Frederick Community College
Course Syllabus
MA 105 – FUNDAMENTAL CONCEPTS OF MATHEMATICS I
Section - 04 FALL 2011
Class Begins: August 23, 2011
Class Ends: December 8, 2011
Last Day to Withdraw: November 2, 2011
Instructor Information:
Instructor:
Derek Beet
Office: N/A
Email: dbeet@frederick.edu
Phone Number: N/A
Office Hours:
Campus Mailbox Number: 830
By appointment only
Course Information:
Course: MA105
Credits: 4
Prerequisites: A grade of C in MA 82 or appropriate score on placement exam
Co-requisites: none
Course Description:
A study of the real number system for early childhood education and elementary education students.
Provides a comprehensive conceptually based background in elementary mathematics. Topics include
historical development of numeration systems, decimal notation, arithmetic algorithms in decimal and other
bases, elementary set theory and number theory. Emphasizes problem solving strategies.
This course will be included in the portfolio requirement for the AAT degree.
Core Learning Outcomes: You will be able to:
1.
2.
3.
4.
5.
6.
7.
articulate the concepts of the real number system. This will be accomplished through writing and
speaking in effective, organized, clear, and grammatically correct English appropriate for
mathematics.
interpret and analyze tables, graphs, and diagrams to convey quantitative information and solve
mathematical problems appropriate for elementary teachers.
perform mathematical operations and apply them to practical situations.
generate and evaluate alternative solutions to mathematical problems appropriate for elementary
teachers.
demonstrate a variety of problem-solving techniques using different mathematical tools and
alternative representations of numerical and analytical concepts with application to numerical data.
use the technology of a changing world appropriate to practical mathematics.
display academic honesty and adhere to professional standards in their fields.
Specific Learning Outcomes: You will be able to:
apply problem-solving strategies to solve a variety of mathematical problems.
use set theory to characterize the real number system, make mathematical conjectures, solve
problems and produce a realization of the part played by each in the development of mathematics.
3. discuss numeration systems with respect to such characteristics as place value, zero and base for
decimal and non-decimal systems.
4. develop a selection of standard and non-standard arithmetic algorithms, including estimation and
mental computation and be able to apply them to decimal (whole numbers, integers and rationals)
and non-decimal number systems.
5. identify and apply the associative, commutative and distributive properties and the properties of
closure, identity and inverse for whole, rational and real numbers.
6. relate the sets of natural numbers, whole numbers, integers, rationals, irrationals and reals. Be able
to express numbers in different forms - as fractions, decimals, percents and non-decimal bases.
7. investigate and develop ideas about the nature of numbers using number theory. Topics in number
theory include primes, composites, divisibility, greatest common factor and least common multiple.
8. discuss relationships between numbers and solve problems using ratio, proportions and percents.
9. use representations and the language of mathematics to express mathematical ideas verbally and
symbolically.
10. recognize and apply mathematics in contexts outside of mathematics.
11. recognize and use connections among different mathematical ideas.
12. gain appreciation for the breadth of mathematics beyond the class curriculum through one or more
co-curricular activities.
1.
2.
Instructional Methods:
Group and collaborative learning methods, lecture, student and teacher demonstrations. Mathematics is a
skill and must be learned by doing and practice. Homework assignments are extremely important.
Course Texts and Resources:



Mathematical Reasoning for Elementary Teachers, Fifth Edition by Calvin T. Long and Duane W.
DeTemple, Addison, Wesley, 2009
Course Materials Packet (Purchase at FCC bookstore)
Extra Materials: 1 ½ inch - 3 ring notebook with dividers, colored pencils or markers, calculator,
baggies, scissors
Progress Report:
Students will receive some form of written assessment of their progress in the course no later than the sixth
week of a fifteen week semester or one-third of the instructional time for shorter sessions.
Assessment Method:
Tests (3)
Take Home Exam
Basic Skills Proficiency Test
Quizzes (7 – Drop One!)
Group Summaries (3)
Assignments (7)
Praxis Review (2)
Class Participation/Attendance
Notebook
300 pt
100 pt
100 pt
120 pt
60 pt
140 pt
50 pt
60 pt
20 pt
Total
950 pt
The above is subject to change at instructor’s discretion.
