Pre-Algebra

Whether you are currently studying Pre-Algebra, are looking to get ahead and learn all of Pre-Algebra, or are in Algebra 1, Algebra 2, or beyond and are struggling with your fundamentals, this course is for you!  The course includes topics covered in Pre-Algebra curricula in schools all across the globe.  Get ready for a thorough, energetic, and engaging journey towards mastering Pre-Algebra!

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Chapter 1: Algebraic Expressions & Operations with Integers

This chapter jumps into an overview of the basics of Algebra. You will begin with translating words into Algebraic expressions while learning about variables. From there you will tune up your order of operations skills before taking a tour through practicing addition, subtraction, multiplication, and division of integers.  Note how you will learn the processes involved and also why these process make sense!

Chapter 2: One-Step Equations & Inequalities

This chapter is a sweet road through the fundamentals of your future Algebra studies! You will begin by learning about properties of numbers and simplifying variable expressions. From there you will explore and master the concepts involved in solving one-step equations involving addition, subtraction, multiplication, and division. How to translate word problems into simpler equations is distributed throughout the chapter. You will finish off the chapter with solving one-step inequalities and discover the very rad reason behind why inequality signs can flip directions!!

Chapter 3: Operations and Equations With Decimals

This chapter rolls into the world of decimals! You will begin your studies with a focus on adding and subtracting decimals before heading into multiplying and dividing them. From there you will be treated to learning about formulas. The chapter finishes with lessons on how to solve equations involving decimals. Decimals are simpler and less frightening than they may first appear!

Chapter 4: Factors, Simplifying Fractions, and Exponent Rules

This chapter is a tour through divisibility rules and lessons in the basics of exponents and calculations involving exponents in the order of operations. You will then revisit and master factoring, including finding the GCF before simplifying fractions and converting between improper fractions and mixed numbers. A most awesome quick journey through rational numbers is next. The chapter closes out with a detailed look at the rules of exponents and scientific notation. You will come away with an understanding of why the rules make sense and how they built off one another!!

Chapter 5: Fraction Operations & Solving Equations with Fractions

This chapter is the place for mastering all operations with fractions! You will begin with finding the least common multiple and ordering fractions before converting between fractions and decimals. From here you will go on a detailed, yet simple tour of mastering adding, subtracting, multiplying, and dividing fractions. Toward the end of the chapter a great lesson on converting units and something awesome called dimensional analysis is rocked! The chapter closes out with solving one-step equations involving fractions and the final major exponent rule of raising a fraction to a power is taught. Time to make fractions your friends!

Chapter 6: Operations and Uses of Ratios, Proportions, & Percents

This chapter has everything you need to know about ratios, proportions, and percents! You will start out learning what ratios, rates, and proportions are and the operations and word problems involving them. From there, you will study how to solve proportions involving variables and then use these proportion solving skills in your travels through similar figures and scale factors. The second half of the chapter is devoted to mastering percents. From the foundations of converting between fractions, percents, and decimals to finding percents, the part, or the whole, through to calculating percent of change, you will leave this chapter knowing percents and how to use them in any way you could possibly need them in Pre-Algebra and beyond!

Chapter 7: Solving Equations and Inequalities

This chapter is a deep dive into solving many types of equations and inequalities. You will begin by learning how to solve two-step and multi-step equations. After rocking these topics you will master solving equations with variables on both sides. The chapter then turns to a neat exploration of solving two-step inequalities and literal equations. You will close out this part of your math trip with a lesson on simple and compound interest. Throughout the chapter an emphasis is placed on undoing the order of operations – a concept that will come in handy throughout your current and future math studies!!

Chapter 8: Relations & Functions, Slope, Lines, and Graphing

This chapter is a spring board into your studies in Algebra 1 of functions and linear equations. You will start with graphing data from tables and learn to describe and predict patterns and sequences. The next stop involves writing function rules and learning all the ins and outs of relations, functions, domain, range, and the vertical line test. The chapter rolls into the all-important study of graphing linear equations before you rock arguably the most important concept in all of Mathematics – slope or rate of change. From here you will learn all about slope-intercept form (y=mx+b), which is super rad!! The chapter closes out with a thorough introduction into solving systems of linear equations and linear inequalities by graphing. This chapter is filled with important yet also very cool Algebraic concepts.

