Description:

This is the first of a two-course sequence for prospective teachers of elementary and middle school mathematics. The focus of this course is an in depth investigation of the mathematical principles and concepts encountered in grades K-8. Topics include set theory, numeration systems, number sense, critical thinking, and problem solving strategies. The use of appropriate techniques and tools, such as calculators, computers and manipulatives, will be integrated throughout the course in order to enhance the depth of understanding. 3 hrs. lecture/wk.

Supplies: Refer to the instructor’s course syllabus for details about any supplies that may be required.

Textbook(s): For information see - http://bookstore.jccc.net

Course Fees: NONE

Course Objectives:

Upon successful completion of this course the student should be able to:

1. Apply set theory concepts.
2. Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers, and number systems.
3. Demonstrate an understanding for whole number, integer, fraction, and decimal operations.
4. Explain whole number, integer, fraction, and decimal algorithms.
5. Demonstrate the use of factors, multiples, prime factorization, and relatively prime numbers to solve problems.
6. Use strategies of estimation to judge the reasonableness of results.
7. Demonstrate the use of the place-value structure of the base-ten number system.
8. Describe mathematical relationships and functions with tables, graphs, and rules.
9. Apply ratios, proportions, and percents in problem solving.
10. Describe how various cultures have impacted the historical development of mathematics.
11. Identify characteristics of functions.

Content Outline & Competencies:

I. Set Theory
   A. Determine if two sets are equal or equivalent.
   B. Write the subsets and proper subsets of a given set.
   C. Find the intersection of two sets.
   D. Find the union of two sets.
   E. Find the complement of a set.
   F. Find the Cartesian product of two sets.
   G. Use Venn diagrams to determine the validity of a set statement.

II. Whole Numbers
   A. Use the definitions and properties for addition, subtraction,
multiplication, and division of whole numbers.
   B. Model situations that involve whole numbers using objects, pictures,
and symbols.
   C. Estimate the results of whole number calculations.
   D. Use a variety of problem solving strategies and critical thinking
skills with applications involving whole numbers.

III. Integers
   A. Use the definitions for addition, subtraction, multiplication, and
division of integers.
   B. Use the properties of integer addition such as closure, commutative,
associative, identity element, and inverse.
   C. Use the properties of integer multiplication such as closure,
commutative, associative, distributive, zero multiplication, identity
element, and inverse.
   D. Apply the definitions and properties of exponents to integers.
   E. Demonstrate operations on integers using a variety of
manipulatives.
   F. Use a variety of problem solving strategies and critical thinking
skills with applications involving integers.

IV. Number Theory
   A. Use divisibility tests to determine if a given number is divisible
by another.
   B. Classify numbers as prime or composite.
   C. Apply the Fundamental Theorem of Arithmetic.
   D. Use the Sieve of Eratosthenes to find the primes less than a given
number.
   E. Determine if two or more positive numbers are relatively prime.
   F. Find the greatest common divisor and the least common multiple of
numbers using a variety of methods.

V. Rational Numbers
   A. Write fractions in simplest form.
   B. Determine if fractions are equivalent.
   C. Arrange a set of fractions in numerical order.
   D. Use the definitions and properties of addition, subtraction,
multiplication, and division of fractions.
   E. Solve for the missing term of a proportion.
   F. Apply the definitions and properties of exponents to fractions.
   G. Demonstrate operations on fractions using a variety of
manipulatives.
   H. Use a variety of problem solving strategies and critical thinking
skills with applications involving fractions.

VI. Decimals
   A. Write decimals in expanded form.
   B. Convert numbers from words to numerals.
   C. Convert a fraction to a decimal and vice versa.
   D. Convert from standard decimal notation to scientific notation and
vice versa.
   E. Arrange decimals in numerical order.
   F. Use the definitions and properties of addition, subtraction,
multiplication, and division of decimals.
   G. Round decimals to a specific place value.
   H. Convert a repeating decimal to a fraction and vice versa.
   I. Convert numbers in percent form to fractional or decimal form and
vice versa.
   J. Demonstrate operations on decimals using a variety of
manipulatives.
   K. Use a variety of problem solving strategies and critical thinking
skills with decimal and percent applications.

VII. Numeration Systems
   A. Convert Roman numerals to Hindu-Arabic numerals and vice versa.
   B. Convert Egyptian numerals to Hindu-Arabic numerals and vice versa.
   C. Convert Babylonian numerals to Hindu-Arabic numerals and vice
versa.
   D. Write Hindu-Arabic numerals in expanded form.
   E. Write the counting numbers in bases other than base ten.
   F. Trace the historical development of the Hindu-Arabic number system.

VIII. Functions and Relations
   A. Determine whether relations are reflexive, symmetric, or
transitive.
   B. Identify relations as functions.
   C. Identify the domain and range of functions.

Methods of Evaluation of Competencies:

Evaluation of student mastery of course competencies will be accomplished using the following methods:

Unit Exams, Unit Papers, and/or Unit Projects 40%-80% of grade
Homework, Quizzes, and/or Small Projects   0%-50% of grade
Final Exam        10%-40% of grade 

Grade Criteria:
A = 90 – 100%  
B = 80 – 89% 
C = 70 – 79%  
D = 60 – 69%  
F = 0  – 59% 

The final exam must count at least as much as any unit exam, unit paper or
unit project.  At the instructor’s discretion, the grade on all or any part
of the final exam may replace any lower test score.   

Caveats:

1. The majority of mathematics courses are sequential. Students must earn a grade of C or higher in a prerequisite mathematics course to progress to its subsequent mathematics course.
2. In accordance with the assertion made on your billing statement, during the first two weeks of the semester, if a student is found not to have successfully fulfilled the prerequisite(s) for this course, the student will be dropped from the course. He/she will be allowed to enroll in the appropriate lower level course on a space-available basis with an even exchange of tuition. After the first two weeks, students who have not met the prerequisite(s) will be dropped from the course with no refund of tuition.
3. COMPUTER LITERACY - Students will need basic computer knowledge, word processing and Internet searching skills for the completion of some papers and/or exercises.

Disabilities:

If you are a student with a disability, and if you will be requesting accommodations, it is your responsibility to contact Access Services. Access Services will recommend any appropriate accommodations to your professor and his/her director. The professor and director will identify for you which accommodations will be arranged.

JCCC provides a range of services to allow persons with disabilities to participate in educational programs and activities. If you desire support services, contact the office of Access Services for Students With Disabilities (913) 469-8500, ext. 3521 or TDD (913) 469-3885. The Access Services office is located in the Success Center on the second floor of the Student Center.