Tests:
Tests cannot be made up! If you need to miss a test, talk to me before the test, and we will work
something out… if you provide a convincing argument that your absence is unavoidable and legitimate you
may be allowed to take it ahead of time. There are 3 tests. Unit One – CH 1 & 2, Unit Two – Ch 3 & 4, Unit
Three – Ch 5, 7 & 8
Take Home Final Exam:
This is a cumulative exam that is done at home. You must do your own work!
Basic Skills Proficiency Test:
This tests your basic skills of adding, subtracting, multiplying and dividing whole numbers, fractions, and
decimals. The test also includes work with percents. To prepare for the test, study the practice sheets in
your course materials packet (p. 1 - 3 green). You need an 80% to pass this test!
Below an 80% is a score of 0. (Not passing!)
80% or above allows you to keep the score you earned on the test. (Passing!)
No calculator is allowed! No partial credit given.
You will take the test on the 2nd day of class. If you don’t pass it, you will be given 3 more tries throughout
the semester.
Quizzes:
Quizzes cannot be made up! If you know ahead of time you will be out for a quiz, you can take it ahead of
time. If you are absent, a score of 0 will be recorded. (The top 6 scores will be counted.) All quizzes come
from homework problems – so do your homework!
Group Summaries:
With your group you will be responsible to present 3 times during the semester. Group summaries review the
objectives covered in the previous class. Here is your chance to be creative! You can come up with an
activity or game to help the class review the material. You must be present on the day of the presentation to
get credit!
Assignments:
Written Assignments are due as noted on the topical outlined! Two points will be deducted for each day (not
day class meets, but day of the week) the assignment is late – this includes excused absences too!
Assignments must show you have put the time, effort and thinking into doing the problems.
Some assignments include a class presentation. You must be present on the day of the presentation to get
credit!
Praxis Review:
You will complete 2 graded Praxis Reviews this semester. If you still need more practice get a study book
and visit the Frederick County Public Library site at www.FCPL.org , click research, online databases, then
Learn A Test. After registering (you need your library card number), go to Teaching and then choose Praxis.
Homework:
ALL homework problems should be completed in order to learn the skills in each section. Homework
problems will show up on all quizzes and some tests. It will be checked for completeness when notebooks
are graded.
Class Participation/Attendance:
I take attendance every day. You will receive 1 point a day for being on time and 1 point a day for
participating fully for the whole class time and being an active learner! Read below for a description of an
active learner. If you are absent you lose both points.
An Active Learner…
(1) Asks questions, (2) Responds to questions posed during class, (3) Is punctual in arriving at
class and is ready to learn at the moment the class begins, (4) Strives to attend every class
session, and notifies group members and the instructor when unavoidable circumstances prevent
attendance, (5) Is attentive during lectures and takes notes when appropriate, (6) Participates
energetically and effectively in group and team activities, taking a leadership role when the need
arises, (7) Completes homework assignments and is prepared to review those assignments in
class, (8) Volunteers to present problem solutions to the class, using the blackboard when
necessary, (9) Assists classmates in mastering learning targets, (10) Is willing to devote out-ofclass time to working with classmates on learning targets, (11) Always believes in the power of the
present and the future to provide new learning opportunities.
Notebook:
This course will be included in the portfolio requirement for the AAT degree. The notebook is your
mathematics portfolio. See specific requirements below.
At least a 1 ½ inch - 3 ring binder with labeled dividers organized into the following sections:
1. Chapters 1 and 2 (Thinking Critically; Sets and Whole Numbers)
2. Chapters 3 and 4 (Numeration and Computation; Number Theory)
3. Chapters 5, 6, & 7 (Integers; Fractions and Rational Numbers, Decimals and Real Numbers)
4. Quizzes and Tests
5. Assignments and Praxis Reviews
Each section should include notes, class activities, and homework. It will be graded on the last day of the
semester.
Participation Policy:
Students are expected to attend all class sessions! In case of serious illness, emergency, religious
holidays, or participation in official college functions, students remain responsible for completing the
requirements of the course.
