Course Description
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.
Prerequisite(s)
Appropriate assessment score or MATH 1424 with a grade of C or better and completion of geometry requirement (MATH 1453 or one year of high school geometry with a C or better) - Must be completed prior to taking this course.
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.
Topical Outline
1. Mathematics and Problem Solving
2. Exploration with Patterns
3. Reasoning and Logic: An Introduction
4. Describing Sets
5. Other Set Operations and Their Properties
6. Numeration Systems
7. Addition and Subtraction of Whole Numbers
8. Multiplication and Division of Whole Numbers
9. Addition and Subtraction Algorithms, Mental Computation and Estimation
10. Multiplication and Division Algorithms, Mental Computation, and Estimation
11. Divisibility
12. Prime and Composite Numbers
13. Great Common Divisor and Least Common Multiple
14. Addition and Subtraction of Integers
15. Multiplication and Division of Integers
16. The Set of Rational Numbers
17. Addition, Subtraction, and Estimation with Rational Numbers
18. Multiplication, Division, and Estimation with Rational Numbers
19. Proportional Reasoning
20. Introduction to Finite Decimals
21. Operations on Decimals
22. Repeating Decimals
23. Percents and Interest
2. Exploration with Patterns
3. Reasoning and Logic: An Introduction
4. Describing Sets
5. Other Set Operations and Their Properties
6. Numeration Systems
7. Addition and Subtraction of Whole Numbers
8. Multiplication and Division of Whole Numbers
9. Addition and Subtraction Algorithms, Mental Computation and Estimation
10. Multiplication and Division Algorithms, Mental Computation, and Estimation
11. Divisibility
12. Prime and Composite Numbers
13. Great Common Divisor and Least Common Multiple
14. Addition and Subtraction of Integers
15. Multiplication and Division of Integers
16. The Set of Rational Numbers
17. Addition, Subtraction, and Estimation with Rational Numbers
18. Multiplication, Division, and Estimation with Rational Numbers
19. Proportional Reasoning
20. Introduction to Finite Decimals
21. Operations on Decimals
22. Repeating Decimals
23. Percents and Interest