Course Syllabus: Pre-Algebra 101
with CEU Certificate*
An understanding of algebra is a foundational skill to virtually all topics in higher-level mathematics, and it is useful in science, statistics, accounting, and numerous other professional and academic areas. This course builds a bridge between simple whole-number arithmetic operations, such as addition, subtraction, multiplication, and division, and algebra.
The course begins by reviewing the basic arithmetic operations and their mutual relationships, and it then goes on to develop an understanding of fractions and how to perform operations on them. Exponents and their properties are then derived, and radicals (and other roots) are presented.
The course shows how exponents and roots are related, as well as how these are related to multiplication and division. Throughout this first portion of the course, the use of symbols in place of numbers is introduced and developed, leading to an investigation into variables and algebraic relations in the latter portion of the course.
The course also describes how to graph algebraic relations and how to solve simple linear equations. Finally, the course applies these various concepts to geometry by considering some of the characteristics of triangles, rectangles, and circles, and it also applies them to basic probability and statistics.
Thus, the course not only provides a fundamental set of algebra skills, but it demonstrates how these skills can be used to study various problems that have real-world applications.
1. Review of basic arithmetic operations (addition/subtraction, multiplication/division)
2. Fractions I
3. Fractions II
4. Decimals, percents, and ratios
5. Exponents I: Introduction and order of operations
6. Exponents II: Rules of exponents
7. Radicals I
8. Radicals II
9. Variables and algebraic relations
10. Graphing algebraic relations
11. Solving linear equations
12. Geometry I
13. Geometry II
14. Introduction to probability
15. Introduction to statistics
No additional course materials required to complete this course.
A brief 10 pt. quiz will follow each lesson. Students will successfully complete this course with 70% or better
|Lesson 1 Exercises||7|
|Lesson 1 - Review of Basic Operations||10|
|Lesson 2 Exercises||9|
|Lesson 2 – Fractions I||10|
|Lesson 3 Exercises||8|
|Lesson 3 – Fractions II||10|
|Lesson 4 Exercises||10|
|Lesson 4 – Decimals, Percents, and Ratios||10|
|Lesson 5 Exercises||8|
|Lesson 5 – Exponents I||10|
|Lesson 6 Exercises||9|
|Lesson 6 – Exponents II||10|
|Lesson 7 Exercises||8|
|Lesson 7 – Radicals I||10|
|Lesson 8 Exercises||6|
|Lesson 8 – Radicals II||10|
|Lesson 9 Exercises||4|
|Lesson 9 Variables and Algebraic Relations||10|
|Lesson 10 – Graphing Algebraic Relations||10|
|Lesson 11 Exercises||4|
|Lesson 11 Solving Linear Equations||10|
|Lesson 12 Exercises||3|
|Lesson 12 – Geometry I: Rectangles and Triangles||10|
|Lesson 13 Exercises||4|
|Lesson 13 – Geometry II||10|
|Lesson 14 Exercises||5|
|Lesson 14 Introduction to Probability||10|
|Lesson 15 Exercises||6|
|Lesson 15 Introduction to Statistics||9|
|The Final Exam||220|
- How to Add, Subtract, Multiply, and Divide Fractions
- The Mathematical Rules of Solving Exponent Problems
- How to Solve Geometry Problems involving Rectangles and Triangles
- How to Graph Algebraic Relations
- What is Statistics?
- Applied Statistics: Repeated Measures
- What is Skewness in Statistical Terms?
- How to Add and Subtract Vectors Algebraically
- Solving Systems of Linear Equations
- Applied Statistics: Descriptive Statistics II
- Solving Algebraic Functions
- Basic Geometric Shapes: Square, Circle, Rectangle, and Triangle
- What is Geometry?
- Math Skills: How to Do Subtraction
- Solving Geometry Problems Involving Circles