CCBC Catonsville School of Mathematics and Science

CCBC Catonsville School of Mathematics and Science MATH 131 Concepts of Mathematics I SEMESTER: Spring 2012 Section: CTA

INSTRUCTOR: Lisa Sallee EMAIL: [email protected] CLASS MEETING DAYS: Tuesday and Thursday OFFICE LOCATION: E-204G CLASS MEETING TIMES: 5:45 – 7:35 pm OFFICE HOURS: M/W 11:15 – 1:15 INSTRUCTOR PHONE: 443-840-5594 T/Th 10:00 – 11:00 WEBPAGE: see Blackboard supplement Or by appointment

DEPARTMENT CONTACT: Students should first attempt to take concerns to the faculty member. If students are unable to resolve course- related concerns with the instructor they should contact the Catonsville Math Coordinator, Kristin Duckworth, at 443- 840-5963

COURSE PRE-REQUISITES: MATH 083 or MATH 101 or sufficient math placement score; and ENGL 052 or LVE 2; and RDNG 052 or ESOL 054 or LVR 2.

COURSE DESCRIPTION: Students will learn the concepts and principles of mathematics taught in elementary education. Topics include the origin of numbers, system of cardinal numbers, numeration systems, and principles underlying the fundamental operations. This is not a “methods in teaching” course.

REQUIREMENTS: 8 Chapter Assessments 35% of overall course grade 1 Final Exam 20% of overall course grade Manipulative Project (due March 13th) 10% of overall course grade Reflection Paper (due May 8th) 20% of overall course grade Mathematical Connections Responses 15% of overall course grade

ATTENDANCE POLICY FOR THIS COURSE: You are expected to attend all scheduled classes. Should you miss a class you are responsible for all work missed. Please be on time. Students with a legitimate problem about attendance should discuss the situation with their instructor.

TEXT(S): A Problem Solving Approach to Mathematics, 10th Edition, Billstein Libeskind and Lott, Addison Wesley, publisher

COMMENTS: There are no make-up assessments. One of the lowest assessment grades will be dropped.

All Students must be proctored to take the assessments. Makeup work is at the consent of the instructor and must be taken in the Testing Center within a week of the original due date. Students must bring a valid photo ID and a calculator!

CCBC Catonsville Testing Center

E-mail (preferred): [email protected] Phone: 443-840-5246 Location:K-205, Catonsville Campus, Testing Center Course calendar/schedule: http://www.ccbcmd.edu/registration/academic_calendars.html

College wide syllabus policies: For college wide syllabus policies such as the Code of Conduct related to Academic Integrity and Classroom Behavior or the Audit/Withdrawal policy, please go to the Syllabus Tab on the MyCCBC page.

CLASS FINAL EXAM: Tuesday, May 15th 5:30 – 7:30 pm (cumulative) COURSE OBJECTIVES

Upon successfully completing the course students will be able to:

1. apply different problem solving techniques, including the use of calculators and/or other appropriate technology, to solve a variety of mathematical problems (both standard and non-standard) (I, III, IV, V, VI, 1, 4, 6, 7) 2. utilize inductive and deductive reasoning to solve problems, as appropriate (I, III, IV, VI, 1, 3, 4, 6, 7); 3. use set language, notation, and operations to work with various sets, both numerical and non-numerical (I, II, III, V, 1, 2); 4. illustrate the different relationships between sets using Venn diagrams (I, II, 1, 2); 5. compare and contrast decimal and non-decimal numeration systems from various cultures and periods in history using appropriate characteristics (i.e. number base, place value, position, zero, symbol) (III, V, 1, 3, 5); 6. illustrate general characteristics of numeration systems and their operations using various base systems (I, IV, VI, 1, 2, 4); 7. relate general numeration system characteristics to whole numbers, integers, and rational numbers (I, III, 1, 2); 8. perform arithmetic operations with whole numbers, integers, and rational numbers using algorithms, manipulatives, calculators, etc. (I, III, 1, 2, 4); 9. demonstrate the need for the order of operations and apply its principles to arithmetic calculations (I, II, III, 1, 2, 4, 5) 10. illustrate the properties of closure, identity, inverse, commutativity, associativity and distributivity for arithmetic operations as they apply to whole numbers, integers, and rational numbers (I, II, III, 1, 2); 11. apply the number theory topics of primes, composites, tests of divisibility, least common multiple, greatest common factor (divisor), and the fundamental theorem of arithmetic appropriately (I, III, 1); 12. demonstrate the property of denseness and order relationships (e.g. less than, greater than, etc.) using whole numbers, integers, and rational numbers using manipulatives, graphs and other mediums to solve problems as appropriate (I, II, III, 1, 2, 3, 4, 6, 7); 13. apply rational number concepts to practical situations using ratios, proportions and percents (I, II, III, IV, 1, 2, 3, 6, 7); 14. analyze a variety of standard and non-standard basic operation algorithms using manipulatives, estimation, mental computation, and error pattern detection (II, III, VI, 1, 2, 4, 7); 15. relate the concepts discussed throughout the course to the students’ physical surroundings (III, VI, 7); 16. utilize the Internet and other resources to research course-related topics (I, III, VI, 1, 3, 5, 6, 7). MAJOR TOPICS:

1. Problem Solving a. George Polya’s process for solving problems b. Problem solving techniques c. Inductive and deductive reasoning 2. Sets and Their Applications a. Descriptions and definitions b. Set operations c. Venn diagrams 3. Numbers and Numeration Systems a. Numeration systems other than Hindu-Arabic b. Hindu-Arabic numeration system c. Base arithmetic 4. Whole Numbers (with and without calculators) a. Operations b. Exponents c. Properties d. Estimation and mental computational techniques e. Error patterns 5. Integers (with and without calculators) a. Operations b. Properties c. Estimation and mental computational techniques d. Error patterns 6. Number Theory a. Primes and composites b. Divisibility c. Least common multiples and greatest common factors 7. Rational Numbers (with and without calculators) a. Fractions (concepts and operations) b. Decimals (concepts and operations) c. Estimation and mental computational techniques d. Error patterns e. Ratio, proportion, and percent

RATIONALE: Concepts of Mathematics for Teachers I explores the concepts and principles of mathematics taught in elementary education. This course is designed to help students develop a deeper understanding of elementary mathematics. It will also prepare students who plan to pursue a bachelor’s degree in education for the methods in teaching mathematics courses that they will be required to take.