It is expected that you registered for this class because you have no conflicts with transportation, work
schedules or child care during class meeting times. If you are having difficulty, see me as soon as possible
for extra help. Your attendance will be considered into your Class Participation grade. BE ON TIME TO
CLASS! Being on time also counts towards your Class Participation grade.
In case of absence, it is the responsibility of the student to confer with the instructor about the material
covered, homework assigned, and announcements made during absence. No late work will be accepted
without prior consent!
MATH LEARNING CENTER (B112) FALL 2011
MONDAY – THURSDAY
FRIDAY
SATURDAY
8:30 am – 8:30 pm
9:00 am – 12:30 pm
9:00 am – 1:00 pm
TESTS WILL ONLY BE GIVEN DURING THESE TIMES in B112
MONDAY
TUESDAY
WEDNESDAY
THURSDAY
FRIDAY, SATURDAY
1:30 pm – 7:30 pm
12:00 pm – 1:00 pm
2:00 pm – 7:30 pm
12:00 pm – 1:00 pm
2:00 pm – 8:30 pm
12:00 pm – 2:00 pm
3:00 pm – 6:30 pm
9:00 am – 12:30 pm
DROP IN TUTORING in B112
MONDAY—THURSDAY
MONDAY
TUESDAY
WEDNESDAY
THURSDAY
FRIDAY AND SATURDAY
10:30 am – 11:30 am
1:30 pm – 5:00 pm
5:00 pm– 6:30 pm
1:30 pm – 2:30 pm
4:30 pm – 5:30 pm
4:30 pm – 6:30 pm
9:00 am –12:30 pm
Codes of Academic Integrity and Student Conduct:
Students are required to uphold the Code of Academic Integrity and the Code of Student Conduct. Students
who violate either of these codes may receive a failing grade in the class. Information about these codes
and other student policies, procedures, and penalties is available on the Student Policy and Procedures web
page at http://www.frederick.edu/student_services/studentpolicies.aspx .
Student Services:
A variety of services are available to assist students in succeeding at FCC. Students can learn more about
these services by visiting the Student Services web page:
http://www.frederick.edu/student_services/index.aspx.
Students with disabilities who are in need of accommodations or who have questions related to disabilities
services should contact the Services for Students with Disabilities (SSD) office at 301-846-2408. Students
can learn more about these services by visiting the Services for Students with Disabilities web page:
http://www.frederick.edu/student_services/disability.aspx .
Email Communication:
All students will receive and be expected to use their FCC email address for their correspondence with
faculty and staff at the college. Students can establish and access their FCC email accounts at the login
page: https://myfcc.frederick.edu.
Blackboard:
To access blackboard go to:
http://frederick.blackboard.com/
click login
Username: W_ _ _ _ _ _ _ (7 digit student ID #)
Password: _ _ _ _ (last 4 digits of student ID #)
Click on course enrolled.
Look for announcements, assignments, and your grades.
Inclement Weather?:
(Check more than one source!) Check TV Ch23, call the FCC switchboard 301-846-2400, check the website
www.frederick.edu, listen to the radio AM930, FM99.9, FM103.1, etc.
If FCC opens at 9:30 am we will hold class starting at that time!
ALL ELECTRONICS ARE TO BE TURNED OFF BEFORE ENTERING THE
CLASSROOM! If you have an emergency, and must have your phone on, please contact me
before class and, to avoid being rude, keep phone on vibrate! NO TEXTING DURING CLASS!
MA 105 Fundamentals of Mathematics
Topical Outline
Topic
Date
Day 1
1.1 An Introduction to Problem Solving
1.2 Polya’s Problem - Solving Principles
1.3 More Problem-Solving Strategies

Day 2
Solve problems following Polya’s
problem solving principles and the
following strategies: guess and check,
make an orderly list, and draw a diagram,
look for a pattern, make a table, use a
variable, working backwards, and
eliminate possibilities.
1.4 Algebra as a Problem-Solving Strategy
1.5 Additional Problem- Solving Strategies
Assignment
Read: 1.1, 1.2, 1.3
Do: p. 6 (1a, b, c, 2, 6, 7)
p. 18 (1, 2, 12, 13, 15, 16, 17)
p. 32 (1, 23, 24)
Read 1.4, 1.5
Buy supplies
Organize Notebook
Prepare for the Proficiency Test. Practice
sheets are the p. 1 - 3 (green) in your course
materials packet.
