Rowan University
Department of Mathematics
Structures of Mathematics I – Math 01.201
Fall 2011
Professor Natalie Kautz
Course Syllabus
COURSE SYLLABUS:
A student’s presence in this class after the first meeting signifies that the student has read this
syllabus and agrees to the policies and procedures herein.
COURSE DESCRIPTION:
This 3-semester-hours course is designed to help students to improve their understanding and use
of the mathematical practices. Prerequisite: students are expected to have completed the
equivalent of Basic Algebra II.
INSTRUCTOR INFORMATION:
1. Professor: Natalie Kautz
2. Meeting time and location:
Tuesdays and Thursdays, 10:50 a.m. – 12:05 p.m., in Education Hall, room 1081
3. E-mail address: kautzn@rowan.edu (my preferred form of communication).
4. Webpage: http://www.rowan.edu/colleges/las/departments/math/facultystaff/Adjuncts/Kautz/
5. Office hours: Tuesdays and Thursdays, 9:30 – 10:30 a.m., in Robinson Hall, room 206,
phone 256-4500 ext. 3513 during those times.
6. Phone: Mathematics Department, 2nd floor Robinson Hall, call 256-4844 to leave a message.
COURSE OBJECTIVES:
This course will help students to:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
9. Understand the place value system.
10. Use place value understanding and properties of operations (commutative, associative,
distributive, identity, inverse) to perform computations with whole numbers, decimals,
fractions, and integers.
11. Classify and create word problems by operation and sub-type of operation (e.g., add to, take
away, part-part-whole, compare, array multiplication, sharing division).
12. Use Polya’s four-step problem-solving process.
13. Name and describe sets of numbers (natural/counting, whole, integers, rational, irrational,
real).
14. Use equivalent fractions as a strategy to add and subtract fractions.
15. Compute fluently with whole numbers, decimals, fractions, mixed numbers, integers, and
rational numbers.
16. Understand ratio concepts and use ratio reasoning to solve problems; analyze proportional
relationships and use a variety of solution methods to solve real-world and mathematical
problems.
17. Understand and explain how specific algorithms for operations with whole numbers,
decimals, fractions, or integers work.
18. Improve their ability to do mental math and to use estimation as a part of the problem-solving
process.
19. Demonstrate understanding of computations with whole numbers, decimals, fractions, mixed
numbers, and integers using concrete materials and diagrams (e.g., using area, discrete, and
linear models).
20. Understand and find factors, prime factors, least common multiple, and greatest common
factor.
21. Recognize that perfect squares have an odd number of factors and explain why.
22. Compare, order, and demonstrate equivalence of rational numbers and percents using concrete
materials and diagrams.
23. Use a variety of methods to solve percent problems (equivalent fractions, benchmark
fractions, percent table, etc.).
24. Recognize irrational numbers as non-terminating, non-repeating decimals.
REQUIRED MATERIALS:
1. Course Textbook: Mathematics for Elementary Teachers with Activity Manual. Beckmann,
Sybilla. 3rd Edition. Addison-Wesley, 2011. This is a textbook bundled with an activity
manual. Available for purchase at the Rowan bookstore.
2. Calculator. Students may not use a cell phone as a calculator.
3. Rowan network account (access to email).
4. Internet access (go to http://webct.rowan.edu and click on the link Browser Check to be sure
that your web browser is properly configured). Rowan’s technical assistance:
www.rowan.edu/ir/supportdesk/students/ .
COURSE GRADING POLICY:
1. Grades assigned for this course are: A = 95-100, A- = 90-94, B+ = 87-89, B = 83-86, B- =
80-82, C+ = 77-79, C = 73-76, C- = 70-72, D+ = 67-69, D = 63-66, D- = 60-62, F = 0-59.
2. Grades will be calculated using the following weightings:
5% attendance and participation
15% graded homework assignments (“Problems for Selection” homework)
15% in-class weekly quizzes (based on “Practice Exercises” homework problems)
20% in-class test #1 (covers chapters 1, 2, 3)
20% in-class test #2 (covers chapters 4, 5, 6)
25% cumulative final exam (covers chapters 1, 2, 3, 4, 5, 6, 7, 8)
3. Rowan University is committed to the success of all students. Please refer to the Mathematics
Department website http://www.rowan.edu/mars/depts/math for information regarding
University policies about learning accommodations. The Academic Success Center is located
on the 3rd floor of Savitz Hall and can be reached at 256-4234.
STUDENT INFORMATION GUIDE:
As a student of Rowan University, you have various rights and responsibilities. University-wide responsibilities are explained in detail in the Student Information Guide: www.rowan.edu/studentaffairs/infoguide .
These include the
• Academic Integrity Policy
• Student Accommodation Policy
• Class Attendance Policy
• Classroom Behavior Policy
• Laptop Computer in Classroom Policy
It is your responsibility to read these policies, understand them, and abide by them.
STUDENT RESPONSIBILITIES:
1. To review material on your own, complete the assignments, and ask questions to promote
comprehension.
2. To seek help from the professor or to get tutoring when you don’t understand something.
3. To complete the readings and homework exercises. Expect to spend two hours of time
outside of class for every hour spent in class.
