MATH 181: Fundamentals of Mathematics I: Numbers & Operations
Instructor:
Office phone:
Office:
Office hrs:
Bill Blubaugh, Ph.D.
970-351–2028
Ross Hall 2239D
9:00 – 10:00 (M W F),
1:30 – 2:30 (M W F)
Others by appointment
Email:
Math office:
FAX:
Credit:
Fall, 2011
[email protected]
970-351–2820
970-351–1225
3 semester hours
Course Description: This is the first of a 3-course sequence particularly pertinent to prospective
elementary teachers, presenting fundamentals of mathematics from a modern approach. Its
primary emphasis is the development of the real number system in conjunction with the four
arithmetic operations. Explorations focus on elementary mathematical structures with attention
to subsets of the real numbers, including natural numbers, integers, and rational numbers, via
analyses of patterns, relationships, and properties. Mathematics content is presented in a problem
solving and exploratory context.
Required Text and Activities Manual: Beckmann, S. (2011). Mathematics for Elementary
Teachers (3rd ed.). Boston, MA: Pearson Addison Wesley and Beckmann, S. (2011). Activities
Manual to Accompany Mathematics for Elementary Teachers (3rd ed.). Boston, MA: Pearson
Addison Wesley.
Required Materials: Colored pencils and a calculator. I recommend the Texas Instruments
Graphing Calculator (TI-73), which you can continue through the MATH 181/182/387 sequence.
Online Manipulatives: In class we will use various manipulatives. The following link provides
some of these manipulatives virtually and you can use them to practice the ideas from class and
get help for your assignments. You will be given manipulatives during in-class tests. National
Library of Virtual Manipulatives: http://nlvm.usu.edu/en/nav/vlibrary.html
Course Obligations: As part of the General Education Program, successful completion of
MATH 181 and 182 satisfies the Category 2 Mathematics Skills Area requirement. The ultimate
goal of this course sequence is to increase content knowledge, broaden teaching practices, and
foster confidence in teachers of elementary mathematics. MATH 181 course content involves:
• Use of mathematics to structure understanding of and investigate questions in the world
around us.
• Treatment of mathematical content at an appropriate level.
• Use of numerical, graphical, and algebraic representations.
• Interpretation of data, analysis of graphical information, and communication of process and
solutions in written and oral form.
• Use of mathematics to formulate and solve problems.
• Use of technology such as calculators and computers to support the use of mathematics.
Method of Evaluation:
There will be three full-period tests, three quizzes, four or five collected homework assignments,
about 5 in-class assignments and a final examination. The final exam will be comprehensive and
will be given at the schedule time during Final Exam Week. Each of the three tests will be worth
50 points, each quiz will be worth 25 to points, and each homework and in-class graded
assignments will be worth 5 to 15 points. The total number of evaluation points in the course is
400. The lowest homework grade will be dropped.
Evaluation:
Approximate Number of Points Per Graded Task
♦ 50 points In-class grades work
♦ 100 points Homework/Quizzes
♦ 150 points Tests
♦ 100 points Comprehensive Final Examination
Final Grade Assignment as Percent of Total Points Obtained
A: 92.5% or greater
A-: 90.0 to 92.4%
B+: 87.5% to 89.9%
B: 82.5% to 87.4%
B-: 80.0% to 82.4%
C+: 77.5% to 79.9%
C: 72.5% to 77.4%
C-: 70.0 to 72.4%
D+: 67.5% to 69.9%
D: 62.5% to 67.4%
D-: 60% to 62.4%
F: 59.9% or below
Descriptions and Expectations of Assessments:
Homework: We will take a few minutes every class period to address any questions from the
homework. You will always have a class period to ask questions about the homework before
having a quiz over it.
• Late work will not be accepted.
• Work is expected to be organized and stapled in order.
• Homework is the responsibility of each individual; however, you are encouraged to work
with others outside of class time to complete your homework.
• Homework is your study material for tests! Justify your results, even if you used a
calculator or mental math. Explain yourself using words or drawings. You should ask
yourself: Will I be able to understand my work when reviewing for the test? Keep your
homework after it is returned.
• Each homework question will be worth 2 points. Two points will be awarded if the
solution is completely correct, one point will be awarded for a solution with an error, and
no points will be awarded for incorrect and incomplete solutions.
• Since some of the in-class work will be group assignments, it is vital that you attend all
classes. You will not receive credit for the assignment if you are not in class to work on
the project/assignment.
• Late homework will not be accepted.
Quizzes: Typically each quiz will consist of 5 questions. You will not be able to make up any
missed quizzes. Each quiz is worth 20 points.
Tests and Final Comprehensive Exam: All 3 regular tests will be in-class and notes may not
be allowed. Some portions of an exam may include a non-calculator portion. You will not be
allowed to make up a missed test. Evaluation of the examinations is based on point values of
each test item, with partial credit awarded as appropriate.
