Essential Algebra 1: A Practical Guide
Essential Algebra 1 is our introductory algebra text. Written in a clear, easy to read English it covers the fundamental concepts of algebra through a study of variables, sets, linear equations and linear inequalities. Each chapter progressively develops the critical thinking skills necessary for addressing more complex mathematical material through the use of examples and practical applications from fields as diverse as information theory, cartography and physics.
Our approach to course design at this level emphasizes examples over lengthy explanations. Sections start with a brief technical description and a plan English explanation then go into a collection of examples. The examples are selected so that they show not only the basic procedure but also any special cases and unusual situations that a student might encounter.
In the mathematics world, there are two versions of the subject. The "pure" version is extremely abstract. These mathematicians have little interest in real world applications and develop their ideas and theories purely to see where they lead. Applied mathematicians, on the other hand, are explicitly interested in the way mathematica can be used to describe real world situations. The textbooks in our Essentials series take an overtly practical approach to the material. Applications are briefly discussed at multiple points throughout each chapter and each chapter ends with a project students can do to see how the material is used in real world professions as diverse as law enforcement, cartography and cooking.
Chapter 1: Comparing Distances in Two Dimensions This chapter includes a discussion of number lines and how they can be used to determine distances. This project adapts that to two different methods for determining the distance between two points on a map.
Chapter 2: Information Theory In this chapter, we talk about variables and their application in developing formulas like the formula for converting between Fahrenheit and Celcius temperatures. The project discusses a special kind of procedure called a check sum and how check sums are used to validate data like credit card numbers.
Chapter 3: Determing Average Speed Solving linear equations is one of the core algebraic concepts covered in this course. This project applies that procedure to finding the average speed of a moving vehicle.
Chapter 4: Boiling Sugar Chapter 3 focused on working with equations that have one variable. In this section, we go one step further and discuss linear equations with two variables. The project has students collect data on the rate at which the temperature of boiling sugar increases and graph the results.
Chapter 5: Affect of Temperature on the Solubility of Salt In Chapter 3's project, we collected data and interpreted the results visually. In this section, the students collect a new set of data, calculate the linear equation that descries it and use the results to make predictions.
Chapter 6: Center of Gravity In this final chapter, students learn how to find the intersection point of two lines. The project shows how the intersection of lines can be used to find the center of gravity of a solid object.