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.
This is a Writing Intensive Course: A requirement for students at Queensborough Community College is that at least two classes taken be designated as writing intensive (WI). The purpose is to facilitate and foster writing abilities at the college level. In this class, as in all WI sections, the following features are incorporated: (1) Students will spend time during the semester writing in the service of learning. (2) A minimum of 10 pages of writing will be assigned. (3) The professor will respond to and return these 10 pages at least once so that students have an opportunity to revise the paper (or papers) before a final grade is given. (4) Writing will be discussed regularly in class. (5) Students’ written work will be a significant part of the course grade. (6) At least one exam will have a written component.
Curricula for which the course is required/recommended:
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, Loose-Leaf Version
Plus MyLab Math Media Update – Access Card Package, 7 Ed
by Calvin T. Long, Duane W. DeTemple, and Richard S. Millman
Pearson 2018.
(ISBN 9780135229989)
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 policy: Academic honesty is expected of all students. Any violation of academic integrity is taken extremely seriously. All assignments and projects must be the original work of the student or teammates if applicable. Plagiarism will not be tolerated. Any questions regarding academic integrity should be brought to the attention of the instructor. The following is the Queensborough Community College Policy on Academic Integrity: “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. At the faculty member’s discretion and with the concurrence of the student or students involved, some cases though reported to the Office of Student Affairs may be resolved within the confines of the course and department. The instructor has the authority to adjust the offender’s grade 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.” Please refer to the college’s Academic Integrity Policy.
Disabilities: Any student who feels that he or she may need an accommodation based upon the impact of a disability should contact the office of Services for Students with Disabilities in Science Building, Room S-132, 718-631-6257, to coordinate reasonable accommodations for students with documented disabilities. You can visit the Services for Students with Disabilities website.
| TOPICS | SECTIONS | SUGGESTED HOURS |
| Problem-Solving: Pattern Exploration, Numerical Sequences, Problem-Solving and Reasoning Mathematically (Inductive and Deductive Reasoning). | 1.1-1.6 | 5 |
| Whole Numbers: Deductive Reasoning. Addition, Subtraction, Multiplication and Division Models of Whole Numbers. | 2.2-2.4 | 3 |
| Numeration Systems: Babylonian, Egyptian, Mayan, Roman, Indo-Arabic, Nondecimal Positional Systems, Algorithms for Addition, Subtraction, Multiplication, and Division of Whole Numbers, Estimation. | 3.1-3.5 | 5 |
| 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. | 6.1-6.4 | 8 |
| Geometric Figures: Figures and Polygons in Plane, Figures in Space. | 9.1-9.3 | 4 |
| Transformations in Geometry: Rigid Motions, Similarity Transformations, Patterns, Symmetries. OPTIONAL: Tilings and Escher-like Designs. | 11.1-11.2 11.3 13.1-13.2 | 5 4 |
| Exams, Reviews, Project Presentations | Total: | 6_______45 |
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).
Whole Numbers
4. Ability to solve problems using deductive reasoning.
5. An understanding of addition, subtraction, multiplication and division models of whole numbers.
6. The ability to use algorithms for addition, subtraction, multiplication and division of whole numbers.
Numeration Systems
7. Understanding of different numeration systems of the past and present.
8. The ability to round numbers and estimate computations.
9. The ability to add and subtract numbers in nondecimal positional systems (example: time).
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.
OPTIONAL: Ability to construct tiling’s with irregular polygons or Escher-like Design.
Statistics
23. Ability to create and analyze dot plots, stem and leaf plots, histogram, bar graphs, line graphs and box and whisker plots.
24. Define and calculate the mean, median, and mode of data set.
25. Define and calculate the range, quartiles, IQR, and outliers of data set.
The Learning Goals are guidelines; they can be modified at the discretion of the instructor.
SUGGESTED MA-303 COMPUTER LABORATORY SCHEDULE
Software
Microsoft Word
Microsoft Excel
Geogebra or similar program (resources and various labs can be found at
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 | Suggested Topic |
| 1 | Introduction to MathXL, online homework management system. Code is included with loose leaf text if purchased in on campus bookstore. Homework assignments are at the discretion of the instructor. |
| 2 | Introduction to Equation Editor in Microsoft Word. |
| 3 | Presenting solutions to mathematical problems using the Equation Editor. |
| 4 | Introduction to the Internet and various mathematics related websites. Using search engines to research topics in mathematics and mathematics education (e.g. NCTM National Council of Teachers of Mathematics principles and standards, or explore lesson plans/activities on NCTM illuminations. https://illuminations.nctm.org. Practice to build, analyze, or deliver quality teaching resources). |
| 5 | Project I, Part 1: Researching a topic in mathematics or mathematics education on the Internet |
| 6 | Project I, Part 2: Completing the internet research. |
| 7 | Introduction to Geogebra (sample labs activities can be provided by the Mathematics Education Committee). |
| 8 | Project II, Part 1: Problem Solving using Geogebra. |
| 9 | Project II, Part 2: Completing the project on Problem Solving using Geogebra. |
| 10 | Using Geogebra to discover characteristics of various polygonal curves. |
| 11 | Introduction to spreadsheets in Microsoft Excel. |
| 12 | Creating and editing spreadsheets in Excel using data from real world mathematics applications (e.g. creating and editing a gradebook) |
| 13 | Project III, Part 1: Problem Solving using Excel. |
| 14 | Project III, Part 2: Completing the project on Problem Solving using Excel. |
CS/SC/NK/DC:cs FALL 2021 REVISED 2021