Do: p. 44 (3, 4, 11, 23, 28, 29)
p. 54 (2, 4, 6, 9, 22, 23)
Work on Assignment # 1 – Problem Solving
Study for Quiz # 1
Cut out colored manipulative shapes.
Read 2.1
Day 3
2.1 Sets and Operations on Sets
 Define a set using a word description,
listing in braces, and set builder notation.
 Use a Venn Diagram to represent a set.
Find the complement of a set, a subset of
a set, the intersection of sets, and the
union of sets.
Do: p. 87 (1a, 2a, 3a,c, 4a,c, 6, 7, 10a, c,
d, e,14a, c, e, 15, 27, 28)
Assignment # 1 due today (20 pt)
Quiz # 1 – Chapter 1 (20 pt)
Day 4
2.1 Sets and Operations on Sets
Continued
Finish homework from 2.1
Read 2.2
Retake # 1 Proficiency Test in B112 by
Proficiency Test (100 pt)
No calculator allowed!
Day 5
GS # 1 on 2.1
2.2 Sets, Counting and Whole Numbers
 Classify a number as cardinal, ordinal, or
nominal.
 Use a Venn Diagram and set theory to
solve problems.
_____ (if needed). Bring your photo ID! No
calculator allowed.
Do: p. 100 (1, 2, 3, 11, 13, 14, 35, 36, 37, 38)
Work on Assignment # 2 – Set Theory
Read 2.3
Day 6
GS # 2 on 2.2
2.3 Addition and Subtraction of Whole Numbers
 Identify and illustrate the properties of
addition.
 Illustrate whole number addition using set
models, rods and number lines.
 Illustrate the 4 conceptual models of
subtraction.
Do: p. 116 (1, 2, 4, 7, 8, 10, 13, 40, 41, 42, 43)
Read 2.4
Assignment # 2 due today (20 pt)
Day 7
Day 8
GS # 3 on 2.3
2.4 Multiplication and Division of Whole Numbers
 Illustrate the conceptual models of
multiplication.
 Identify and illustrate the properties of
multiplication.
 Illustrate the conceptual models of
division.
 Work with exponents.
GS # 4 on 2.4
Review and catch up
Do: p. 136 (1, 2, 5a, c, e, 7, 13a, 14, 16, 20, 21,
22, 39, 40, 41)
Work on Assignment # 3 – Conceptual
Models
Study for Quiz # 2
Study for Test # 1 Chapters 1 & 2
Organize notebook
Assignment # 3 due today (20 pt)
Quiz # 2 – Chapter 2 (20 pt)
Day 9
Test # 1 – Chapters 1 & 2 (100 pt)
Read 3.1
Work on Assignment # 4 – Numeration
Report
Day 10
3.1 Numeration Systems Past and Present
 Write numbers using the Egyptian,
Roman, Babylonian, and Mayan
systems.
Do: p. 159 (1, 2, 3, 4, 5, 26, 27, 28, 29)
Read 3.2
Assignment # 4 due – Group
presentations (20 pt)
Day 11
Day 12
Day 13
3.2 Non-decimal Positional Systems, Base 5
system
 Use unifix cubes, and base ten blocks to
model counting and numbers in base 10.
 Write numbers in base ten to base five.
 Write numbers in base five to base ten.
Do: p. 165 (5, 6, 7, 8, 11)
GS # 5 on 3.2 Base Ten and Base Five
3.3 Algorithms for Adding and Subtracting Whole
Numbers
 Add and subtract whole numbers in base
ten using base ten blocks and place
value cards.
 Add and subtract whole numbers in base
five using base five blocks and place
value card.
GS # 1 on 3.3
3.3 Algorithms for Adding and Subtracting Whole
Numbers – continued
Do: p. 181 (1, 2, 3, 4, 7, 14, 16, 33, 34, 35, 36)
Read 3.3
Retake # 1 Proficiency Test in B112 by
TODAY (if needed). Bring your photo ID! No
calculator allowed.
Retake # 2 Proficiency Test in B112 by
_____ (if needed). Bring your photo ID! No
calculator allowed.
