The Everything Guide to Pre-Algebra

A Helpful Practice Guide Through the Pre-Algebra Basics - in Plain English!

Jane Cassie

• Publisher: Everything
• Year: 2013
• ISBN:
  9781440566417
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

Master the building blocks of mathematics! Not everyone is born a math whiz. Sometimes, all you need is a little extra help and practice to improve your comprehension. If you're a student encountering complex math for the first time, a parent wanting to help with homework, or an adult returning to school, The Everything Guide to Pre-Algebra is perfect for you. This essential guide uses simple explanations, step-by-step examples, and lots of review exercises to cover all the pre-algebra basics, including:

• Rational and irrational numbers
• Fractions, decimals, and percents
• Variables and functions
• Expressions and equations
• Number properties
• Inequalities
• Absolute values
• Plane geometry

With unique study strategies and proven test-taking tips, The Everything Guide to Pre-Algebra will help boost your math knowledge--and your confidence--one right answer at a time.

Chapter 1
Study Strategies

Let’s face it: becoming good at math takes work. Not only do you have to study; you have to study hard. But studying hard isn’t enough. If you’re studying the wrong way, all of your work is not going to pay off. After all, practice only makes things permanent, but practicing the right way makes them perfect. This means that if you’re practicing incorrectly, you’re just cementing bad habits into place. That’s actually even worse than doing nothing! And you certainly shouldn’t waste your time doing work that isn’t helping. Before you start learning all the details of pre-algebra math, it is important to review how to study pre-algebra. This chapter will give you some ideas as to how you can effectively study so that you can use this book in the way that’s most helpful to you. Your goal should be to pick up a few pointers, so that when the quiz or test or final comes along, you’ll be able to show what you’ve learned!

Don’t Call Yourself “Bad at Math”

All students encounter subjects that come naturally to them and concepts that they find a little bit harder to understand. It can be really frustrating to work on something when you feel like the people around you don’t have to work quite as hard. But the fact of the matter is that you’re reading this book because you have to learn math. Whether it’s to get ready for high school or to pass a college course, learning pre-algebra is a step you have to complete to get where you want to go.

Most people who believe they are “bad at math” usually have one or two concepts that they didn’t completely understand somewhere within their math education, whether those steps were in second grade or in middle school. When that happens, they have a weak foundation. And when they start trying to build other stuff on top of that foundation, it doesn’t go very well. That doesn’t mean they are bad at math. It just means they have to find the area or areas they don’t really understand and spend a little time fixing the foundation in that area.

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If you “don’t like math,” it might be time to switch your mindset. Instead of focusing on liking or disliking math, focus on liking the feeling of understanding something. When the goal is to understand a concept instead of to enjoy that concept, it’s easier to achieve.

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Don’t ever say you “can’t do math.” Can you split a bag of candy in half? Can you figure out how much money two things will cost when you know the price of each one? Can you calculate how much money you’ll earn this month if you earn $5 every day? Then you can do math. Math on paper (and in class, on quizzes, and on tests) is just a code that represents what happens with numbers in the real world. Learn the code, one piece at a time, and you’ll be able to do it.

Ask for Help

This is one of the most important actions you can take, because it’s something that students don’t often think to do. Asking for help doesn’t mean that you can’t do it yourself. It doesn’t mean you’re stupid. It doesn’t mean you don’t know what you’re doing.

What it means is that you’re a good student. Good students ask for help, wherever they can get it. That’s how you learn. The people who learn the most in life are the ones who ask questions.

Whether you’re totally lost, or you just have one little question, get an answer. Math builds on itself, and if there is a hole in your understanding, your foundation for future topics is going to be weak. Ask your classmates. Ask your older brother or sister. Ask your parent or tutor. Ask in a forum online. And, of course, ask your teacher! Don’t just ask the day before the test—ask as soon as the problem comes up.

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There are so many great resources for learning and practicing pre-algebra online. If the explanation in your textbook or class doesn’t make sense to you, try doing a Google or YouTube search for the topic at hand. Sometimes a slight change in the wording of an explanation is enough to make something click!

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Explain It to Someone Else

Sometimes you hear your teacher explain a concept in class, and it makes perfect sense. Then you get home to do your homework, and you just can’t figure out how to get to the answer. Other times, it doesn’t make sense even during class, but everyone else seems to get it.

