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Models for operations with whole numbers are developed and relationships between the operations are studied. Numeration systems and additional properties of whole numbers are explored, leading to the development of fractions and integers. In addition, calculators, elementary logic, and Polya's four-step process are used in problem solving. This course cannot be used to satisfy the math requirement for an associate degree.
General Education Outcomes are the knowledge, skills, abilities, attitudes, and behaviors that students are expected to develop as a result of their overall experiences with any aspect of the college, including courses, programs, and student services, both inside and outside of the classroom. The General Education Outcomes specifically learned in this course are:
- Communication
- Critical Thinking
Models for operations with whole numbers are developed, and relationships between the operations are studied. Numeration systems and additional properties of whole numbers are explored, leading to the development of fractions and integers. In addition, calculators, elementary logic, and Polya's four-step process are used in problem-solving. This course cannot be used to satisfy the math requirement for an associate degree.
General Education Outcomes
- Communication
- Critical Thinking
Course Outcomes
- Demonstrate an understanding of the structure, properties, and nature of the real numbers.
- Demonstrate an understanding of core concepts underlying the performance of operations on real numbers.
- Illustrate multiple approaches for solving problems.
- Recognize the validity and comparative mathematical sophistication of alternative solutions to problems.
- Clearly and thoroughly explain mathematical ideas that may be presented in an elementary classroom using language, diagrams, and symbols.
- Connect mathematical topics visually, verbally, and symbolically using mathematical principles.
Faculty Contact Information
| Monday/Wednesday | 12:00–1:00 PM | South Extension Center |
| Monday/Wednesday | 5:00–5:30 PM | R303 |
| Tuesday/Thursday | 12:30–1:30 PM | R303 |
Course Information
At the end of this course, students will be able to:
- Demonstrate an understanding of the structure, properties, and nature of the real numbers
- Demonstrate an understanding of core concepts underlying the performance of operations on real numbers.
- Illustrate multiple approaches for solving problems.
- Recognize the validity and comparative mathematical sophistication of alternative solutions to problems.
- Demonstrate the ability to clearly and thoroughly explain mathematical ideas you will present in your classroom using language, diagrams, and symbols.
- Connect seemingly different mathematical topics visually, verbally, and symbolically using mathematical principals.
- Mathematics and Problem Solving
- Exploration with Patterns
- Reasoning and Logic: An Introduction
- Describing Sets
- Other Set Operations and Their Properties
- Numeration Systems
- Addition and Subtraction of Whole Numbers
- Multiplication and Division of Whole Numbers
- Addition and Subtraction Algorithms, Mental Computation and Estimation
- Multiplication and Division Algorithms, Mental Computation, and Estimation
- Divisibility
- Prime and Composite Numbers
- Great Common Divisor and Least Common Multiple
- Addition and Subtraction of Integers
- Multiplication and Division of Integers
- The Set of Rational Numbers
- Addition, Subtraction, and Estimation with Rational Numbers
- Multiplication, Division, and Estimation with Rational Numbers
- Proportional Reasoning
- Introduction to Finite Decimals
- Operations on Decimals
- Repeating Decimals
- Percents and Interest
| Primary OER Text | Clifford, L. E. (2025). Math for Elementary Teachers I: An Active, Problem-Solving Approach. Mohave Community College. CC BY-NC-SA 4.0. |
| Supplemental OER Text | Hobson, N. (2025). Mathematics for Elementary Education I. Tacoma Community College. CC BY-NC-SA 4.0. |
| Formal Logic OER | Levin, O. (2025). Discrete Mathematics: An Open Introduction (4th ed.). CC BY-NC-SA 4.0. Only selected sections from Chapter 1 are used. |
| Calculator | A basic or scientific calculator is recommended. A non-cell-phone calculator may be required for quizzes and exams at the instructor's discretion. |
| Other Materials | Notebook or binder, pencils, access to Canvas or the learning management system, and any instructor-provided handouts or manipulatives. |
Copyright and OER Attribution Note
| This course uses open-educational resources. Students should access materials through the links or PDFs provided in Canvas. OER materials may have different Creative Commons licenses, and students should preserve attribution when sharing or adapting materials. This syllabus is subject to change based on course needs, institutional policy, and student progress. |
| Homework and OER Practice | 25% |
| In-Class Activities, Participation, and Attendance | 15% |
| Projects, Presentations, and Teaching Explanations | 15% |
| Exams | 25% |
| Final Exam or Culminating Assessment | 20% |
Liberal Arts & Sciences
Dean, Jennifer Huggins; 815-802-8484; R310; jhuggins@kcc.edu; Division Office- W102; 815-802-8700
Homework and OER Practice
Homework is an essential part of any mathematics course. Assignments may include practice problems from the OER texts, instructor-created problems, Canvas quizzes, written explanations, and reflective prompts. Students should show work clearly and use appropriate mathematical vocabulary. Homework is designed to support learning and should not be completed by copying answers from another person, website, calculator, or artificial intelligence tool.
