SRJC Course Outlines

6/22/2024 7:56:52 AMMATH 74 Course Outline as of Fall 2024

Changed Course
CATALOG INFORMATION

Discipline and Nbr:  MATH 74Title:  NUMBER SYSTEMS  
Full Title:  Mathematics for Elementary School Teachers - Number Systems
Last Reviewed:1/9/2024

UnitsCourse Hours per Week Nbr of WeeksCourse Hours Total
Maximum4.00Lecture Scheduled4.0017.5 max.Lecture Scheduled70.00
Minimum4.00Lab Scheduled06.5 min.Lab Scheduled0
 Contact DHR0 Contact DHR0
 Contact Total4.00 Contact Total70.00
 
 Non-contact DHR0 Non-contact DHR Total0

 Total Out of Class Hours:  140.00Total Student Learning Hours: 210.00 

Title 5 Category:  AA Degree Applicable
Grading:  Grade Only
Repeatability:  00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As: 
Formerly: 

Catalog Description:
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Students will learn mathematical concepts needed for teaching elementary school mathematics including quantitative reasoning, number systems and subsystems, basic number theory, logical thinking, and applications. Content is relevant to national curriculum standards and Common Core State Standards.

Prerequisites/Corequisites:
Completion of MATH 161 or MATH 154 or MATH 156 or AB705 placement into Math Tier 2 or higher


Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
Students will learn mathematical concepts needed for teaching elementary school mathematics including quantitative reasoning, number systems and subsystems, basic number theory, logical thinking, and applications. Content is relevant to national curriculum standards and Common Core State Standards.
(Grade Only)

Prerequisites:Completion of MATH 161 or MATH 154 or MATH 156 or AB705 placement into Math Tier 2 or higher
Recommended:
Limits on Enrollment:
Transfer Credit:CSU;
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP

ARTICULATION, MAJOR, and CERTIFICATION INFORMATION

Associate Degree:Effective:Fall 2023
Inactive: 
 Area:B
MC
Communication and Analytical Thinking
Math Competency
 
CSU GE:Transfer Area Effective:Inactive:
 B4Math/Quantitative ReasoningFall 2024
 
IGETC:Transfer Area Effective:Inactive:
 
CSU Transfer:TransferableEffective:Fall 2023Inactive:
 
UC Transfer:Effective:Inactive:
 
C-ID:

Certificate/Major Applicable: Both Certificate and Major Applicable



COURSE CONTENT

Student Learning Outcomes:
At the conclusion of this course, the student should be able to:
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1. Analyze the structure and properties of different number systems including real numbers and their subsystems.
2. Use basic number theory including divisibility tests, prime and composite numbers, and the Fundamental Theorem of Arithmetic.
3. Develop and reinforce conceptual understanding of mathematical topics through the use of patterns, problem solving, communication, connections, modeling, reasoning, and representation.
4. Explain national and state standards for elementary school curriculum, including Common Core.
 

Objectives: Untitled document
At the conclusion of this course, the student should be able to:
1. Perform calculations with place value systems including base ten and other natural number bases.
2. Apply concepts and algorithms from number theory to determine divisibility, least common multiple or greatest common divisor for positive integers and solve related application problems. 
3. Understand the implications of the Fundamental Theorem of Arithmetic. 
4. Expound on the concept of rational numbers by illustrating them through both ratio and decimal representations. 
5. Describe the arithmetic algorithms for operations on rational numbers. 
6. Describe the structure and properties of integers, rational numbers, and real numbers. 
7. Develop, model, and solve problems using reasoning, logic, and pattern recognition. 
8. Develop activities implementing curriculum standards. 
9. Utilize sets, functions, patterns, connections, modeling, as well as deductive or inductive reasoning as a collective toolkit for problem-solving.
10. Prove mathematical statements involving positive integers by using the Principle of Mathematical Induction.

Topics and Scope
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I. Numeration Systems
    A. Historical
    B. Hindu-Arabic
    C. Place-value
         1. Base 10
         2. Other bases
II. Basic Number Theory
    A. Divisibility
    B. Prime and composite numbers
    C. Prime factorization
    D. Fundamental Theorem of Arithmetic
    E. Least common multiple
    F. Greatest common divisor
III. Integers
    A. Structure
    B. Properties
    C. Computational algorithms
IV. Rational Numbers
    A. Structure
    B. Properties
    C. Computational algorithms
    D. Ratio and proportion
    E. Decimal representation
V. Real Numbers
    A. Structure
    B. Properties
    C. Irrational numbers
    D. Decimal representation
    E. Number line representation
VI. Conceptual Understanding
    A. Patterns
    B. Problem solving
    C. Reasoning
    D. Modeling
VII. National and State Standards
    A. Process standards
         1. Problem-solving
         2. Reasoning
         3. Communication
         4. Representation
         5. Connection
    B. Mathematical proficiency
         1. Adaptive reasoning
         2. Strategic competence
         3. Conceptual understanding
         4. Procedural fluency
         5. Productive disposition

Assignments:
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1. Reading outside of class (0-60 pages per week)
2. Problem set(s) (1-8 per week)
3. Quiz(zes) (0-4 per week)
4. Project(s) (0-10)
5. Exams (2-6)
6. Final exam

Methods of Evaluation/Basis of Grade.
Writing: Assessment tools that demonstrate writing skill and/or require students to select, organize and explain ideas in writing.Writing
0 - 0%
None
This is a degree applicable course but assessment tools based on writing are not included because problem solving assessments are more appropriate for this course.
Problem solving: Assessment tools, other than exams, that demonstrate competence in computational or non-computational problem solving skills.Problem Solving
5 - 20%
Problem set(s)
Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams.Skill Demonstrations
0 - 0%
None
Exams: All forms of formal testing, other than skill performance exams.Exams
70 - 95%
Quiz(zes); exams; final exam
Other: Includes any assessment tools that do not logically fit into the above categories.Other Category
0 - 20%
Project(s)


Representative Textbooks and Materials:
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A Problem Solving Approach to Mathematics for Elementary School Teachers. 13th ed. Billstein, R., Libeskind, S., and Lott, J.W. Pearson. 2020.
Mathematical Reasoning for Elementary Teachers. 7th ed. Long, C., De Temple, D., and Millman R. Pearson. 2019.

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