# Course Syllabus: Pre-Algebra 101

no certificate

with CEU Certificate*

## Course Description

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.

## Course Requirements

## Course Topics

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

## Course Materials

No additional course materials required to complete this course.

## Grading Policy

A brief 10 pt. quiz will follow each lesson. Students will successfully complete this course with 70% or better

## Learning Outcomes

- Describe basic operations or numbers and signs.
- Solve simple to complex fraction problems.
- Solve problems involving decimals, percents, and ratios.
- Solve problems involving exponents.
- Solve problems involving radicals.
- Know variables and algebraic relations.
- Graph algebraic relations.
- Solve linear equations.
- Solve problems involving basic geometry, rectangles and triangles.
- Solve probability and statistics problems, and
- Demonstrate mastery of lesson content at levels of 70% or higher.

## Assessment Guide

Introduction Assignment | 1 |

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 |

Total Points: | 461 |

## Related Articles

- An Introduction to Fractions
- The Mathematical Rules of Solving Exponent Problems
- The Four Basic Mathematical Operations
- What is a Linear Equation?
- How to Solve Geometry Problems involving Rectangles and Triangles
- Applied Statistics: Repeated Measures
- Solving Higher-Degree Polynomials and Asymptotes of Rational Functions
- Solving Geometry Problems Involving Circles
- Applied Statistics: One-Way ANOVA
- Understanding Congruent Triangles in Geometry
- Applied Statistics: Factor Analysis
- How to Add, Subtract, Multiply, and Divide Decimals
- How to Calculate Mean, Median, and Mode
- How to Solve Algebra Word Problems
- Math Skills: How to Do Multiplication