# SRJC Course Outlines

 6/22/2024 5:41:34 PM MATH 74 Course Outline as of Fall 2023 New Course (First Version) CATALOG INFORMATION Discipline and Nbr:  MATH 74 Title:  NUMBER SYSTEMS Full Title:  Mathematics for Elementary School Teachers - Number Systems Last Reviewed:1/9/2024

 Units Course Hours per Week Nbr of Weeks Course Hours Total Maximum 4.00 Lecture Scheduled 4.00 17.5 max. Lecture Scheduled 70.00 Minimum 4.00 Lab Scheduled 0 6.5 min. Lab Scheduled 0 Contact DHR 0 Contact DHR 0 Contact Total 4.00 Contact Total 70.00 Non-contact DHR 0 Non-contact DHR Total 0

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

Title 5 Category:  AA Degree Applicable
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.

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: BMC Communication and Analytical ThinkingMath Competency CSU GE: Transfer Area Effective: Inactive: B4 Math/Quantitative Reasoning Fall 2024 IGETC: Transfer Area Effective: Inactive: CSU Transfer: Transferable Effective: Fall 2023 Inactive: 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 algorithms from number theory to determine divisibility in a variety of circumstances.
3. Explain and use the Fundamental Theorem of Arithmetic.
4. Explain the concept of rational numbers using 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.

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
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
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