Missed Materials: Outside of my office (Ross 2239D), you will find a file for your class. This
folder is for handouts, graded homework, tests, quizzes, etc. that you may not have picked up
during class. You can pick up these materials at any time – I do not need to be present. Please do
not use this folder for materials that you want to turn into me.
Student Guidelines for Participation in Meaningful Mathematical Discussions
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Listen carefully to the ideas being express to see if they make sense to you.
As appropriate ask for clarification if you do not understand what is being talked about.
Very likely you are not the only person who is confused.
Depending on the context, express your ideas in such a way that your entire group or class
can hear you idea.
Asking if anybody has any questions about what you said can be a great way to help clarify
the ideas you are trying to present.
In the final analysis, you are responsible for finding a way to make sense of the mathematics,
which is covered in the class.
UNC Policies
• Student Handbook UNC’s policies and recommendations for academic misconduct will
be followed. Consult your student handbook for university policies on student conduct in
the classroom, cheating, plagiarism, and other academic expectations
(http://www.unco.edu/dos/handbook/index.html).
You are expected to attend class and take responsibility for your own learning.
• Disability Support Services: Students who believe that they may need accommodations
in this class are encouraged to contact the Disability Support Services at (970)-351-2289
as soon as possible to ensure that accommodations are implemented in a timely fashion.
• Honor Code: All members of the University of Northern Colorado community are
entrusted with the responsibility to uphold and promote five fundamental values:
Honesty, Trust, Respect, Fairness, and Responsibility. These core elements foster an
atmosphere, inside and outside of the classroom, which serves as a foundation and guides
the UNC community’s academic, professional, and personal growth. Endorsement of
these core elements by students, faculty, staff, administration, and trustees strengthens the
integrity and value of our academic climate.
• Portable Electronic Devices - Please extend courtesy to your instructor and fellow
students by turning off your portable electronic devices such as: cell phones, pagers, and
iPods. Although not an audio issue, text-messaging is a distraction to other students and
prevents you from full participation in class. You should keep your portable electronic
devices in your backpack or purse during class. Your personal electronic devices should
not be on your desks. If you know that you may need to accept an emergency phone call
during class or if you have children in childcare or school, please let the instructor know.
If you need to take a phone call during class, please step out of the classroom while you
complete your call. Thank you for your cooperation.
Tutoring Services: There are two resources you can seek out for tutoring:
o The Math Lab, located in Ross Hall Room 1250, provides drop-in tutoring services for
MATH 181 and other students. Available times will be posted on the door and online at
http://hopper.unco.edu/mathed/tutoring.
o Tutoring is also available at the Center for Human Enrichment in the basement of
Michener. Appointments are necessary for each one-hour appointment. To schedule an
appointment, you need to go to the center. Sessions with a tutor are provided for one
hour. An appointment has to be made for each tutoring session.
Important Dates:
• August 26, 2011: Last day to add a course
• September 2, 2011: Last day to drop a course
• September 5, 2011: Labor Day - No Classes
• October 14, 2011: Last day to withdraw from course
• November 23-27: Thanksgiving Break – No Classes
• December 2, 2011: Last Day of Classes
• December 7, 2011 (10:45 – 1:15) Course Final
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Course Objectives: Upon successful completion of this course, you will be able to:
• Solve mathematical problems involving number and operations using a variety of strategies.
• Reason about number and operations including making and investigating mathematical
conjectures and developing and evaluating mathematical arguments.
• Communicate clearly and precisely mathematical ideas about whole numbers, integer
numbers, rational numbers, and real numbers.
• See connections between number and operations and algebra and geometry.
• See connections between the mathematical ideas of the course - whole numbers, integer
numbers, rational numbers, real numbers, and arithmetic operations.
• Use representations to model and explore real-world phenomena.
• Evaluate and consider the reasonableness of mathematical solutions in the area of number
and operations.
• Select appropriate tools for computation, whether mental computation, estimation, paper and
pencil techniques, or technology based approaches.
• Be aware of the role of culture and history in the development of the real number system.
• Understand and be able to explain the mathematics that underlies the procedures used for
operating on whole numbers, integer numbers, rational numbers, and real numbers.
• Understand and be able to explain the distinctions among whole numbers, integers, rational
numbers, and real numbers.
• Convert effectively among fractions, decimals, and percents.
• Understand and be able to explain fundamental ideas of number theory.
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Use an activity-oriented approach to learning and teaching mathematics.