FOR ALL COLLEGE WIDE SYLLABUS POLICIES GO TO MyCCBC on the CCBC web page and view the SYLLABUS TAB. Paper – Reflection

Write a well written 500 – 750 word paper. o Double spaced o 1 inch margins o Professional font

Write about:

 What was your favorite topic of class?  What type of class setting did you favor (group work, lectures, etc)?  What did you learn that was new?  What did you learn that was unexpected?  How has this class changed your attitudes and beliefs toward mathematics?  etc etc etc

If emailed, PAPER MUST BE SENT AS AN ATTACHMENT in MS Word or .rtf format and DOUBLE SPACED Project – NLVM game

Choose TWO games on http://enlvm.usu.edu/ma/nav/bb_dlib.jsp The game must be from the “Numbers and Operations” or “Algebra” rows.

Write a well written 400 – 600 word paper. o Double spaced, 1 inch margins, professional font

The paper should include the following:  A short summary of each game.  A list of the topics/ objectives in each game.  Discuss if you liked the game and if you think children would like the game.  Discuss any improvements you think could be made. TENTATIVE SCHEDULE AND HOMEWORK – ALL MATHEMATICAL CONNECTIONS ASSIGNMENTS DUE THE DAY OF THE ASSESSMENT FOR THAT CHAPTER

CHAPTER 1 (1.5 WEEKS) Assessment 1-1A: 1, 5, 6, 11, 15. For 5, 6, 11, 15, list the strategy you used. Mathematical Connections 1-1: 1, 2, 3, 11, 12

Assessment 1-2A: 1, 2, 3, 9, 17. Mathematical Connections 1-2: 1, 11, 12. 15

Assessment 1-3A: 7, 11, 13, 17 Mathematical Connections 1-3: 7, 13

CHAPTER 2 (1.5 WEEKS) Assessment 2-1A: 1, 7, 13, 25 Mathematical Connections 2-1: 10

Assessment 2-2A: 1, 2, 3, 9 Mathematical Connections 2-2: NAEP Question

Assessment 2-3A: 3, 5, 9, 17, 21 Mathematical Connections 2-3: 8, 12

CHAPTER 3 (2 WEEKS) Assessment 3-1A: 3, 6, 13, 15, 17 Mathematical Connections 3-1: 1, 3, 5, 6, 17

Assessment 3-2A: 1, 5, 7, 9 Mathematical Connections 3-2: 3, 7, 11, 13

Assessment 3-3A: 1, 5, 6, 9, 25, 27 Mathematical Connections 3-3: 1, 5, 11, 17

Assessment 3-4A: 1, 3, 7, 15, 17 Mathematical Connections 3-4: 5, 11

Assessment 3-5A: 1, 7, 15 Mathematical Connections 3-5: 1, 3, 5, 9, 11

CHAPTER 4 (1.5 WEEKS) Assessment 4-1A: 1, 2, 4, 9 Mathematical Connections 4-1: 1, 5, 6

Assessment 4-2A: 1, 5, 8 Mathematical Connections 4-2: 5, 6, 8

Assessment 4-3A: 1, 4, 9, 15 Mathematics Connections 4-3: 1, 3, 14, 16

CHAPTER 5 (2 WEEKS) Assessment 5-1A: 1, 9, 10, 19 Mathematics Connections 5-1: 1, 3, 15, 17

Assessment 5-2A: 3, 5, 7, 15 Mathematics Connections 5-2: 15, 16, 17

Assessment 5-3A: 1, 3, 14, 15 Mathematical Connections 5-3: 5, 14, 16, 21

Assessment 5-4A: 3, 13, 16, 18 Mathematical Connections 5-3: 3, 7, 12, 13, 14

Assessment 5-5A: 2, 3, 18 21 Mathematical Connections 5-4: 2, 5, 15

Assessment 5-6A: 1, 2, 3, 7, 9 Mathematical Connections 5-5: None

CHAPTER 6 (1.5 WEEKS) Assessment 6-1A: 3, 9, 11, 17 Mathematical Connections 6-1: 1, 3, 9, 11, 15, 19

Assessment 6-2A: 1, 3, 9, 13, 21 Mathematical Connections 6-2: 1, 3, 5, 17

Assessment 6-3A: 1, 13, 15, 21, 23 Mathematical Connections 6-3: 1, 5, 16, 21, 23

CHAPTER 7 (2 WEEKS) Assessment 7-1A: 5, 11, 16 Mathematical Connections 7-1: 13, 14

Assessment 7-3A: 1, 2, 13, 15 Mathematical Connections 7-3: 1, 9

Assessment 7-4A: 2, 5, 13, 14, 21 Mathematical Connections 7-4: 3, 6, 12, 16

Assessment 7-5A: 3, 5 Mathematical Connections 7-5: 7, 8

CHAPTER 8 (1.5 WEEKS) Assessment 8-1A: 1, 3, 5, 9, 17 Mathematical Connections 8-1: 1, 3, 14, 15, 17

Assessment 8-2A: 1, 5, 11, 14, 23 Mathematical Connections 8-2: 2, 8, 14, 15, 18