Carolyn Wheater - Practice Makes Perfect: Algebra I Review and Workbook, Third Edition

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An old joke tells of a tourist, lost in New York City, who stops a passerby to ask, How do I get to Carnegie Hall? The New Yorkers answer comes back quickly: Practice, practice, practice! The joke may be silly, but it contains a truth. No musician performs on the stage of a renowned concert hall without years of daily and diligent practice. No dancer steps out on stage without hours in the rehearsal hall, and no athlete takes to the field or the court without investing time and sweat drilling on the skills of his or her sport.

Math has a lot in common with music, dance, and sports. There are skills to be learned and a sequence of activities you need to go through if you want to be good at it. You dont just read math, or just listen to math, or even just understand math. You do math, and to learn to do it well, you have to practice. Thats why homework exists, but most people need more practice than homework provides. Thats where Practice Makes Perfect Algebra comes in.

When you start your formal study of algebra, you take your first step into the world of advanced mathematics. One of your principal tasks is to build the repertoire of tools that you will use in all future math courses and many other courses as well. To do that, you first need to understand each tool and how to use it, and then how to use the various tools in your toolbox in combination. The almost 1000 exercises in this book are designed to help you acquire the skills you need, practice each one individually until you have confidence in it, and then combine various skills to solve more complicated problems. Since its also important to keep your tools in good condition, you can use Practice Makes Perfect Algebra to review. Reminding yourself of the tools in your toolbox and how to use them helps prepare you to face new tasks that require you to combine those tools in new ways.

One tool that continues to grow in importance is the calculator, specifically, the graphing calculator. Generations of students learned algebra without using any sort of calculator, and if you do not have access to one, you can still learn all the algebra you need. As calculators became available, they provided the opportunity to explore ideas without worrying about whether the arithmetic would get too difficult. The rise of graphing calculators means that you can investigate properties of functions and their graphs without spending lots of time drawing those graphs by hand. Throughout this book, youll see Calculator Notes. These are ideas on how a graphing calculator might help you check your work, or solve a problem when youre stuck.

These tips are not meant to replace you learning the skills and doing the work. That will always be essential. The Notes are based on a commonly used graphing calculator, which is sometimes introduced in algebra. If you have one, you might be interested in the Notes. If you dont have one, theres no need to rush to get one. With patience and practice, youll find that youve assembled an impressive set of tools and that youre confident about your ability to use them properly.

The skills you acquire in algebra will serve you well in other math courses and in other disciplines. Be persistent. You must keep working at it, bit by bit. Be patient. You will make mistakes, but mistakes are one of the ways we learn, so welcome your mistakes.

Tools in this chapter: Understand how our number system works Learn the rules for performing common operations Write and evaluate numerical and variable expressions In arithmetic, we learn to work with numbers: adding, subtracting, multiplying, and dividing. Tools in this chapter: Understand how our number system works Learn the rules for performing common operations Write and evaluate numerical and variable expressions In arithmetic, we learn to work with numbers: adding, subtracting, multiplying, and dividing.