In-Class Activities and Attendance
Attendance and active participation are expected. Many class meetings will include collaborative problem solving, mathematical discussions, model building, error analysis, and teaching-focused explanations. Students are responsible for any missed work due to absence and should contact the instructor before class when an absence is unavoidable.
Projects, Presentations, and Teaching Explanations
Projects and presentations will ask students to connect mathematical procedures to conceptual understanding. These assignments may include explaining an algorithm, comparing student solution strategies, designing a visual model, analyzing common errors, or preparing a brief teaching demonstration for an elementary classroom. Proper grammar, mathematical vocabulary, clarity of reasoning, and correct computation will be part of the grading.
Exams and Final Exam
Exams may include short-answer questions, computation, written explanations, multiple representations, error analysis, and selected-response questions. The final exam or culminating assessment will be cumulative and will emphasize connections among number systems, operations, rational numbers, proportional reasoning, and teacher-ready explanations.
Calculator Usage
Students may use a calculator when permitted by the instructor. Because this course emphasizes conceptual understanding, estimation, mental computation, and reasoning, calculators may be restricted during selected activities, quizzes, or exams. Cell-phone calculators may be allowed on non-assessment days only at the instructor's discretion.
Artificial Intelligence Policy
Artificial intelligence tools may be used as learning support when permitted by the instructor, such as for reviewing vocabulary, generating extra practice, or asking for explanations after an honest attempt. AI may not be used to complete homework, projects, quizzes, exams, or written explanations on behalf of the student. Students must be able to explain their own work. Misuse of AI may result in a warning, a zero on the assignment, or additional action consistent with the academic integrity policy.
Academic Integrity
Academic integrity is expected. Cheating, plagiarism, unauthorized collaboration, copying solutions, or submitting work that is not the student's own may result in a zero on the assignment or assessment and may be referred according to institutional policy.
Accommodation
Students who have an official accommodation letter should provide it to the instructor as early as possible. Accommodations can only be implemented according to institutional policy and may need to be submitted before assessments or major assignments.
Because this course is delivered online, students are expected to participate in a respectful, professional, and academically responsible manner. The online classroom includes Canvas announcements, discussion boards, messages, submitted assignments, group activities, and any live virtual meetings that may be scheduled.
- Communicate respectfully. Use professional language when interacting with the instructor and classmates. Disagreement is acceptable, but personal attacks, insulting remarks, discriminatory language, harassment, or disruptive behavior will not be tolerated.
- Practice appropriate online etiquette. Write clearly, avoid typing in all capital letters, and review messages before posting. Discussion responses should contribute meaningfully to the conversation rather than simply stating agreement or disagreement.
- Participate consistently. Log in to Canvas regularly, review announcements and course materials, and monitor your institutional email. Students are responsible for completing readings, discussions, assignments, quizzes, and other activities by the posted deadlines.
