art of problem solving pre algebra table of contents

Prealgebra - 2e

(18 reviews)

Lynn Marecek, Santa Ana, California

MaryAnne Anthony-Smith, Santa Ana, California

Copyright Year: 2015

Last Update: 2020

ISBN 13: 9781938168994

Publisher: OpenStax

Language: English

Formats Available

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Reviewed by Michelle Metzger, Assistant Professor of Math and STEM Education, Buena Vista University on 12/24/21

This textbook includes all the necessary topics for a course at this level. The key terms and key concepts sections at the end of each chapter are nice additions. There are good examples provided throughout as well as links to videos which help... read more

Comprehensiveness rating: 5 see less

This textbook includes all the necessary topics for a course at this level. The key terms and key concepts sections at the end of each chapter are nice additions. There are good examples provided throughout as well as links to videos which help explain the mathematical content in the lessons.

Content Accuracy rating: 5

This textbook appears to be error-free.

Relevance/Longevity rating: 5

This textbook is relevant and uses contemporary examples.

Clarity rating: 5

The textbook is written in accessible language for those who might need to take this course. The mathematical content is appropriate and easy-to-read.

Consistency rating: 5

The textbook is consistent throughout each chapter with its design and layout.

Modularity rating: 5

The textbook layout is typical for a prealgebra textbook. Each chapter seems self-contained which would easily lead to rearranging chapters to suit the instructor’s design while teaching a prealgebra course.

Organization/Structure/Flow rating: 5

The textbook design is in this order and easy to follow: (1) objectives, (2) mathematical content with examples infused, and (3) homework/exercises to practice which include: real-world problems, writing problems, and a self-checklist for the user to evaluate their current understanding of the lesson.

Interface rating: 5

This textbook is available in various formats (e.g. pdf, html, etc.) which is advantageous for the user and his/her learning preference.

Grammatical Errors rating: 5

I found no grammatical errors.

Cultural Relevance rating: 5

This textbook is culturally sensitive.

Reviewed by Ellyn Gillespie, Instructor, Midlands Technical College on 7/27/21

This textbook covers all the necessary topics to prepare a student for Algebra. I liked the layout of the chapters and would use it in the order it is presented. The homework sections were adequate and I liked the progression from easier to... read more

This textbook covers all the necessary topics to prepare a student for Algebra. I liked the layout of the chapters and would use it in the order it is presented. The homework sections were adequate and I liked the progression from easier to harder. I believe it can be easily read by the student in an online or modular class setting.

The problems that I personally worked had the correct answers.

The book is up to date and I believe it will remain so.

The book was easy to read and understand at the student level.

The chapters and the homework assignments flowed logically. I found the pace and the order of the chapters to be consistent.

I believe the content of the book could be taught in any order and that the content could easily be moved around to meet the needs of any prealgebra teacher.

This textbook is well organized. The structure is consistent. Done by chapter order or using different sections in an assignment would be fine because the flow of the text allows for that.

I found no problems with the interface.

Cultural Relevance rating: 4

Perhaps more examples of cultural content, but at this level, in my mind it is more important to have the students understand the content.

I liked this text and would definitely use it in my course. Very pleased to see a free option for our students.

Reviewed by Kate Kenyon, Associate Professor, Umpqua Community College on 6/14/21

I believe this textbook covers all the essential topics so that students are prepared for Algebra. There are excellent explanations to solve problems and different approaches to problems demonstrated. Key concepts are fine but would be easier to... read more

Comprehensiveness rating: 4 see less

I believe this textbook covers all the essential topics so that students are prepared for Algebra. There are excellent explanations to solve problems and different approaches to problems demonstrated. Key concepts are fine but would be easier to align if at the beginning of the section. The examples take into account the most problematic areas students have. The readiness quiz is a nice addition but providing the answers to the readiness quiz would be helpful. I would have liked to see more video explanations to assist visual learners. I also would have liked more practice problems.

I worked about 75% of the problems and found no errors. I also did not find any errors in vocabulary. There could have been an expanded list of vocabulary words and reminders of words they may have learned in previous chapters. Because not all teachers will assign in order.

I believe this textbook is up to date and will be relevant for many years.

