS COURSE IS
NOT AN APPROPRIATE PREREQUISITE FOR PRECALCULUS OR CALCULUS. Students who must
take precalculus must understand the implications of taking MATH 1101 (See the
instructor immediately if
you have any questions).
2. PREREQUISITE. Knowledge of high school algebra II , or equivalent. This
expressions, first degree equations and inequalities, exponents, radicals,
solving and graphing linear
equations, factoring quadratic expressions, and other topics.
3. COURSE OBJECTIVES.
Algebra. Students will demonstrate the ability to:
a. Graph points.
b. Graph linear, piecewise linear, exponential, logarithmic, and quadratic
functions. and identify horizontal asymptotes.
c. Determine the equation of a line given two points or one point and the slope.
d. Determine the absolute value of a quantity.
e. Solve and estimate solutions to linear, quadratic, exponential, and
including use of the properties of exponents and common and natural logarithms.
f. Solve linear systems of two equations by substitution and elimination,
that have a unique solution, no solution, or many solutions.
g. Simplify expressions using the laws of exponents and logarithms.
h. Calculate average rate of change of any function.
i. Perform arithmetic calculations to answer questions regarding two-variable
presented in tabular, graphical, or equation form.
j. Express and compare very large and very small numbers using scientific
orders of magnitude.
k. Factor quadratic expressions .
l. Complete the square of quadratic expressions.
m. Express the square root of negative numbers in terms of the imaginary unit, i.
n. Given conversion factors, convert units of measure.
o. Use the quadratic formula to solve quadratic equations
Functions. Students will demonstrate:
a. The understanding of the definitions of function, domain, range, independent
dependent variables, and input and output.
b. The ability to determine if tables, graphs, and equations represent
c. The ability to determine the domain and range of functions as mathematical
or in a physical context.
d. The ability to determine from the graph of a function the values of the
variable for which the function increases, decreases, or remains constant.
Linear and piecewise linear functions. Students will demonstrate the
a. Determine when two real-world variables are related by a linear or piecewise
b. Calculate, and interpret average rate of change as slope.
c. Model the behavior of two real-world variables that are directly proportional
related by a linear or piecewise linear function using tables, graphs,
d. Evaluate linear and piecewise linear functions.
e. Use a linear function to approximate the value of a non-linear function.
f. Interpret the intersection of the graphs of linear functions as equilibrium
Exponential Functions. Students will demonstrate the ability to:
a. Determine when two real-world variables are related by an exponential
b. Model the behavior of two real-world variables that are related by an
function using tables, graphs, equations, or combinations thereof including such
applications as population growth and decay, radioactive decay, simple and
interest, inflation, the Malthusian dilemma, musical pitch, and the Rule of 70.
c. Change the base of an exponential function to determine rate of growth/decay,
growth/decay factor, and effective and nominal interest rate .
d. Express continuous growth/decay in terms of the number e.
e. Evaluate exponential functions.
f. Determine the exponential equation model from the table or graphical model.
g. Compare linear to exponential growth.
Logarithmic Functions. Students will demonstrate:
a. The ability to determine when two real-world variables are related by a
b. The ability to model the behavior of two real-world variables that are
related by a
logarithmic function using tables, graphs, equations, or combinations thereof
such applications as pH and the decibel system.
c. The understanding of the natural logarithm.
d. The ability to graph logarithmic functions.
Quadratic Functions. Students will demonstrate the ability to:
a. Estimate horizontal intercepts of quadratic functions from their graphs.
b. Determine the horizontal intercepts of quadratic functions in factored form.
c. Determine the vertex, axis of symmetry, and horizontal and vertical
quadratic functions in either the a-b-c or a-h-k forms.
d. Convert quadratic functions from the a-b-c form to the a-h-k form and vice
e. Determine when two real-world variables are related by a quadratic function
calculating the average rate of change of the average rates of change.
f. Model the behavior of two real-world variables that are related by a
using tables, graphs, equations, or combinations thereof including such
maximum area for fixed perimeter, minimum perimeter for fixed area, free fall ,
maximum profit, and break-even analysis.
4. COURSE COVERAGE. We will cover the following sections from the text:
Chapter 1 Making Sense of Data and Function (1.1 - 1.5)
Chapter 2 Rates of Change and Linear Functions (2.1 - 2.8)
Chapter 3 When Lines Meet: Linear Systems (3.1 - 3.2, 3.4)
Chapter 4 The Laws of Exponents and Logarithms: Measuring the Universe (4.1 -
Chapter 5 Growth and Decay: An Introduction to Exponential Functions (5.1 - 5.6)
Chapter 6 Logarithmic Links: Logarithmic and Exponential Functions (6.1 - 6.5)
Chapter 8 Quadratic and Other Polynomial Functions (8.1 - 8.4)
IMPORTANT NOTE: Georgia State University and its faculty are not responsible for
outcomes due to
individual technical issues, nor scheduled WileyPlus downtimes. It is expected
that the students will be
responsible for completing their work in a timely fashion as to alleviate any
pressures these scheduled
downtimes occur. All students will be notified of these downtimes by WileyPlus
announcements page of the course.
a. Three midterm tests (closed book/notes, 15% each): 45%
b. WileyPlus online homework and quizzes : 20%
c. Excel Projects: 10%
d. Final Exam (closed book/notes, cumulative): 25%
e. Bonus points: For example, each of the Pre-QL and Post-QL questions carry 0.3
Example of Course Grade Computation:
Test Grades: T1 = 88, T2 = 72, T3 = 68; WileyPlus online homework and quizzes =
Excel Project average = 90; Final Exam = 76; Bonus: 2.7.
