Course Outline for Mathematics 41S
Number Systems with Support
Effective: Fall 2019
SLO Rev: 09/13/2018
SLO Rev: 09/13/2018
Catalog Description:
MTH 41S - Number Systems with Support
3.50 Units
Development of quantitative reasoning skills through exploration of mathematical topics. Topics include structure of numeration systems including the real number system and its subsystems, number theory, and computational algorithms. This course is equivalent to MTH 41 with additional lab hours for students who did not place directly into MTH 41 or for students who place directly into MTH 41 but desire additional instruction.
Prerequisite: MTH 55 or MTH 53 or MTH 53B or MTH 55L or MTH 55B or MTH 54 or MTH 54L or Completion of: an appropriate placement through the Mathematics Placement process
1701.00 - Mathematics, General
Letter Grade Only
| Type | Units | Inside of Class Hours | Outside of Class Hours | Total Student Learning Hours |
|---|---|---|---|---|
| Lecture | 3.00 | 54.00 | 108.00 | 162.00 |
| Laboratory | 0.50 | 36.00 | 0.00 | 36.00 |
| Total | 3.50 | 90.00 | 108.00 | 198.00 |
Measurable Objectives:
Upon completion of this course, the student should be able to:
- perform calculations with place value systems;
- evaluate the equivalence of numeric algorithims;
- explain the advantages and disadvantages of equivalent algorithms in different circumstances.;
- apply algorithms from number theory to determine divisibility;
- compare and contrast least common multiple and greatest common divisor;
- analyze the roles least common multiple and greatest common divisor have in standard algorithms;
- explain the concept or rational numbers using ratio and decimal representations;
- analyze, determine and justify the equivalency of arithmetic algorithms of the ratio and decimal representations of rational numbers;
- analyze the structure and properties of different number systems including real numbers and its subsystems;
- define the concept of rational and irrational numbers, including their decimal representation;
- develop and reinforce conceptual understanding of mathematical topics through the use of patterns, problem solving, communication, connections, modeling, reasoning, and representation;
- illustrate the use of a number line representation;
- develop math activities based on the state and national curriculum standards.
Course Content:
- Reflect on Study Skills
- Grit and Growth Mindset
- How Learning Math is Different
- Resources On and Off Campus
- Time Management
- How to Be an Effective Listener and Take Notes
- How to Approach Homework
- How to Study for an Exam
- Overcoming Math and Test Anxiety
- Review Arithmetic Concepts
- Computational Aproach to Prime and Composite
- Factor Trees
- Computational Aproach to Fundamental Theorem of Arithmetic
- Review Algebraic Concepts
- Exponents
- Rules for Expoenents
- Logarithms
- Numeration systems
- Historical
- Hindu-Arabic
- Place-value
- Basic number theory
- Divisibility
- Prime and composite numbers
- Prime factorization
- Fundamental Theorem of Arithmetic
- Least Common Multiple
- Greatest Common Divisor
- Integers
- Structure
- Properties
- Computational algorithms
- Rational numbers
- Structure
- Properties
- Ratio
- Proportions
- Real numbers
- Structure
- Operations
- Properties
- Rational and irrational numbers
- Decimal representations
- Number line representation
- Equivalency of computational algorithms
- Developing conceptual understanding
- Patterns
- Problem Solving
- Communication
- Connections
- Modeling
- Reasoning
- Representation
- National and state standards for elementary school mathematics
Methods of Instruction:
- Lecture/Discussion
- Demonstration/Exercise
- Group Activities
- Textbook reading assignments
- Problem Solving
- Presentation of audio-visual materials
- Computer-based interactive curriculum
- Hands-on Activities
- Diagnostic Quizzes
- Verbal explanation and demonstration.
- Handouts and rule interpretations.
Assignments and Methods of Evaluating Student Progress:
- The NCTM Standards state "All students should solve simple problems involving rates and derived measurements for such attributes as velocity and density." Provide two examples that satisfy this statement and justify your choices.
- An iPod is on sale for $159.20 and its normal price is $199. A student says that the percent discount is 39.8%. Is the student correct? If not, where did the student go wrong?
- What is the largest three-digit prime all of whose digits are prime?
- Class Work
- Homework
- Quizzes
- Group Projects
- Online Assignments
- Class Participation
- Exams/Tests
- Final Examination
Upon the completion of this course, the student should be able to:
- Analyze mathematical problems critically using logical methodology.
- Communicate mathematical ideas, understand definitions, and interpret concepts.
- Increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.
Textbooks (Typical):
- Musser, G. L. Burger, W. F. Peterson, B. E (2013). Mathematics For Elementary Teachers A Contemporary Approach (10th). Wiley & Sons.
- Billstein, R. Libeskind, S. Lott, J. W (2016). A Problem Solving Approch to Mathematics for Elementary School Teachers (12th). Pearson.
- Long, C, T. De Temple, D. W. Millman, R. S (2012). Mathematical Reasoninig for Elementary Teachers (6th). Addison Wesley.
- Scientific Calculator
Abbreviated Class Schedule Description:
Development of quantitative reasoning skills through exploration of mathematical topics. Topics include structure of numeration systems including the real number system and its subsystems, number theory, and computational algorithms. This course is equivalent to MTH 41 with additional lab hours for students who did not place directly into MTH 41 or for students who place directly into MTH 41 but desire additional instruction.
Prerequisite: MTH 55 or MTH 53 or MTH 53B or MTH 55L or MTH 55B or MTH 54 or MTH 54L or Completion of: an appropriate placement through the Mathematics Placement process
Discipline:
Mathematics*