Clarity rating: 4

I found most students were able to understand the explanations. Those that struggled would have struggled with any text.

There is a consistent layout for the entire book which helps students throughout.

I used this book in a different order than was presented because changing the order fit what my students needed. It was easy to do and I had no issues reordering it.

The textbook presents the most basic concepts and moves on from there. There is a logical flow that works well for students from topic to topic.

I had no issues with links and they were used extensively. The images and charts were ok but could have had more contrast. I also found no issues on accessibility requirements other than some colors just did not show up well.

I had no issues with grammatical errors. The few I found were easy to understand and did not distract from the concepts discussed.

I would like to see fewer stereotypical problems between males and females, i.e. males bought the cars, females bought the groceries. Particularly, in ratios and proportions less splitting classes into boys and girls. Try things like eye color or months of birth to separate into groups. Things that do not matter is student identifies as male or female.

I will be using this text again.

Reviewed by Molly Beick, part-time instructor, Lane Community College on 1/11/21

The book starts with very basic instruction on the four arithmetic operations on whole numbers and progresses to working with integers, fractions, and decimal numbers. Everyday math applications are shown throughout the book for every newly... read more

The book starts with very basic instruction on the four arithmetic operations on whole numbers and progresses to working with integers, fractions, and decimal numbers. Everyday math applications are shown throughout the book for every newly introduced concept. Each chapter has a glossary of key terms and phrases.

Although I did not read every word, I did read several sections word-for-word, and found no errors.

The everyday applications relate to money, geometry, and food, for the most part. The examples will easily remain relevant. The simplicity of the subject matter makes the material easy to update if necessary.

The very first chapter is written in very explicit detail for working with the four basic arithmetic operations, making it easy for a true beginner to follow. As the chapters progress, each new skill is explained in the same detail while assuming a mastery of the earlier skills. If mastery has not yet been achieved, the student can easily refer back to the earlier lesson to review. New terminology is defined with examples provided, and practice allowed.

Each chapter section starts with the learning objectives followed by review questions from the previous section. Examples, definitions and concepts are then presented. The examples have links to the solutions so that a student can do it on their own, and are followed by a few self-check problems. The next learning objective is then presented in the same format. Applications are shown with consistent reminders on good strategies for figuring out the problem. Links to YouTube lessons on the topics are presented immediately before the practice exercises for the section. Odd-numbered problems have links to their solutions embedded in the problem number. At the end of the practice exercises, there is a self-check reflection for the student to gauge their understanding and then decide whether they need more help or are ready to continue.

The learning objectives are outlined at the beginning of each chapter section. Each chapter section is divided into smaller sections based on the learning objectives. These smaller sections are headlined with the target concept.

Working with strictly whole numbers is presented first for all of the main concepts - arithmetic operations, evaluating expressions, solving one-step equations, etc. Then integers are introduced and the main concepts are reviewed while working with an expanded set of numbers. Then fractions, then decimals in the same way. The progression in difficulty allows for a student to achieve mastery in a skill with a specific set of numbers, then review these skills with expanding sets of numbers, so that students can continue to review and practice the skills while learning more number concepts.

I experienced no issues with the interface.

Everything seems to be grammatically correct.

There is a smattering of names from a variety of ethnicities and races in the applications, but there could be more diversity. The money, ratios, and rates applications refer to the American culture only.

I thought the book was very well-written with lots of examples and practice opportunities. I like how the odd-numbered problems have links to their solutions for ease of self-assessment. I like the self-check reflection at the end of each section. I like the introduction to solving equations with progressively expanded number sets.

Reviewed by Eileen Perez, Associate Professor, Worcester State University on 6/20/20

The chapter layout and progression through the chapters is well done and comprehensive. Each chapter begins with a clear topic outline. Each topic includes learning objectives, an introduction and often a manipulative math activity to develop a... read more

The chapter layout and progression through the chapters is well done and comprehensive. Each chapter begins with a clear topic outline. Each topic includes learning objectives, an introduction and often a manipulative math activity to develop a good understanding. Examples of each type of problem and solutions are presented in a clear manner. Additional student problems are given. The text also highlights the language of mathematics and uses concise mathematical language in the explanations and problem solutions. The examples using word or application problems follow consistent steps throughout the text.

