Departmental Syllabus
Mathematics for Teachers I
Revised August, 2011
I.
Title: MA 24003 Mathematics for Teachers I
II.
Course Description
Mathematics for Teachers I is the study of set theory, functions, sets of numbers and their properties, number
theory, applications , and problem solving. This course is offered in the Fall and Summer I terms.
Course Rationale:
Mathematics for Teachers I is a degree requirement for the Elementary Education Degrees for P-4 and 4-8 levels.
III.
Course Objectives
At the completion of this course the student will be able to do the following:
a.) Use problem solving steps and strategies to come to correct conclusions given real life situations.
b.) Use set theory and Venn Diagrams to come to correct conclusions given situations involving sets and in solving
logic problems.
c.) Correctly determine if a relationship is a function or not.
d.) Use number theory to come to correct conclusions in solving problems involving whole numbers, integers, and
fractions.
e.) Solve open ended problems by group and lab activities in class.
IV.
Course Prerequisites
A student must have a “C” or better in MA 14043 College Algebra.
V.
Required Texts and Materials
The required test is Mathematics for Teachers; An Interactive Approach for Grades K-8 by Sonnabend,Fourth Edition,
Published by Brooks/Cole Cengage Learning.
Each student needs to have a scientific calculator, compass, and protractor.
VI..
Basis for Final Grade
Two 100-Point Exams
Points Possible
200
Homework Quizzes , In-Class Activities
About 100
Final Exam
VII.
125
About 425
Grading Scale
90-100
80 - 89
70 - 79
60 - 69
0 - 59
A
B
C
D
F
.VIII.
Grades of "Incomplete":
The current College policy concerning incomplete grades will be followed in this course. Incomplete grades are
given only in situations where unexpected emergencies prevent a student from completing the course and the
remaining work can be completed the next semester. Your instructor is the final authority on whether you qualify
for an incomplete. Incomplete work must be finished by the midterm of the subsequent semester or the “I” will
automatically be recorded as an “F” on your transcript.
IX.
Email: Arkansas Northeastern College has partnered with Google to host email addresses for ANC students.
myANCmail accounts are created for each student enrolled in the current semester and is the email address your
instructor will use to communicate with you. Access your email account by going to
http://mail.google.com/a/smail.anc.edu and using your first and last names, separated by a period for your
username. Your default password is the last six digits of your Student ID. If you cannot access your student
email, contact the MITS department at 762-1020 ext 1150 or ext 1207 or send an email to
[email protected].
Internet: This course has a web component on myANC.
The student should periodically log on to myANC to find out what his or her average is for the class. The average
and grades for assignments can be found at MYANC in the proper course under grade book. The grade book
should be updated about every two weeks.
Computer Labs: In addition to general-purpose classrooms, a number of
computer laboratories are provided for instructional and student use. These
networked laboratories are state-of-the-art and fully equipped with
computers, printers, Internet connections and the latest software. The labs
are open to students enrolled in one or more credit hours at the College.
Technology Support: A lab assistant is generally present in the computer lab
in B202 for assistance in using the College computers. These assistants
cannot help you with course assignments; specific questions regarding the
technology requirements for each course should be directed to the instructor of the course. Problems with
myANC or College email accounts should be addressed by email to [email protected].
X.
Course Policies: Student Expectations
Disability Access: Arkansas Northeastern College is committed to providing reasonable accommodations for all
persons with disabilities. This First Day Handout is available in alternate formats upon request. Students with
disabilities who need accommodations in this course must contact the instructor at the beginning of the semester
to discuss needed accommodations. No accommodations will be provided until the student has met with the
instructor to request accommodations. Students who need accommodations must be registered with Dr. Blanche
Sanders or Suzanne Robinson at the Learning Assistance Center, Room L104.
Academic Conduct Policy:
Academic dishonesty in any form will not be tolerated. If you are uncertain as to what constitutes academic
dishonesty, please consult ANC’s Student Handbook (http://www.anc.edu/docs/anc_handbook.pdf) for further
details. Students are expected to do their own work. Plagiarism, using the words of others without express
permission or proper citation, will not be tolerated. Any cheating (giving or receiving) or other dishonest activity
will, at a minimum, result in a zero on that test or assignment and may be referred, at the discretion of the
instructor, to the Department Chair and/or Vice President of Instruction for further action.
See the Academic Integrity Policy. Policy hand-outs are provided to students at the beginning of each semester.
Learning Assistance Center: The Learning Assistance Center (LAC) is a free resource for ANC students. The LAC
provides drop-in assistance, computer tutorials and audio/visual aids to students who need help in academic
areas. Learning labs offer individualized instruction in the areas of mathematics, reading, writing, vocabulary
development and college study methods. Tutorial services are available on an individual basis for those having
difficulty with instructional materials. The LAC also maintains a shelf of free materials addressing specific
problems, such as procedures for writing essays and term papers, punctuation reviews, and other useful materials.