Outline of Course Content:
• Basic Set Theory
o Venn diagrams
o Sets, subsets, intersection, and union
• Whole Numbers
o Place value of the base-ten number system
 Numeration systems
o Arithmetic Operations
 Order of operations
 Standard and alternative algorithms
 Number properties of the whole numbers
 Inverse operations
o Structure of the Whole Numbers – Number Theory
 Fundamental Theorem of Arithmetic
 Prime Number Test
 Divisibility
 Factors and multiples
• Integers
o Comparing and ordering integers
o Arithmetic operations
 Standard and alternative algorithms
 Number properties of the integers
• Rational Numbers
o Definition of ratio and rational numbers
o Fractions
 Types of fractions
 Mixed and improper fractions
 Comparing and ordering fractions
 Arithmetic operations
 Standard and alternative algorithms
o Decimals
 Terminology and notation
 Comparing and ordering decimals
 Arithmetic operations
 Standard and alternative algorithms
o Connections between fractions and decimals
 Negative exponents
 Terminating and repeating decimals
 Density of rational numbers
 Number properties of the rational numbers
o Percents
 Proportions
 Calculations with percents
• Real Numbers
o Irrationals
 Definition of irrational
 Number properties of the real numbers
These instructional goals are aligned with Standards 1 and 6 of the Colorado Model Content
Standards for Mathematics, the Number and Operations Standard of the National Council of
Teachers of Mathematics, and the Number and Operations recommendations for elementary
teacher preparation by the Conference Board of the Mathematical Sciences.
For Colorado Model Content Standards for Mathematics see:
http://www.cde.state.co.us/cdeassess/documents/OSA/standards/math.htm
For Searchable Content Standards for Mathematics see:
http://www.cde.state.co.us/cdeassess/UAS/CoAcademicStandards.html
For National Council of Teachers of Mathematics see: http://www.nctm.org/
Note: Read each Section to be addressed in class once or twice before class-time.
Tentative Class Schedule
Week of:
Week 1
8/22/11
Week 2
8/29/11
Collect Homework –
Wednesday
Week 3
9/5/11
Quiz #1 – Wednesday
Week 4
9/12/11
Test #1 – Wednesday
Topics
Chapter 1: Numbers and the Decimal System
• 2.2 Interlude: Solving Problems & Explaining Solutions
1.1 The Counting Numbers
• 1.2 Decimals and Negative Numbers
• 1.3 Comparing Numbers in the Decimal Numbers
• 1.4 Rounding Numbers
Chapter 2: Fractions
• 2.1 The Meaning of Fractions
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• 2.3 Fractions as Numbers
• 2.4 Equivalent Fractions
• 2.5 Comparing Fractions
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2.6 Percents
Chapter 3: Addition and Subtraction
• 3.1 Interpretations of Addition and Subtraction
Week 5
9/19/11
Week 6
9/26/11
Collect Homework –
Wednesday
Week 7
10/3/11
Week 8
10/10/11
Quiz #2 – Monday
Week 9
10/17/11
Collect Homework–
Wednesday
Week 10
10/24/11
Week 11
10/31/11
Test #2 – Monday
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3.2 The Commutative & Associative Properties of
Addition, Mental Math & Single-Digit Facts
• 3.3 Why the Common Algorithms for Adding and
Subtracting Decimal Numbers Work
• 3.4 Adding and Subtracting Fractions
• 3.5 Adding and Subtracting Negative Numbers
Chapter 4: Multiplication
• 4.1& 4.2 Interpretations of Multiplication &
3Multiplying by 10
• 4.3 The Commutative and Associative Properties of
Multiplication, Areas of Rectangles, and Volumes of
Boxes
• 4.4 The Distributive Property
• 4.5 Properties of Arithmetic Mental Math, & SingleDigit Multiplication Facts
• 4.6 Why the Common Algorithm for Multiplying
Whole Numbers Works
Chapter 5: Multiplication of Fractions, Decimals, and
Negative Numbers
• 5.1 Multiplying Fractions
• 5.2 Multiplying Decimals
• 5.3 Multiplying by Negative Numbers
• 5.4 Powers and Scientific Notation
Chapter 6: Division
• 6.1 Interpretations of Division
• 6.2 Division & Fractions and Division with Remainders
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6.3 Why the Common Long Division Algorithm Works
6.4 Fraction Division for the “How Many Groups?”
Perspective
• 6.5 Fraction Division for the “How Many in One
Groups?”
Perspective
Chapter 7: Common Multiplication and Division:
Proportional Reasoning
• 7.1 The Meaning of Ratio, Rate, and Proportion
• 7.2 Solving Proportional Problems by Reasoning with
Multiplication and Division
Week 12
11/7/11
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Quiz #3 – Wednesday
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Week 13
11/14/11
Chapter 8: Number Theory
• 8.1 Factors and Multiples
• 8.2 Greatest Common Factor and Least Common
Multiple
• 8.3 Prime Numbers
• 8.4 Even and Odd
Week 14
11/21/11
7.3 Connecting Ratios and Fractions
7.4 When You Can Use a Proportion and When You
Cannot
7.5Percent Revisited: Percent Increase and Percent
Decrease
Thanksgiving Vacation
Week 15
11/28/11
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8.5 Divisibility Tests
8.6 Rational and Irrational Number
Test #3 – Friday
Finals Exam &
Homework on Chapter 8
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December 7, Wednesday, 10:45 – 1:15