The index is present and effective. No overall glossary is present, but the summary at the end of each chapter is particularly well done. Key terms, concepts, properties and how to solve problems are all clear and concise.

I completed a few problems in each of the chapters and found them to be clear and error free. The prose, including the explanations given are accurate.

The content is rather timeless and the book will not become out of date quickly.

The text is well written and mathematical terms are well explained.

The text also highlights the language of mathematics and uses concise mathematical language in the explanations and problem solutions.

Modularity rating: 4

The content is modular and depending on the class some sections could be omitted without disrupting the flow.

The chapter layout and progression through the chapters is well done. Each begins with a clear topic outline. Each topic includes learning objectives, an introduction and often a manipulative math activity to develop a good understanding. Examples of each type of problem and solutions are presented in a clear manner. Additional student problems are given. The text also highlights the language of mathematics and uses concise mathematical language in the explanations and problem solutions. The examples using word or application problems follow consistent steps throughout the text

Interface rating: 4

Media sections are embedded in the text that refer to additional online resources. These videos are of good quality and are segmented into topics and subtopics in a logical fashion. The length of the videos however is a bit long for most of my students. Breaking them up into several shorter videos would benefit some developmental students.

No grammatical errors found.

No cultural insensitivity found.

The flow of the materials is unique. The book begins with whole numbers, as most other textbooks do, but then it moves into the language of algebra, Next it moves on to integers, fraction, decimals and percent. Finally, the book covers, real numbers, solving linear equations, math models, polynomials, and graphs. The authors clearly understand developmental students when they state in the preface, they may think they know some math, but their core knowledge is full of holes and that in addition to math they need to learn study skills and time management and how to deal with math anxiety. The textbook and its progression clearly aim to fill in the holes in the students’ knowledge. The flow of the text and chapter summary sections help the student address study skills and test anxiety.

Reviewed by Sasha Verkhovtseva, Professor, Anoka-Ramsey Community College on 6/3/19

The textbook is very comprehensive, and covers all traditional topics in a prealgebra course. It also includes a few extra topics, like polynomials, and graphs of equations, to give students an introduction to basic algebra concepts. There is a... read more

The textbook is very comprehensive, and covers all traditional topics in a prealgebra course. It also includes a few extra topics, like polynomials, and graphs of equations, to give students an introduction to basic algebra concepts. There is a list of learner outcomes at the beginning of each section. There is also a cumulative review, tables, geometric formulas, and index at the end.

Pretty accurate, I did not find any errors. One can find a list of past errata changes on the book page on openstax.org

Content is pretty relevant and up-to-date. It will not be difficult to update the text or implement the updates.

I was impressed with the clarity of the text. Easy-to-follow examples, lots of diagrams and clear instructions and descriptions. Great book for the pre-algebra level student.

The book is very consistent, the order is logical and very well thought through. Each topic builds upon previously developed material.

The modularity is based on the number systems: whole numbers, integers, fractions, etc. There are some algebra topics included. Some topics may be interchanged or omitted. Chapters are subdivided into sections, and it is easy to skip some of the sections if needed.

The order of topics is logical and helps students understand each concept thoroughly, gradually progressing from whole numbers to integers, and then to fractions, decimals, and so on.

The interface is great, no distortion of images or graphs, the text is very clear and easy to navigate. It is great to have an option of both, pdf and online text versions. No confusion or distractions for the reader.

The text introduces prealgebra concepts while addressing the needs of students with diverse backgrounds and learning styles. It would be great to include more examples with relevant cultural content.

Overall, this is an excellent textbook, and I would highly recommend it for a pre-algebra course. Thank you for making this available to students at no cost. I plan to adapt this book in the near future.

Reviewed by Bill Diss, Math Instructor, Portland Community College on 8/2/18

The book is certainly comprehensive. The table of contents is fine, there is no index or glossary. read more

The book is certainly comprehensive. The table of contents is fine, there is no index or glossary.

Accuracy is good. I did not notice on least one of the checks that only an = sign was used and not a ? over the = sign.

Relevance/Longevity rating: 4

Relevance and longevity is good. I liked that the authors did not put in a lot of stories or events for a particular era. It seems many authors try and put in "cute" little stories or problems and these get out of date quickly.