Then the overall course score is 0.15*(88+72+68) + 0.20*85 + 0.10*90 + 0.25*76 +
2.7 = 81.9
6. GRADING SCALE. We will use the following grading scale (the letter
grade A + is NOT available):
7. Makeup Policy: Your final exam grade will replace your missed exam
grade. No make-up exams will
be given unless in some extreme situations. Absence from the final exam will
result in a grade of F for the
course unless arrangements are made PRIOR (at least one week before the final
exam) to its administration.
8. CALCULATOR Policy . You are recommended to have a scientific calculator
or agraphing calculator .
If you are not strong in mathematics, I strongly recommend you obtain a graphing
calculator. You are not
allowed to share calculator with any other party in your class during any in
class quiz or exam, unless
permitted by your instructor.
2. Visit the Math Assistance Complex (MAC), Kell Hall 122 (phone: 404-413-6462).
3. Visit the Counseling Center for Learning assistance,
Test anxiety classes, and Student support
services (phone: 404-413-1641)
4. African American Student Services (phone: 404-413-1530)
5. A private tutor list is available at Math Assistance Complex and Math
Arithmetic and Problem Solving
Brief description: A deep examination of topics in
mathematics that are
relevant for elementary school teaching. Problem solving . Number systems:
whole numbers, integers, rational numbers (fractions) and real numbers (dec-
imals) and the relationships between these systems. Understanding multipli-
cation and division, including why standard computational algorithms work.
Properties of arithmetic. Applications of elementary mathematics.
Course Objectives: To strengthen and deepen knowledge and understand-
ing of arithmetic, how it is used to solve a wide variety of problems, and
how it leads to algebra. In particular, to strengthen the understanding of
and the ability to explain why various procedures from arithmetic work.
To strengthen the ability to communicate clearly about mathematics, both
orally and in writing. To promote the exploration and explanation of mathe-
matical phenomena. To show that many problems can be solved in a variety
Problem solving: Polya’s principles. Writing explanations.
Numbers: The natural numbers, the whole numbers, the rational numbers
(fractions), and the real numbers (decimals). The decimal system and place
value. Representing decimals with bundled objects. Representing decimals
on a number line. Comparing sizes of decimals. Finding decimals in between
decimals. Rounding decimals. The meaning of fractions. The importance
of the whole associated with a fraction. Improper fractions . Equivalent
fractions. Simplest form of a fraction . Fractions as numbers on number
lines. Comparing sizes of fractions: by giving them common denominators,
by converting to decimals , and by cross-multiplying. Using other reasoning to
compare sizes of fractions. Solving fraction problems with the aid of pictures.
Percent. Benchmark percentages and their common fraction equivalents.
Solving percentage problems with the aid of pictures. Solving percentage
Addition and subtraction : Interpretations of addition and
relationship between addition and subtraction. Explaining why the standard
algorithms for adding and subtracting whole numbers and decimals work.
Using regrouping in situations other than base 10, for example in calculating
elapsed time by replacing 1 hour with 60 minutes. Adding and subtracting
fractions. Explaining why we add and subtract fractions the way we do.
The importance of the whole when adding and subtracting fractions, espe-
cially in story problems. Recognizing and writing story problems for fraction
addition and subtraction. Recognizing story problems that are not solved
by fraction addition or subtraction. Mixed numbers. Understanding when
percentages should and should not be added. Calculating percent increase
and decrease with the aid of pictures. Calculating percent increase and de-
crease numerically. Percent of versus percent increase or decrease. The
commutative and associative properties of addition and their use in mental
arithmetic. Using properties of addition to aid the learning of basic addition
facts. Other (mental) methods for adding and subtracting : rounding and
compensating, subtracting by adding on. Writing equations that correspond
to a mental method of calculation (to demonstrate the connection between
mental arithmetic and algebra).
Multiplication: The meaning of multiplication. Ways of showing multiplica-
tive structure: with groups, with arrays, and with tree diagrams. Using the
meaning of multiplication to explain why various problems can be solved by
multiplying. Explaining why multiplication by 10 is easy in the decimal sys-
tem. Why the commutative and associative properties of multiplication and
the distributive properties make sense and how to illustrate them with arrays,
areas of rectangles, and volumes of boxes. Using properties of arithmetic in
solving arithmetic problems mentally. Writing equations that correspond
to a mental method of calculation (to demonstrate the connection between
mental arithmetic and algebra). Using properties of arithmetic to aid in the
learning of basic multiplication facts. The distributive property and FOIL.