Day 14
Day 15
3.4 Algorithms for Multiplication and Division of
Whole Numbers
 Multiply whole numbers using expanded
notation, an instructional algorithm, and
the final algorithm.
 Divide numbers using the division
algorithm and short division.
Do: p. 192 (1, 2, 4, 7, 8, 9, 10, 11, 35, 36, 37,
38)
GS # 2 on 3.4
4.1 Divisibility of Natural Numbers
 Find the multiples and factors of a
number.
 Determine whether a number is prime or
composite.
 Find the prime factorization of a number.
Do: p. 241 (1, 3, 6, 7, 8, 9, 10, 11, 12, 16, 35,
36, 37, 38)
Read 4.1
Read 4.2
Assignment # 5 – Base Five due (20 pt)
Quiz # 3 – Chapter 3 (20 pt)
Day 16
GS # 3 on 4.1
4.2 Tests for Divisibility
 Test numbers for divisibility by 2, 3, 5, 9,
10, and 11.
Do: p. 253 (1, 2, 4, 5, 6, 7, 23, 24)
Day 17
GS # 4 on 4.2
4.3 Greatest Common Divisors (GCD) and Least
Common Multiples (LCM)
 Find the greatest common divisor and
least common multiple of two numbers.
Do: p. 265 (1, 2, 3, 4, 17a, 18a, 31, 33, 34)
GS # 5 on 4.3
Review and catch up
Study for Test # 2 – Chapters 3 & 4
Organize notebook
Day 18
Study for Quiz # 4
Quiz # 4 – Chapter 4 (20 pt)
Day 19
Day 20
Test # 2 – Chapters 3 & 4 (100 pt)
5.1 Representation of Integers
5.2 Addition and Subtraction of Integers
5.3 Multiplication and Division of Integers
 Use colored counters and a number line
to represent integers.
 Find the opposite and absolute value of a
number.
 Add and subtract integers using colored
counters and a number line.
 Add and subtract integers without using a
calculator.
 Multiply and divide integers without using
a calculator.
PRAXIS REVIEW – Part I due (25 pt)
11/2
LAST DAY TO WITHDRAW
Read 5.1, 5.2, 5.3
Work on Praxis Review
Part I
Do: p. 292 (1, 7a, c, 8, 10, 17a, b, 29, 30)
p. 311 (1, 3, 4, 5, 9, 11, 12, 19, 42, 43, 44)
p. 322 (1, 2, 6, 23)
Study for Quiz # 5
Read 6.1
Retake # 2 Proficiency Test in B112 by
TODAY (if needed). Bring your photo ID! No
calculator allowed.
Day 21
GS # 1 on Chapter 5
6.1 The Basic Concepts of Fractions and
Rational Numbers
 Model fractions using a set model,
fraction strips, and a number line.
 Find the common denominator of two or
more fractions. Write equivalent fractions.
 Simplify fractions
 Order fractions.
Do: p. 357 (1, 2, 3, 4, 5, 9, 11, 14, 15, 17, 18,
20, 22, 23, 29, 41, 42, 43, 44, 45, 46)
Read 6.2
Retake # 3 Proficiency Test in B112 by
_____ (if needed). Bring your photo ID! No
calculator allowed.
Quiz # 5 – Chapter 5 (20 pt)
Day 22
Day 23
Day 24
GS # 2 on 6.1
6.2 Addition and Subtraction of Fractions
 Write improper fractions as mixed
numbers.
 Write mixed numbers as fractions.
 Add and subtract fractions using models.
 Add and subtract fractions without a
calculator.
Do: p.372 (1a, 3, 4a, 5a, 6, 7, 8, 9a, 11a, 12, 31,
32)
GS # 3 on 6.2
6.3 Multiplication and Division of Fractions
 Multiply and divide fractions using
models.
 Multiply and divide fractions without a
calculator.
Do: p. 387 (1, 4, 5, 7a, 10, 11, 12, 26, 27, 29
30, 31, 35, 36, 37)
6.4 Rational Number System
 Identify and use the properties of addition
and multiplication.
 Order rational numbers.
 Solve problems using rational numbers.