4. To prepare for tests.
ATTENDANCE POLICY:
1. Attendance is mandatory due to the nature of the course. All students should make attending
class a priority.
2. Attendance will be taken at the beginning of the class.
3. If a student is absent or tardy:
a. To be an excused absence, the student must provide a written note explaining it.
b. Without a note, the absence or tardy is considered unexcused.
c. After 3 unexcused absences, I reserve the right to issue a NC (no credit) grade for
this course.
4. Attendance is expected as your presence and participation in class has a direct correlation to
your success with passing the course.
5. If absent from class, please following along with the assignments in the syllabus.
6. A missed quiz or test will be made up as soon as possible.
CLASS PARTICIPATION:
1. Students are expected to participate in small-group and whole-class discussions as a means of
promoting their own learning and contributing to the progress of the classroom community.
2. Sharing, critiquing, and discussing ideas are part of class participation.
3. Class participation requires that a student be
• in class
• on time for class
• prepared for class by reading the assignments and having homework completed
4. It is to be understood that the development of mathematical ideas within a community
frequently involves discussing ideas that are later determined to be invalid. Thus, for the
participation grade, students are graded according to thoughtful participation and not
mathematical correctness.
5. Ask questions when you do not understand. The questioning process is an integral part of
your learning.
6. Class participation will be graded through the use of a rubric filled out at three points in the
semester (5 weeks, 10 weeks, and at the end of the semester). Students will self-assess their
participation and the professor will either agree or state why she disagrees.
WHERE TO GET HELP:
A few weeks into the semester, tutoring schedules will be posted on the bulletin board outside the
math department on the second floor of Robinson Hall. Students can attend at any time during
those posted hours and do not need an appointment. Math tutors are generally available during the
day Monday through Friday. There is no fee.
CLASSROOM BEHAVIOR:
1. Improper and disruptive behavior will not be tolerated.
2. While in class, please be respectful of others. Please do not talk while instruction is taking
place as this becomes a distraction for fellow classmates and the instructor.
3. Please silence all cell phones, pagers, and other electronic devices during class.
4. Please do not listen to music during class time.
5. As a courtesy to other classmates, students are asked not to leave their seats during class
except for emergencies. Please use the restroom before class begins.
ACADEMIC INTEGRITY:
1. Students are encouraged to collaborate with others for classwork assigned in this course.
2. However, each student must independently complete homework assignments, quizzes, tests,
and the final exam.
3. Students will abide by Rowan’s student code of conduct (Please refer to Rowan’s Student
Information Guide) and policy on academic honesty (www.rowan.edu/provost/policies).
HAVE A GREAT SEMESTER!
"Problems for Section"
in textbook:
Will be collected
and graded.
p. 10 #1-8
p. 11 #3
1.2
Decimals and
1E, 1G,
p. 12-19
p. 19-20 #1-12
p. 23-25
negative numbers
1H
1.3
Comparing numbers in
1N
p. 25-28
p. 29 #1-11
Readings in Textbook
p. 1-10
Discuss course syllabus
1.1
Counting numbers
Classwork:
Activities from
Activity Manual
1D
Section
Objectives
"Practice Exercises" in
textbook: show your work,
check your answers.
Will be checked for
completion. Weekly
quizzes will be based on these
problems.
9/7
Section of Textbook
Date
(fill in as assigned)
Homework
read syllabus
#2, 7-10, 12, 13
p. 31-32 #3, 5,
11
the decimal system
1.4
Rounding Numbers
1Q, 1R
p. 32-34
p. 34 #1-4
p. 35 #2, 4, 7