- Protect privacy. Do not record, copy, photograph, download, or share class discussions, student work, live-session content, or personal information without permission.
- Use technology responsibly. During any live online meetings, minimize distractions and follow the instructor’s directions regarding microphones, cameras, chat features, screen sharing, and participation. Technology problems should be reported as soon as possible rather than after an assignment deadline has passed.
- Complete your own work. Unauthorized collaboration, copying, plagiarism, sharing answers, or submitting work completed by another person or an artificial intelligence tool violates academic integrity expectations. Students must be able to explain and defend all work they submit.
- Support a productive learning environment. Online participation should help classmates feel comfortable asking questions, making mistakes, and discussing mathematical ideas. Students are expected to contribute to a learning community focused on problem solving, clear reasoning, and respectful mathematical communication.
| Week and Dates | Unit | Topics and Readings | Assignments Important Dates |
|---|---|---|---|
Week 1: Aug. 17–21 | Unit 1 | Topic 1: Mathematics and Problem Solving. Clifford Unit 1, pp. 1–11; Appendix I problem-solving exercises, PDF pp. 119–154. Course orientation, mathematical mindset, Polya’s four-step process, and multiple solution strategies. | HW 1: Problem-solving reflection and Polya practice due Friday, Aug. 21. |
Week 2: Aug. 24–28 | Unit 2 | Topic 2: Exploration with Patterns. Clifford Unit 2, pp. 12–22. Patterns, reasoning, conjectures, and mathematical communication. | HW 2: Patterns and reasoning problems due Friday, Aug. 28. |
Week 3: Aug. 31–Sept. 4 | Unit 2 | Topic 3: Reasoning and Logic. Levin Sections 1.1–1.3, pp. 13–61. Statements, negation, connectives, implications, truth tables, and rules of logic. | Logic practice set and teaching reflection due Friday, Sept. 4. |
Week 4: Sept. 8–11 | Unit 3 | Topics 4–5: Describing Sets and Other Set Operations. Clifford Unit 3, pp. 23–30; Levin Section 5.1, pp. 389–402. Set notation, subsets, union, intersection, complement, difference, and Venn diagrams. | Monday, Sept. 7: Labor Day—college closed. HW 3: Sets and Venn diagrams due Friday, Sept. 11. |
Week 5: Sept. 14–18 | Unit 4 | Topic 6: Numeration Systems. Clifford Unit 4, pp. 31–44; Hobson Sections 0.1–0.3, pp. 7–17. Historical numeration, base ten, quinary, place value, and other bases. | HW 4: Numeration systems and place-value models due Friday, Sept. 18. |
Week 6: Sept. 21–25 | Unit 5 | Topics 7 and 9: Addition and Subtraction of Whole Numbers; Algorithms, Mental Computation, and Estimation. Clifford Unit 5, pp. 45–63; Hobson Sections 2.1–2.3, pp. 43–57. | HW 5: Addition/subtraction models, strategies, estimation, and error analysis due Friday, Sept. 25. |
Week 7: Sept. 28–Oct. 2 | Unit 5 | Topics 8 and 10: Multiplication and Division of Whole Numbers; Algorithms, Mental Computation, and Estimation. Clifford Unit 5, pp. 45–63; Hobson Sections 3.1–3.4 and 4.1–4.3. | Exam 1 is due Friday, Oct. 2. It covers problem solving, patterns, logic, sets, numeration systems, and whole-number operations. |
Week 8: Oct. 5–9 | Unit 6 | Topics 11–12: Divisibility; Prime and Composite Numbers. Clifford Unit 6, pp. 69–78; optional Levin Section 6.2.1, pp. 432–434. | HW 6: Divisibility, factors, multiples, primes, composites, and prime factorization is due Friday, Oct. 9. |