If you think you don’t understand a concept, try explaining it to someone else. Maybe you’ll be able to explain it, and then you’ll see that you really do understand it. If not, you’ll be able to clarify what it is that you’re having trouble with, because it will be where you get stuck during the explanation. Explaining is a way to make sure you understand the reasoning behind each step. When you understand the reasoning, you’ll really understand what’s going on. That’s the road to success.

This is really hard to do, but it works. It’s much harder to try to explain something than to have it explained to you, because it makes you vulnerable. But don’t be afraid to make a mistake: this is an excellent way to learn. Try to explain to someone who already knows the material so that he or she can tell you if you’re making a mistake and help you when you get stuck. Give it a try!

Take It One Bite at a Time

Some math problems involve using ten or twenty different skills. It looks like one problem, but it has a whole series of intricate steps and skills that have to be done correctly to get the right answer!

If you are having trouble, break the problem down one step at a time to see if you can catch where your mistake is occurring. Maybe you actually understand the concept, but you’re making an arithmetic mistake. Maybe you are doing all the arithmetic right, but you don’t understand exactly what the question is asking you to find. If you can figure out which step you’re having trouble with, you can get a better explanation, re-read your textbook, or do some more practice problems of the same type.

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Don’t try to go too fast. Everyone learns at his or her own speed, and if you don’t understand a concept yet, you haven’t really learned it. If you feel like class is going too fast for you, you should try to schedule some extra practice time each week. That will slow down the speed at which you have to learn, which will allow you to go at your own pace.

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Cement Good Habits

Doing something correctly once is not enough to say that you know it. It’s proof that you can do it, but it’s just a start to really learning. Once you’ve learned something, you know how to do it when it shows up again.

That means that you have to practice the steps you take to solve a problem enough times that they are consistent and comfortable in the future. The best way to practice math is to practice in short, frequent study sessions. When you try to cram while learning a skill, you don’t get the most out of the problems. If you do thirty of the same problem type in a row, you are really only thinking on the first one; after that, you’re basically copying what you did on the previous problem. But if you do ten problems today, and then ten again tomorrow, and then ten later in the day, you will probably remember the steps much more clearly.

Math is a skill, and it’s best learned the way you learn other skills, like playing a sport or a musical instrument. Just like you can’t abstain from exercise all week and then complete eight hours of football practice on Sunday without an issue, you really shouldn’t try to cram for math.

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Treat your homework like what it is: preparation for the test. Homework is designed to give you a chance to practice what you learned, so the more you treat it like a test, the better.

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Try It with Numbers

The biggest difference between pre-algebra and the math you’ve done before pre-algebra is the presence of variables (letter symbols that represent quantities in math). Sometimes it’s hard to learn too many new things at once, and the variables can be just an added burden. So, try replacing the variables in a problem with numbers, and see if you can make sense of it that way!

When it comes to understanding new concepts, practice them with numbers first, and see what happens. Look at the solution and see what the variable equals, and then plug that answer in for the variable. Then, try manipulating the equation or expression so that you can understand how the numbers relate to one another. It might help you understand the rules...

Table of contents

• Title page
• Contents
• Top 10 Reasons Why Pre-Algebra Is Worth Mastering
• Introduction: Why Bother Learning Algebra?
• Chapter 1: Study Strategies
• Chapter 2: Types of Numbers
• Chapter 3: Factoring
• Chapter 4: Prime Numbers
• Chapter 5: Fractions
• Chapter 6: Decimals and Percent
• Chapter 7: The Four Functions
• Chapter 8: Exponential Powers
• Chapter 9: Manipulating Exponential Expressions
• Chapter 10: Base-Ten System
• Chapter 11: Simplifying Expressions and Equations (Without Variables)
• Chapter 12: Introduction to Algebraic Expressions
• Chapter 13: Manipulating Expressions with Variables
• Chapter 14: Introduction to Equations
• Chapter 15: Number Properties (with Variables)
• Chapter 16: Systems of Equations
• Chapter 17: Inequalities
• Chapter 18: Absolute Value
• Chapter 19: Plane Figure Geometry
• Chapter 20: Test-Taking Strategies
• Appendix A: Solutions
• Appendix B: Glossary
• Acknowledgments
• Copyright