QUEENSBOROUGH COMMUNITY COLLEGE
MATHEMATICS AND COMPUTER SCIENCE DEPARTMENT
COURSE OUTLINE
MA-303
NUMBER SYSTEMS
Pre-requisite: MA-119 C or better or permission of the Department.
Hours: 3 Class Hours
1 Recitation Hour
3 Credits
Course Description:
This course is designed to instruct students in areas of mathematics that are related to the elementary school
curriculum, to clear up common misunderstandings of mathematical concepts, and to use current computer
technologies with the concepts developed in the course as tools for solving problems. Topics covered will be
chosen from numeration systems, number theory, mathematical systems, statistics and geometry.
Recommended for future teachers.
Curricula for which the course is required/recommended:
A.S. Degree Programs in Liberal Arts and Sciences (Science and Mathematics), A.A. Degree in Liberal Arts
and Sciences and Education.
General Education Objectives:
Use analytical reasoning skills to identify issues or problems and evaluate evidence in order to make
informed decisions; reason quantitatively and mathematically as required in their fields of interest and in
everyday life; integrate knowledge and skills in their program of study; use information management and
technology skills effectively for academic research and lifelong learning.
Course Objectives/ Expected Student Learning Outcomes: Students will develop further perspective
and insight into some of the mathematical concepts taught in elementary school. Students will use a
variety of representations to communicate mathematically; students will be able to express a mathematical
problem in a visual format; students will use Pólya’s problem-solving principles, deductive and inductive
reasoning, and other problem-solving techniques such as geometric reasoning; students will use base-ten
algorithms, the properties of basic operations on whole numbers and extend the concept of number to include
fractions; students will be able to apply Number Theory to a number of real world problems; students will
use technology such as graphing calculators and computer software for data representations and
computations.
Text:
Mathematical Reasoning for Elementary Teachers, Custom Edition for QCC,
by Calvin T. Long, Duane W. DeTemple, and Richard S. Millman
Pearson/Addison Wesley, 2015.
ISBN-10: 1-269-93665-4, ISBN-13: 978-1-269-93665-1
Methods by which student learning will be evaluated:
The student’s evaluation will be based upon the quality of written and oral presentations in the form of
homework, group work, projects, tests and quizzes.
The general guidelines for assessing grades are as follows:
•
•
Examinations, Assignments and Classroom Performance: 70%
Final Examination: 30%
The distribution may be changed at the discretion of the individual instructor.
Group work, projects, written and oral presentations, use of technology such as the graphing calculator,
computer software and the internet supplemented by lecture will be the primary methods of instruction.
Academic Integrity:
Academic honesty is taken extremely seriously and is expected of all students. All assignments must be the
original work of the student (and partners or group, if applicable). All questions or concerns regarding ethical
conduct should be brought to the course instructor. “It is the official policy of the College that all acts or
attempted acts that are violations of academic integrity be reported to the Office of Student Affairs (OSA).
At the faculty member’s discretion and with the concurrence of the student or students involved, some cases,
though reported to the OSA, may be resolved within the confines of the course and department. The
instructor has the authority to adjust the offender’s grades as deemed appropriate, including assigning an F to
the assignment or exercise or, in more serious cases, an F to the student for the entire course.” (Taken from
the QCC Academic Integrity Policy, 2/14/2005.)
NOTE: Any student who feels that he/she may need an accommodation based upon the impact of a disability
should contact the instructor privately to discuss his/her specific needs. Please contact the office of Services
for Students with Disabilities in Science Building, room 132 (718 631 6257) to coordinate reasonable
accommodations for students with documented disabilities.
TOPICS
SECTIONS
HOURS
Problem-Solving: Pattern Exploration, Numerical Sequences,
Problem-Solving and Reasoning Mathematically.
1.1-1.6
6
Sets and Whole Numbers: Reasoning with Venn Diagrams (Instructor
Notes). Addition, Subtraction, Multiplication and Division Models of
Whole Numbers.
2.2-2.4
3
Numeration Systems: Babylonian, Egyptian, Mayan, Roman,
Indo-Arabic, Binary, Nondecimal Positional Systems, Algorithms for
Addition, Subtraction, Multiplication, and Division of Whole
Numbers, Estimation.