2.1
The Meaning
of Fractions
2A, 2C,
2D
p. 38-42
p. 42-43 #1-9
p. 45-47
#3-10, 14-16
2.2
Solving Problems and
Explaining Solutions
none
p. 48-53
none
none
2.3
Fractions as Numbers
2I
p. 53-55
p. 55-56 #1-7
2.4
Equivalent
2J, 2L,
p. 58-62
p. 62-63 #1-10
Fractions
2M, 2O
p. 57 #1-8
p. 65-67 #1, 5,
8-15,
17, 18, 21, 24
Comparing
2Q,
p. 68-73
p. 74 #1-7
Fractions
2R, 2S
2.5
2X, 2Y
p. 76-77
#2-4, 6, 7, 17
3.1 Addition & Subtraction
3B, 3D
p. 92-97
p. 98 #1-5
p. 99 #1, 4
3.2
Commutative and
Associative Properties
of Addition
3E, 3I,
3L
p. 100107
p. 107-108
#1-12
p. 109-110
#1, 3, 7, 11-13
3.3
Common Algorithms:
Adding & Subtracting
3N,
3O
p. 111116
p. 117 #1-7
p. 118-120
#2, 3, 8-12
3.4
Adding & Subtracting
3T, 3V,
p. 121-
Fractions
3Y, 3Z
126
Adding & Subtracting
none
p. 132-
3.5
Negative Numbers
STUDY FOR TEST
read Chapter
Summary
TEST #1
p. 126-127 #111
p. 130-131
#1-3, 6, 7, 10-13
p. 136 #1-4
p. 137 #3, 4
135
#1
Covering Chapters 1-3
&
Study Items
p. 36-37, 90, 91, 137-139
and
complete
participation
rubric
4.1
Interpret Multiplication
4A
p. 140-144
p. 145 #1-3
p. 146 #1
4.2
Multiplying Numbers
in the Decimal System
4D,
4E
p. 147-148
p. 148 #1-2
p. 149 #1-4
Commutative and
Associative Properties
4G,
4I,
p. 150-157
p. 157-158
#1-11
p. 159 -162
#3, 6, 10, 13,
of Multiplication,
Area & Volume
4J,
4K
4.4
Distributive Property
4O,
4P
p. 163-168
p. 169 #1-10
p. 171-172
#1, 5-10, 16, 18
4X,
p. 173-175
p. 175-176 #1-7
p. 179-181
4.5
Properties of
Arithmetic,
Mental Math, and
4.3
14, 16, 21, 22
4U,
#4, 7, 8, 10, 16
Single-digit
multiplication facts
4V,
4W
4.6
Common Algorithm:
Multiplying
4Y, 4Z,
4AA
p. 182-186
p. 186-187 #1-6
p. 189-190
#3, 4, 7, 10, 12
5.1
Multiplying Fractions
5B, 5C,
5D
p. 194-198
p. 199 #1-5
p. 200-202
#3-5, 8, 11, 19
5.2
Multiplying Decimals
5H
p. 203-205
p. 205 #1-4
p. 206-207
#1, 3, 6, 10-12
5.3
Multiplying Negatives
5J, 5M
p. 207-209
p. 209 #1-3
p. 210 #1
5.4
Powers and
Scientific Notation
5N,
5O
p. 210-214
p. 215 #1-7
p. 216-217
#1, 3, 5-7, 11
6.1
Interpretations
of Division
6A, 6B,
6C
p. 219-224
p. 224 #1-8
p. 226 #1, 2, 6, 8
Division and
Fractions, Division
with Remainder
6D,
6F
p. 231 #1-5
p. 232-234
#1, 2, 4,
7, 11, 13
Common Long
6I, 6K,
Division Algorithm
6G, 6H,
6.2
6.3
p. 226-230
p. 246-249
p. 234-243
p. 243-244 #111
6J
6.4
6.5
6.6
Fraction Division:
How
6R,
Many Groups?
6S
Fraction Division:
How
Many in One Group?
Diving
Decimals
6T, 6U,
STUDY FOR TEST #2
read Chapter
&
Summary
TEST #2
and
7.1
Ratio, Rate,
and Proportion
16, 23, 24
p. 250-254
p. 255 #1-4
7A, 7B,
7C
p. 256-258 #1-3,
6-8, 10, 12, 13,
15
p. 258-262
p. 262-263 #1-6
6V
6X,
6W
#2-5, 8,
p. 264-265
#2, 6-11
p. 266-270
p. 270-271 #1-9
p. 272-273
#3, 5, 6
Covering Chapters 4-6
Study Items
p. 191-193,217-
218, p. 274-276
complete
participation
rubric
p. 277-282
p. 282 #1-4
p. 283-284 #3-8
7.2
Solving
Proportion Problems
by Reasoning
7D, 7F
p. 284-288
p. 288-289 #1-6
p. 292-294
#1, 3, 5, 7, 8,
11, 14, 17, 18
7.3
Ratios and Fractions
7H, 7I
p. 295-297
p. 297 #1-2
p. 298-299 #2, 4
7.4
When to Use
Proportions
7J
p. 299
p. 300 #1-2
p. 301
#2-4, 6
7.5
Percent
Increase and
Decrease
7M, 7N
p. 301-306
p. 307 #1-8
8.1
Factors and Multiples
8D
p. 314-316
p. 316 #1-4
p. 309-311 #1,
2, 4, 6-10, 12,
13, 15, 20, 22
p. 318 #3-9
Greatest Common
Factor and Least
Common Multiple
8E, 8F,
8G
8.3
Prime
Numbers
8.4
8.5
8.2
p. 323-325
#1, 6-8, 11,
13, 16, 18
p. 318-322
p. 322 #1-7
8K, 8L,
8M
p. 325-329
p. 329 #1-5
p. 330
#1-3, 5, 6
Even
and Odd
8N,
8O
p. 331-332
p. 332 #1-3
p. 333-334
#2, 3, 5-7, 9
Divisibility
8Q
p. 334-336
p. 336 #1-3
p. 337-338 #1,
3-6, 9-11, 13,
14
p. 349-351
#1-4, 6, 10, 20
Tests
8.6
Rational and
Irrational Numbers
8R, 8S,
8U
p. 338-347
p. 347 #1-13
8.7
Number Systems
none
p. 352-353
none
STUDY FOR FINAL EXAM
read Chapter
&
Summary
FINAL EXAM
Room:
and
(Cumulative)
Study Items
complete
p. 353 #1-2
Covering all
Chapters 1-8
p. 312-313,
354-355
Time:
participation
rubric