For more information, visit the LAC website at http://www.anc.edu/LAC or stop by room L104 in the Adams/Vines
Library Complex.
Other Student Support Services: Many departments are ready to assist you reach your educational goals. Be sure
to check with your advisor; the Learning Assistance Center, Room L104; Student Support Services, Room S145; and
Student Success, Room L101 to find the right type of support for you.
XI.
Important Dates to Remember
Withdrawal Deadline: November 22, 2011
Final Exam Week: December 8, 12-14, 2011
XII.
Unit Outline
A. Mathematical Reasoning
B. Sets and Functions
C. Whole Numbers
D. Number Theory
E. Integers
F. Rational Numbers as Fractions
Unit and Instructional Objectives with Schedule*
Unit Objectives
A.
Mathematical Reasoning
Rationale: Problem solving steps and strategies are needed to correctly solve problems involving real life
situations. The principles of inductive and deductive reasoning must be applied to solve real life problems.
At the conclusion of this unit, the student should have had the opportunity to do the following:
1.
2.
3.
4.
Apply Polya;s Four Steps to Problem Solving to solve word problems.
Apply the “Guess and Check” Strategy to appropriate word problems.
Use the three types of “Guess and Check” Strategies which are: Random, Systematic, and Inferential.
Apply the strategy “Use a Variable” to word problems when equations can be used to come to a correct
conclusion.
5. Solve problems using the “Make a List or Table” Strategy.
6. Solve application problems using the “Draw a Picture” Strategy.
7. Solve problems using the “Solving a Simpler Problem” Strategy
8. Use the strategy ”Look for a Pattern” in solving real life situations, number patterns, and in finding the
remaining terms in a sequence of numbers.
9. Given real life situations, solve problems using Inductive Reasoning.
10. Apply Deductive Reasoning to solve real life situations, form proofs, and come to correct conclusions.
11. Use Inductive Reasoning to determine if a sequence is arithmetic, geometric, or neither.
12. Use Deductive Reasoning to find additional terms of the various sequences.
Chapter One, Sections 1 through 6
B.
Sets and Functions
Rationale: Set theory is to be applied in order to determine set relationships and to solve logic problems.
Apply the definition of function in order to determine if mappings, pairings, and other relationships are
functions or not.
At the conclusion of this unit, the student should have had the opportunity to do the following:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Use Set Builder Notation, Listing, and Verbal Description Methods to define sets.
Use basic set definitions to draw Venn Diagrams to show set relationships such as unions,
intersections, subsets, and operations on sets.
Given Venn Diagrams, determine set relationships and set operations shown.
Determine set complements, subsets, unions, and intersection of sets given information about the sets.
Given a real life situation and information about the people or objects in the sets involved, draw a
correct Venn Diagram with correct numbers in the various areas of the Venn Diagram.
Answer questions from a Venn Diagram drawn given information about a real life situation using the
various regions in the Venn Diagram..
Inspect relations, pairings, mappings, or equations relating X and Y to determine if each one is a
function, or not.
Given information about two sets in a real life situation, determine if the relationship is a function, or
not.
Use the Vertical Line Test to determine if a graph is the graph of a function, or not.
Chapter 2, Sections 1 through 3
C.
Whole Numbers
Rationale: Properties of and the operations on whole numbers need to be recognized, utilized, and
illustrated.
At the conclusion of this unit, the student should have had the opportunity to do the following:
1.
Convert Base Ten numerals to Roman numerals.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
Convert Roman numerals to Base Ten numerals.
Represent Addition of Whole Numbers using Set Models and Whole Number Line Models.
Represent Subtraction of Whole Numbers using Set Models and Whole Number Line Models with the
Take Away Approach.
Use sets to show Subtraction of Whole numbers with a Comparison Model.
Use the Missing Addend Approach for subtraction in equation form.
Use the various properties for Addition and Subtraction of Whole Numbers to correctly label given
examples of properties with appropriate names..
Apply Closure Properties for Addition and Subtraction of Whole Numbers to specific sets to determine
set closure under addition and subtraction.
Illustrate Multiplication of Whole Numbers using Set Models or Whole Number Line Models with the
Repeated Addition Approach.
Illustrate Multiplication of Whole Numbers with a Rectangular Array Approach using Set Models or
Measurement Models.
Illustrate Division of Whole Numbers with the Repeated Subtraction Approach using Symbolic
Models or Whole Number Line Models.
Use the Missing Factor Approach for Division in equation form.
Use Properties of Whole Number Multiplication and Division to determine the correct labels for given
examples of the properties
Use Closure properties for Whole Number Multiplication and Division to determine closure for
specific sets under multiplication and division.