Week 9: Oct. 12–16 | Unit 6 | Topic 13: Greatest Common Divisor and Least Common Multiple. Clifford Unit 6, pp. 69–78. GCD, LCM, factorization methods, and contextual applications. | HW 7: GCD/LCM applications are due Friday, Oct. 16. Teaching Explanation Project assigned. |
Week 10: Oct. 19–23 | Unit 7 | Topic 14: Addition and Subtraction of Integers. Clifford Unit 7, pp. 64–68. Number-line models, opposites, zero pairs, signed counters, and contextual applications. | HW 8: Integer addition and subtraction models due Friday, Oct. 23. |
Week 11: Oct. 26–30 | Unit 7 | Topic 15: Multiplication and Division of Integers. Clifford Unit 7, pp. 64–68. Sign patterns, properties, models, and word problems. | Exam 2 due Friday, Oct. 30. Covers number theory and integer operations. |
Week 12: Nov. 2–6 | Unit 8 | Topics 16–17: The Set of Rational Numbers; Addition, Subtraction, and Estimation. Clifford Unit 8, pp. 79–88; Hobson Sections 1.4, 1.5, 2.4, 2.5, and 4.2. | HW 9: Fraction representations, equivalence, comparison, addition, subtraction, and estimation due Friday, Nov. 6. |
Week 13: Nov. 9–13 | Unit 8 | Topic 18: Multiplication, Division, and Estimation with Rational Numbers. Clifford Unit 8, pp. 79–88; Hobson Sections 5.1, 5.2, 5.5, and 5.6. | Wednesday, Nov. 11: Veterans Day—no classes. HW 10 and Teaching Explanation Project draft are due Friday, Nov. 13. |
Week 14: Nov. 16–20 | Unit 9 | Topics 19–20: Proportional Reasoning and Introduction to Finite Decimals. Clifford Unit 9, pp. 89–99; Hobson Sections 1.1–1.2, pp. 21–28. Ratios, rates, unit rates, proportional relationships, decimal place value, models, and comparison. | HW 11: Proportional reasoning, ratio models, and finite-decimal representations due Friday, Nov. 20. |
Week 15: Nov. 23–25 | Unit 9 | Topics 21 and 23: Operations on Decimals; Percents and Interest. Clifford Unit 9, pp. 89–99; Hobson Sections 2.6, 5.3, and 5.4. Decimal operations, fraction-decimal-percent connections, percent bars, applications, and simple interest. | Exam 3 due Wednesday, Nov. 25, by 5 p.m. Thanksgiving break begins at 5 p.m. College closed Nov. 26–27. No work due during the closure. |
Week 16: Nov. 30–Dec. 4 | Unit 9 | Topic 22: Repeating Decimals. Terminating versus repeating decimals, converting repeating decimals to fractions, real-number connections, course synthesis, and final review. | Teaching Explanation Project due Friday, Dec. 4. Final-exam review completed. |
| Finals Week: Dec. 7–10 | Final Exam | Cumulative review of all assigned OER sections and course outcomes. | Recommended online final-exam window: opens Monday, Dec. 7, and closes Thursday, Dec. 10. |
College Policies, Resources and Supports
For information related to the Student Code of Conduct Policy, Withdrawal Policy, Email Policy, and Non- Attendance/Non-Participation Policy, please review the college’s Code of Campus Affairs and Regulations webpage, which can be found at catalog.kcc.edu under the Academic Regulations & Conduct Guide.
KCC offers various academic and personal resources for all students. Many services are offered virtually, as well as in person. Please visit Student Resources - Kankakee Community College to access student resources services such as:
- Clubs and organizations
- Counseling and referral services
- Office of disability services
- Student complaint policy
- Transfer services
- Tutoring services, etc.
The materials on this course are only for the use of students enrolled in this course for purposes associated with this course. Further information regarding KCC's copyright policy is available at https://kcc.libguides.com/copyright.
|Course syllabus/calendar is subject to change.