Using multiplication to estimate how many. The partial products multiplica-
tion algorithm. Using pictures and the distributive property to explain why
the standard and partial products procedures for multiplying whole numbers
are valid. Explaining why non-standard strategies for multiplying can be
correct or incorrect, such as explaining why 23 × 23 ≠ 20 × 20 + 3 × 3
and explaining why 32 × 28 = 30 × 30 − 2 × 2. The meaning of multi-
plication for fractions. Recognizing and writing story problems for fraction
multiplication. Recognizing story problems that are not problems for frac-
tion multiplication. Explaining why the procedure for multiplying fractions
works. Powers. (Optional: scientific notation.) Multiplication of decimals:
explaining why the procedure for the placement of the decimal point is valid.
Multiplication of negative numbers. Understanding that multiplication does
not always “make bigger.”
Division: The meaning of division (two interpretations, with or without re-
mainder). Understanding when the answer to a story problem solved by
whole number division is best expressed as a decimal, as a mixed number,
or as a whole number with a remainder. Why dividing by zero is unde-
fined. The scaffold method of division. Explaining why the scaffold and
standard longhand procedure for dividing whole numbers works. Explaining
why some non-standard methods of division are valid. The relationship be-
tween fractions and division: explaining why .
representations of fractions. Explaining the relationship among remainder,
mixed number, and decimal answers to division problems .
Chapter 1 Problem Solving, Chapter 2 Numbers, Chapter 3 Fractions, Chap-
ter 4 Addition and Subtraction, Chapter 5 Multiplication, Chapter 6 Multi-
plication of Fractions, Decimals, and Negative Numbers, Chapter 7 Division,
through section 7.3 only.
Math 7001: for graduate credit, students must complete an additional
course project. The project could consist of several essays, or a longer paper,
in which the student discusses some aspect of the course material in depth,
or in which the student relates the course material to their future teaching
(e.g., with a collection of lesson plans or with a discussion of some lesson
plans). However, other creative ideas could also be acceptable. For example,
students might think of a creative way to tie their course project for math
7001 to something they will be doing for one of their other courses.
Students will learn the geometric characteristic
of the ellipse equation. Some of the characteristics will be
the elliptical focus points, eccentricity, and extremities.
Students will learn that when the eccentricity
(e) is between
0 and one, it is an ellipse. If e = 0, it is a circle.
The student will learn to convert an elliptical quadratic
formula to a more visual equation by completing the square.
The student will see the minor differences of the equation
from a circle equation. The student will also learn about the
other parameters of the elliptical polynomial equation. For a
real life application, the student will go through an exercise
of determining the Mars’ elliptical orbit.
The teacher will give a string that is longer
than the width of
the focus points. Students are to pair up and use the string
and a writing instrument to draw an elliptical shape.
Students will write down objects have the elliptical shapes
Teacher will review the quadratic equation. The
review how to represent it with polynomials by completing
the square. The teacher will review the quadratic equation of
a circle and parabola. The teacher will show a picture of
ellipse. The teacher will squeeze a circle to an elliptical
shape. The teacher will give the quadratic equation (using
the polynomial format) of an ellipse and its characteristics:
eccentricity, focus, and extremities.
The students will break into groups of three to
four and work
on textbook problems . They will work on exercises to
convert elliptical quadratic equations to its polynomial
format. They will identify the focus, extremities of the minor
axis, and vertices. They will draw the elliptical shape. They
will work as a group to determine the elliptical polynomial
equation on the orbital path of Mars. They should seek
assistance from their peers first. If they need help outside of
their group, the teacher can assist or an advanced student
will be asked to help. If they finish early, they can start on
their homework assignments.
Assessment (based on
The student will be given equations, eccentricity
and geometric figures in a test. The student will be asked to
determine which are associated to an ellipse. Quadratic
formulas will be given. The student will be asked to translate
it to the quadratic polynomial equation of an ellipse. The
student will be asked what the eccentricity, the foci, and
other elliptical parameters are. The students will be asked to
derive the orbital path of Mars given different orbital
parameters that differ from its real parameters..
students or special
Students will enter in their journal the
eccentricity, axis, axes, focal point, focus, and other words
they don’t know. They are to write down their questions.
The teacher or their peers will answer the questions . They
will write down the answers in their journal . They are advise
to use the free tutoring classes or come in early or after
school for sessions with the teacher
Extensions (for gifted
Students will go on the Internet and research
discovery that the Mars orbital path was elliptical with the
Sun being at one of the focus. Students will investigate the
orbits of Halley’s comet which has a more elongated
elliptical orbit. The students will determine when we will
see Halley’s comet again. The students can also determine
the intercontinental orbit used for a space vehicle to travel
from Earth to Mars.
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