Unlock the gateway to your future success with Pre-Algebra 101. This isn't just a course; it's your launchpad to a world of possibilities. Immerse yourself in an engaging journey where numbers transform into powerful allies. With each step, from comprehending the basics to mastering complex concepts, you'll gain the confidence of true mathematical fluency. This course doesn't just open doors--it arms you with the skills to breeze through challenges, whether you're venturing into science, statistics, or beyond. Discover the magic of math in everyday life and emerge not just with solutions, but with the curiosity to ask bigger questions. Empower your knowledge, transform your future--take the first step with us today, where every lesson is a leap forward.
Focusing on basic arithmetic principles like the commutative property and operations with negative numbers, this lesson connects mathematical theory with practical problem-solving. It offers strategies for mastering operations and emphasizes the cognitive benefits of minimizing calculator use, setting a robust foundation for continued study in mathematics.
Lesson 1-
Lesson 1 - Review of Basic Operations+
This lesson reviews the basic operations and some associated ideas, setting the stage for learning about fractions, the first main topic of the course.
Lesson 1 Exercises+
Exam 1B for Lesson 1
Introduction Assignment+
Introduction Assignment
Lesson 2. Fraction Foundations
Fractions introduce the concept of dividing numbers to represent parts of a whole, classifying them as either proper or improper based on the relationship between the numerator and denominator. Understanding equivalent fractions and reducing them to their lowest terms helps in performing operations like addition and subtraction effortlessly.
Lesson 2-
Lesson 2 -- Fractions I+
This lesson provides a foundation for understanding how to add, subtract, multiply, and divide fractions--a topic to which we will turn in the next lesson.
Lesson 2 Exercises+
Exam 2B for Lesson 2.
Lesson 3. Mastering Fractions: Arithmetic and Beyond
This lesson explores the arithmetic of fractions, covering addition, subtraction, multiplication, and division, even when involving integers and complex fractions. Key strategies include finding common denominators and using reciprocals for simplification.
Lesson 3-
Lesson 3 -- Fractions II+
In this lesson, we apply our fundamental understanding of fractions from the previous lesson to the basic arithmetic operations.
Lesson 3 Exercises+
Exam 3B for Lesson 3
Lesson 3 Activity+
Lesson 3 Activity
Lesson 4. Decimals, Percents, and Ratios 101
The lesson introduces decimals, percents, and ratios as essential tools for describing proportions and relationships between numbers. It focuses on improving the ability to convert between these formats seamlessly.
Lesson 4-
Lesson 4 -- Decimals, Percents, and Ratios+
In the previous two lessons, we discussed fractions at length. As you have probably noticed, however, most basic calculators (as well as many more-advanced calculators) do not deal with fractions.
Lesson 4 Exercises+
Exam 4B for Lesson 4.
Lesson 4 Activity+
Lesson 4 Activity
Lesson 5. Exponents: The Stepping Stones to Powers
Exponents reduce repeated multiplication into a concise form and have versatile verbal expressions beneficial for communication in mathematics. The lesson emphasizes following the established order of operations to tackle complex arithmetic expressions correctly.
Lesson 5-
Lesson 5 -- Exponents I+
In this lesson, we introduce exponents, which are a way to represent repeated multiplication (just as multiplication is a way to represent repeated addition).
Lesson 5 Exercises+
Exam 5B for Lesson 5
Lesson 5 Activity+
Lesson 5 Activity
Lesson 6. Exploring Scientific Notation through Exponents
Building on your foundational knowledge of exponents, this lesson delves into rules for multiplying, dividing, and understanding negative exponents. It also highlights how to apply exponents through scientific notation for simplifying complex decimal values.
Lesson 6-
Lesson 6 -- Exponents II+
Specifically, this lesson considers rules for multiplying and dividing expressions with exponents, and it also explores the meaning of negative exponents.
Lesson 6 Exercises+
Exam 6B for Lesson 6
Lesson 6 Activity+
Lesson 6 Activity
Lesson 7. The Power of Roots
In this lesson, we explore the radical symbol, which signifies roots and connects to fractional exponents for an insight into numbers' roots. By mastering radicals, one can evaluate expressions involving roots and apply arithmetic operations efficiently.
Lesson 7-
Lesson 7 -- Radicals I+
By the end of this lesson, you should be able to handle numbers raised to any exponent, and you will also be equipped to study arithmetic operations on radical expressions in the next lesson.
Lesson 7 Exercises+
Exam 7B for Lesson 7.
Lesson 7 Activity+
Lesson 7 Activity
Lesson 8. Working with Radical Expressions
Exploring radical arithmetic involves using properties like associativity and distributivity to simplify expressions, ensuring precise results. Learning to add, subtract, multiply, and divide radicals prepares students for handling complex expressions involving irrational numbers.
Lesson 8-
Lesson 8 -- Radicals II+
The mathematical tools we study in this lesson allow us to at least partially evaluate radical expressions without losing exactness in the result (unlike what would happen if we simply used a calculator).
Lesson 8 Exercises+
Exam 8B for Lesson 8.
Lesson 8 Activity+
Lesson 8 Activity
Lesson 9. Exploring Variables and Simple Equations
This lesson introduces variables and algebraic relations, focusing on the relationship between independent and dependent variables and their roles in forming equations. It provides strategies for evaluating algebraic expressions by substituting values into the independent variable.