Apply algorithms for Whole Number Addition and Subtraction.
Use the technique of “Scratch Addition” to do long addition problems
Apply the Multiplication and Division Algorithms for Whole numbers.
Use the technique of “Lattice Multiplication” to do long multiplication of Whole Numbers.
Illustrate the concepts of Partitive or Measurement Division using Set Models to answer given division
problems.
Apply mental computation techniques including: Compatible Numbers”, Additive Compensation
Method, Multiplicative Compensation Method, and the Equal Additions Method for Subtraction of
Whole Numbers.
Mentally estimate answers using “Compatible Numbers, Rounding, and Front End Estimation
Methods.
Apply Front End Estimation using One-Column, Two-Column, One Column with Adjustment, and
Range Methods.
Apply place value in Base Ten, Base Two, Base Five, and Base Twelve to convert numbers from Base
Ten to these bases.
Convert Base Two, Base Five, and Base Twelve numbers to Base Ten numbers.
Draw a Base Ten number as a Base Two, a Base Five, and a Base Twelve number.
Do Addition, Subtraction, Multiplication, and Division in Base Two and in Base Five.
Do “Lattice Multiplication” and “Scratch Addition” in Base Two and in Base Five.
Chapter 3, Sections 1 through 8.
D.
Number Theory
Rationale: Basic Number Theory such as divisibility rules, definitions of factors, prime, and composite
numbers, and Number Theory theorems are needed to come to correct conclusions in problems involving
number relationships.
At the conclusion of this unit, the student should have had the opportunity to do the following:
1.
2.
3.
4.
5.
6.
Given a specific number, apply the definition of factor (or divisor) to determine factors (or divisors) of
the given value.
Apply the theorems regarding the divisibility of sums and products to come to correct conclusions.
Apply the divisibility tests for2, 4, 4, 5, 6, 9, and 10 given a whole number to test.
Apply the definitions of prime and composite numbers to determine if a given whole number is prime
or composite.
Apply the Prime Factor Test to determine if a given whole number is prime or not.
List the primes from 1 to 100 using the method of the Sieve of Eratosthenes.
7.
Apply the Fundamental Theorem of Arithmetic to find the unique prime factorization of a given whole
number which is a composite number.
8. Given two whole numbers, find the Greatest Common Factor of these numbers using the Listing
Method.
9. Given two whole numbers, find the Greatest Common Factor using the Prime Factorization Method.
10. Given two whole numbers, find the Least Common Multiple using the Listing Method
11. Given two whole numbers, find the Least Common Multiple using the Prime Factorization Method.
Chapter 4, Sections 1 through 4
E.
Integers
Rationale: The properties and operations on integers must be understood in order to correctly compute
with integers as well as to correctly illustrate given examples of properties and problems involving integers.
At the conclusion of this unit, the student should have had the opportunity to do the following:
1.
2.
3.
4.
5.
6.
Show Integer Addition using Set Models or Number Line Models.
Show Integer Subtraction using Set Models or Number Line models with the Take Away Approach.
Show Integer Multiplication with the Repeated Addition Approach using Set Models or Number Line
Models with a positive multiplier.
Illustrate Multiplication of Integers using a Patterns Model with like signed numbers as well as unlike
signed numbers.
Apply the Missing Factor Approach in equation form to illustrate Division of Integers
Apply definitions of the Closure, Commutative, Associative Properties, etc. for Integers to determine
which properties hold true for specific sets given.
Chapter 5, Sections 1 through 3
F.
Rational Numbers as Fractions
Rationale: The properties and operations on Rational Numbers must be understood in order to correctly
compute with fractions as well as to correctly illustrate given examples of properties and problems
involving fractions.
At the conclusion of this unit, the student should have had the opportunity to do the following:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
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15.
Illustrate fractions using Area Models, Number Line Models, or Set Models.
Illustrate equivalent fractions using Area Models, Number Line Models, or Set Models.
Apply the idea of Relatively Prime Numbers and the Fundamental Law of Fractions to simplify
(reduce to lowest terms) fractions.
Order fractions from smallest to largest or from largest to smallest.
Given two fractions, compare them by finding a common denominator.
Given two fractions, compare them using the “Cross Product” Method.
Do addition and subtraction involving fractions.
Change an improper fraction to a mixed number, and vice versa.
Do multiplication and division involving fractions.
Show an Area Model for the multiplication of one fraction times another.
Show reducing to lowest terms (or simplifying) by using groupings in an Area Model which illustrates
one fraction multiplied times another.
Use rounding and other techniques such as “Cluster Estimation” to round answers to problems
involving computation with fractions.
Use the “Compatible Numbers” Method to answer computation problems involving fractions.
Determine the correct order in which to present fraction problems of varying difficulties to student
Detect common error patterns in computations involving fractions.
Chapter 6, Sections 1 through 4