Chapter 9: Foundations of Geometry

This chapter takes you through the fundamentals of geometry! You will begin learning about the building blocks of geometry and how to label and classify them. Then you are off to rocking complementary, supplementary, and vertical angles before discovering the magic behind parallel lines and transversals! A thorough introduction to triangles, polygons, and congruent figures follows. The key parts of circles, circumference and circle graphs is then explored. You will finish off the chapter with the study of three types of transformations: translations, reflections, and rotations.

Chapter 10: Areas of Two- & Three-Dimensional Figures and Volume

This chapter embraces the awesomeness that is area and volume! You will begin with the foundation of it all – perimeter and area of a rectangle. From there you will study the area of parallelograms, triangles, and complex figures before ending your study of the area of two-dimensional figures with trapezoids and circles. Throughout the chapter you will explore not only how to use the correct area formulas but master how the formulas came to be and connect to one another. In the second half of the chapter you will engage in an overview of what solids are before learning the ins and outs of finding the lateral and surface areas of prisms, cylinders, pyramids, and cones. This wild math ride concludes with the study of how to find the volumes of prisms, cylinders, pyramids, cones, and spheres. Jump right on into your studies of the objects that make up so much of the world around you!

Chapter 11: Right Triangles and An Introduction to Trigonometry

This chapter is nothing short of mathemagical!!! You will begin with a study of square roots of perfect squares (positive and negative roots) and classifying numbers as rational or irrational. From there it will be time to explore the Pythagorean Theorem and seeing how the Theorem leads to The Distance Formula. You will then learn about the Midpoint Formula before spending time with the foundations of similar figures. Similar figures acts as a great connection to special right triangles -> 30-60-90 and 45-45-90 triangles!!! The chapter closes out with a deep dive into trigonometry where sine, cosine, and tangent are learned!! You may have heard of this as SOH-CAH-TOA. Word problems involving angles of elevation and depression cap off an epic chapter of math! Trigonometry sounds scary…but you will see it can be made simple.

Chapter 12: Data Analysis: Techniques and Calculations

This chapter visits many ways you can represent real-world data with mathematics. The tour of knowledge begins with a thorough lesson on Mean, Median, Mode, Range, and Outliers. From there you will master how to construct and analyze Box-and-Whisker Plots before making Frequency Tables and Line Plots. You will learn how to make and interpret Histograms and then accomplish the same goals with Stem-and-Leaf Plots. Your learning excursion through Data Analysis rounds out nicely with the study of how to make Bar and Line Graphs. Jump into some very cool data analysis techniques!!

Chapter 13: Probability, Combinations, and Permutations

This chapter is a deep dive introduction into a serious study of probability and counting the number of ways things in this world can happen! Your rad road starts with an introduction to theoretical probability. From there you will learn about the counting principle and why it works (so very cool!!!). A short hop from here you will learn about compound events – A.K.A. independent and dependent events. Your studies continue with permutations, combinations, and a new math operation – factorials!! The chapter ends with explorations into experimental probability and using probability to make predictions. The world around us is full of seemingly countless possibilities and chances…learn how to calculate some of these scenarios!

Chapter 14: Foundations of Non-Linear Functions and Polynomial Operations

This chapter serves as a preview into what is to come in the second half of any Algebra 1 course. You will begin with learning how to graph quadratic equations (parabolas) and absolute value equations (v-shaped graphs) by evaluating x-values. From here you will learn the basics of how to graph and solve basic word problems involving exponential functions. The remainder of the chapter is devoted to a thorough introduction into Polynomials. You will begin with defining, naming, and evaluating polynomials. From there you will rock how to add and subtract polynomials! The chapter closes out with learning how to multiply polynomials using the distributive property and how to factor out a monomial from a polynomial by finding the greatest common factor (GCF). A healthy helping of future Algebra 1 topics is in store!!