Do: p. 399 (5, 6, 13, 16, 17, 22, 41, 42)
Read 6.3
Read 6.4
Work on Assignment # 6 – Fraction
Problems
Study for Quiz # 6
Day 25
GS # 4 on 6.3 & 6.4
7.1 Decimals and Real Numbers
 Write decimals in expanded form and in
expanded exponential form.
 Write fractions as decimals and decimals
as simplified fractions.
 Order decimals.
Read 7.1
Do: p. 431 (1, 2, 3, 5, 6, 7a, b, c, d, 8a, b, 9a, b,
c,10, 31, 32)
Work on Assignment # 7 – Decimal
Computations
Read 7.2
Assignment # 6 due (20 pt)
Quiz # 6 – Chapter 6 (20 pt)
Day 26
GS # 5 on 7.1
7.2 Computations with Decimals
 Round decimals.
 Add and subtract decimals without a
calculator.
 Multiply and divide decimals without a
calculator.
 Write numbers in scientific notation.
Assignment # 7 due – Group
presentations (20 pt)
Do: p. 441 (1, 2, 4, 6, 7, 24, 25, 26, 27, 32, 33,
34, 35)
Read 7.3
Day 27
Day 28
7.3 Proportional Reasoning
 Determine a ratio.
 Determine which whether two ratios
make a proportion.
 Find the missing number in a proportion.
 Solve problems using proportions.
 Determine a ratio.
 Determine which whether two ratios
make a proportion.
 Find the missing number in a proportion.
 Solve problems using proportions.
Do: p. 457 (1a, c, e, 2a, c, e, g, 3, 4a, c, e, 5a, b,
c, 6, 7, 8, 9, 26, 32, 37, 38, 39)
7.4 Percent
 Write ratios as percents and percents as
ratios.
 Write decimals as percents and percents
as decimals.
 Solve problems using percents.
Do: p. 471 (1a, b, c, d, 2, 3, 4a, c, e, 5a, c, e,
6a, 8a, c, 9, 10, 12, 29, 32, 37, 38)
PRAXIS REVIEW – Part II due (25 pt)
Retake # 3 Proficiency Test in B112 by
Read 7.4
Work on Take Home Final due _____.
Work on Praxis Review Part II – due next
class!
Study for Quiz # 7
Work on
Take Home Final due _____.
TODAY (if needed). Bring your photo ID! No
calculator allowed.
Day 29
Review and catch up
Quiz # 7 – Chapter 7 (20 pt)
Take Home Final due today (100 pt)
Day 30
12/12
Study for Test # 3 Chap 5, 6, 7
Organize notebook
Notebook due next day
.
Have a great break!
Test # 3, Chap 5, 6, 7 (100 pts)
Notebook due (20 pt)
Class Participation Grade given (60 pt)
If necessary, Make-up day due to
inclement weather
Test Dates and Scores
MA105 Fundamentals of Mathematics
Grades
Date
Group Sum. # 1
Group Sum. # 2
Group Sum. # 3
Assignment # 1
Assignment # 2
Assignment # 3
Assignment # 4
Assignment # 5
Assignment # 6
Assignment # 7
Praxis Review
(Part I)
Praxis Review
(Part II)
Quiz # 1
Quiz # 2
Quiz # 3
Quiz # 4
Quiz # 5
Quiz # 6
Quiz # 7
Drop Lowest Score!
Test # 1
Test # 2
Test # 3
Proficiency Exam
Take Home Exam
Class Part. /Attend.
Notebook
TOTAL
Possible Score
20
20
20
20
20
20
20
20
20
20
25
25
20
20
20
20
20
20
20
100
100
100
100
100
60
20
950
Student Score
Name: ______________________
Class Participation/Attendance (60 pt)
Grade: _____
I take attendance every day. You will receive 1 point a day for being on time and 1 point a day for
participating fully for the whole class time and being an active learner! If you are absent you lose both
points.
MA105 Notebook (20 points)
_____ Notebook is in a 3 ring binder with dividers.
_____ Notebook is organized either by topics or chapters.
_____ All homework is complete and in notebook.
_____ All graded assignments are included.
_____ Notebook is neat and orderly.
Grade: _____