Lesson 9-
Lesson 9 Variables and Algebraic Relations+
This lesson focuses mainly on the concepts associated with these topics and lays a foundation for studying in later lessons how to graph relations and solve simple equations.
Lesson 9 Exercises+
Exam 9B for Lesson 9.
Lesson 10. From Equations to Images: An Introduction to Graphing Algebraic Relations
Understanding the real number line and the concept of coordinates allows for accurate graphing of complex algebraic relations. Using horizontal and vertical axes, we can visualize the independent and dependent variables effectively.
Lesson 10-
Lesson 10 – Graphing Algebraic Relations+
In this lesson, we learn how to graph simple and moderately complicated algebraic relations.
Lesson 11. Unlocking the Secrets of Linear Equations
By manipulating equations uniformly on both sides, we model how to solve linear equations and delve into principles that can be extended to more complex equations. Central to the lesson is understanding the relationship maintenance between independent and dependent variables.
Lesson 11-
Lesson 11 Solving Linear Equations+
In this lesson, we learn how to manipulate equations by performing operations on both sides of the equation
Lesson 11 Exercises+
Exam 11B for Lesson 11.
Lesson 12. Understanding Basics: Rectangles and Triangles
Students learn to connect algebraic concepts with geometry by calculating perimeters and areas of rectangles and triangles, using mathematical representations and operations. Essential terms related to geometry like points and angles are also detailed for foundational comprehension.
Lesson 12-
Lesson 12 -- Geometry I: Rectangles and Triangles+
In this lesson, we take what we have learned about numbers, operations, and variables and apply it to simple geometry.
Lesson 12 Exercises+
Exam 12B for Lesson 12.
Lesson 13. Circle Geometry: Basics and Beyond
Bridging algebra with geometry, this lesson examines circles by defining circumferential relationships through pi (?) and geometrical terms like radius and diameter. Calculating circle circumference and area shows how mathematical constants interplay in real-world geometric scenarios.
Lesson 13-
Lesson 13 -- Geometry II+
In this lesson, we apply our basic algebra skills to the properties of circles. We look at the circumference and area of a circle, and we introduce the number pi (π)
Lesson 14. The Basics of Fairness and Chance
Understanding probability requires defining key terms such as fair and random and distinguishing between selection with or without replacement in successive events. Calculating probabilities involves determining the ratio of successful outcomes in situations like coin flips, dice rolls, or card draws.
Lesson 14-
Lesson 14 Introduction to Probability+
In this lesson, we take some of the principles we have learned in previous lessons and apply them to some simple concepts and problems in probability.
Lesson 14 Exercises+
Exam 14B for Lesson 14.
Lesson 15. Quantifying the 'Middle': Average, Median, and Mode
Understanding the 'middle' of data sets involves calculating averages, medians, and modes, enabling clearer interpretations although misinterpretation is possible if outlying data skews results.
Lesson 15-
Lesson 15 Introduction to Statistics+
The final lesson of this course looks at statistics, which is a subject that is closely related to probability.
The Final Exam+
The Final Exam
Lesson 15 Exercises+
Exam 15B for Lesson 15.
In This Course
14 Hours average completion time
1.4 CEUs
15 Lessons
36 Exams & Assignments
182 Discussions
16 Videos
170 Reference Files
Mobile Friendly
Last Updated February 2024
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.
This 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.
This 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.
This 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, this 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.
Master Basic Arithmetic: Connect theory with problem-solving.
Merge Algebra and Geometry: Calculate shapes accurately.
What You'll Achieve
Define and identify the commutative properties of addition and multiplication by solving problems with both positive and negative numbers.
Demonstrate the ability to perform basic operations, including addition, subtraction, multiplication, and division, with a focus on understanding the role of negative numbers.
Recognize and describe the parts of a fraction, including the numerator and denominator
Identify and convert between equivalent fractions and express fractions in their lowest terms
Recognize and apply the process of finding a common denominator to add and subtract fractions accurately.
Demonstrate the ability to multiply and divide fractions, including complex fractions, by utilizing the concept of reciprocals and simplifying results when necessary.
Recognize and accurately convert decimals to fractions and vice versa, demonstrating understanding of rational and irrational numbers.
Describe the relationship between percents, decimals, and ratios, and convert between these forms in various contexts.
Recognize and convert repeated multiplication to exponential form accurately
Evaluate simple exponential expressions correctly
Apply the order of operations (PEMDAS) to solve mathematical expressions accurately
Derive and apply the rules for multiplying and dividing exponential expressions with the same base.
Interpret and explain the meaning and application of negative exponents in simplifying expressions and scientific notation.
What I liked most were the tests and assignments. It evaluates my knowledge.
DE
"Extraordinarily Helpful"
★★★★★
I enjoyed this course. I'm also glad I could get on this course as often as I could. I liked the 5 exercises before the assignments in each chapter, plus the videos helped. The break down of the material was good too. Also I noticed that the assignments and the exercises addressed my working knowledge of my work and the test addressed my verbal knowledge, which is good. I notice that I have some problems with verbal knowledge. This has to do with me and maybe a health problem. I'm glad to know this. It tells me what to work on.
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14 Hours average completion time
1.4 CEUs
15 Lessons
36 Exams & Assignments
182 Discussions
16 Videos
170 Reference Files
Mobile Friendly
Last Updated February 2024
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