3.1-3.5
6
Number Theory: Divisibility, Greatest Common Divisor and Least
Common Multiples.
4.1-4.3
5
Fractions and Rational Numbers: Models for fractions, Equivalent
fractions and common denominators, Addition, Subtraction,
Multiplication and Division. Proportional Reasoning.
5.1-5.4
8
Geometric Figures: Figures and Polygons in Plane, Figures in Space.
6.1-6.3
4
Transformations in Geometry: Rigid Motions, Similarity
Transformations, Patterns, Symmetries, Tilings and Escher-like
Designs.
7.1-7.3
6
Total:
7
_______
45
Exams, Reviews, Project Presentations
Student Learning Goals: Upon successful completion of the course, a student is expected to
develop and demonstrate the following capabilities:
Problem-Solving:
1. Make sense of problems, use appropriate tools strategically and persevere in solving them.
2. Ability to form conclusions on the basis of pattern, observations, examples, or experiments
(inductive reasoning).
3. Ability to form conclusions from one or more given statements (deductive reasoning).
Sets and Whole Numbers
4. Ability to solve problems using Venn Diagrams (deductive reasoning).
5. An understanding of addition, subtraction, multiplication and division models of whole numbers.
Numeration Systems
6. Understanding of different numeration systems of the past and present.
7. The ability to use algorithms for addition, subtraction, multiplication and division of whole
numbers.
8. The ability to round numbers and estimate computations.
9. The ability to add and subtract numbers in nondecimal positional systems (base 5, 6, 2)
Number Theory
10. Understanding of definitions for: factor, multiple, unit, prime, composite, even and odd
numbers.
11. The knowledge and ability to apply tests for divisibility by: 2, 3, 4, 5, 6, 9, 10.
12. The ability to calculate Greatest Common Divider, and Least Common Multiple.
Fractions and Rational Numbers
13. Understanding of fraction concepts: models for fractions and equivalent fractions
14. Ability to perform operations with fractions.
15. Ability to reason proportionally.
Geometric Figures
16. Use of applicable definitions and properties to compute solutions to problems involving rays,
angles, angle measure(s), vertical angles, triangles, parallel lines and a transversal.
17. The ability to identify polygons.
18. The ability to properly classify triangles and quadrilaterals.
19. Ability to recognize pyramid, prism, cube, cone, cylinder.
Transformations in Geometry
20. The ability to perform/identify the four rigid motions.
21. Ability to identify congruent figures, dilation, similar figures.
22. The ability to perform/identify reflection, rotation, and point symmetry.
22. Ability to construct tilings with irregular polygons or Escher-like Design.
The Learning Goals are guidelines; they can be modified at the discretion of the instructor.
SUGGESTED MA-303 COMPUTER LABORATORY SCHEDULE
SOFTWARE
Microsoft WORD
The Geometer’s Sketchpad
The approximate hours per chapter and weekly computer topics are guidelines. They can be
modified at the discretion of the instructor. The instructor is responsible for making assignments
and scheduling examinations.
WEEK
TOPIC
1.
Introduction to the Equation Editor in WORD.
2.
Presenting solutions to mathematical problems using the Equation Editor.
3.
Creating an e-Portfolio on the Internet.
Instructor note: Academic Computing Center provides technical support, including
technicians who would help your students create Digication account and linking it you
your Blackboard course.
4.
Researching a topic in mathematics or mathematics education resources on the Internet,
and sharing findings on e-Portfolio.
5.
The Geometer’s Sketchpad Lab 1.
6.
The Geometer’s Sketchpad Lab 2.
7.
The Geometer’s Sketchpad Lab 3.
8.
The Geometer’s Sketchpad Lab 4.
9.
The Geometer’s Sketchpad Lab 5.
10.
The Geometer’s Sketchpad Lab 6.
11.
The Geometer’s Sketchpad Lab 7.
12.
The Geometer’s Sketchpad Lab 8.
13.
The Geometer’s Sketchpad Lab 9.
14.
The Geometer’s Sketchpad Lab 10.
15.
Review
CS/NK:cs SPRING 2015