The book is very clear. I liked that authors did not put a large amount of text in the book. The diagrams for the geometry problems and steps are very clear. I did have some difficulty knowing which problems would give just an answer and which ones would show the a solution and steps.

Consistency is fine between all chapters.

Modularity is fine. A student or teacher should be able to jump from section to section and in different orders if needed.

Organization is fine. I especially like how topics are broken down from more simple problems to harder problems in a sequential way in different sections.

Interface usage is fine. I did see on one check the ? over the = signs were to the left and not center.

I saw no grammar errors.

I thought the cultural relevance is fine. The authors did not go into a lot of details with examples or stories. In other words they are simple and do not have that much of a cultural bias in any direction.

I would like to see the problems numbered at the bottom of each section. As an instructor is it nice to assign problems by numbers. The book had no numbers to identify problems.

I really liked the high quality graphics.

Reviewed by Anna Dubon, Adjunct Instructor of Mathematics, Piedmont Virginia Community College on 3/27/18

- This textbook covers all necessary topics to insure a solid transition into Algebra. The authors give good explanations of multiple, mathematically sound ways to approach problems. - The “Key Concepts” are very good. A better placement of... read more

- This textbook covers all necessary topics to insure a solid transition into Algebra. The authors give good explanations of multiple, mathematically sound ways to approach problems. - The “Key Concepts” are very good. A better placement of those would be at the beginning of each unit, instead of the end. - Good examples are provided throughout the book. It is obvious in the way the lessons are written that the authors understand the common misconceptions students have about various topics. - I like the readiness quiz at the beginning of each section, but I do not see how students know if their answers are correct. - Beginning each section with new vocabulary would be more helpful than placing it at the end of the unit. Adding more vocabulary to the list would be helpful, as well. - The videos that are listed near the end of each unit are good videos. I would like to see many more offered for the students. Ideally, an online text would have video explanations throughout the units. For example, sample problems could be worked out in a video, or answers to examples could be explained. - Although the authors provide a good sample of practice problems, there are not enough within the text to provide an adequate amount of practice. An instructor will need to find, or make, additional practice problems for students. - There are pictures, graphs, tables, and other images throughout the text. More would be better. Small images that could be enlarged by the student would be helpful. -The problems that show all steps are very helpful, and well thought out. Again, it would be nice to have more.

Content Accuracy rating: 4

- I worked approximately 100 problems and found no incorrect answers.

- Within the text, there were a few small inaccuracies that stood out to me. The definition of an isosceles triangle is not correct. I would not say, as the text does, that there are arrows on both “sides” of a line. And, I would not recommend using “B” for one of the bases of a trapezoid since a capital B is usually used to indicate the area of a base of a 3-dimensional figure.

The text is up-to-date, and I believe it will be relevant for many years. The application problems tend to be about things that do not go out of style. In the future, when the application problems need to be updated, it appears that updating the book will be an easy process.

The average eighth grade student would have no trouble reading the text and following the lessons. The math terminology is appropriate and not watered down within the easy-to-read text.

The book's look and layout is consistent from beginning to end, which makes it easy to navigate for students.

The lessons in the text could be rearranged, or parts could be omitted, and the book would still be a useful resource in a Pre-Algebra course. Parts of the text could easily be assigned within an Algebra course as an introduction to various units, or as a tool for remediation.

I have not yet requested an editable version of the text, so I do not know if it is easy (or possible) to add your own lessons and problems within the text, and between units.

The topics are presented in a logical order. The textbook begins with the most basic concepts, such as place-value, fractions, decimals, and subsets of real numbers. The student is then introduced to percents, equation solving, and geometry applications. Then comes a unit on polynomials, which is more than sufficient for a Pre-Algebra student. And all of this is followed by a solid introduction to graphing linear equations.

Interface rating: 3

All of the links that I used for the online videos worked. The links that I clicked on within the text worked as intended.

The aesthetics of the online book are adequate. The recommendations I would make would be to: 1) use more color, 2) use sharper, darker outlines to make tables, images, and sample questions easier to focus on, 3) avoid the pale teal color that is used throughout the text, only because it is not easy to see, 4) use more bold type to separate sections of the units, 5) change the size of the numbers used for numbering items so that they do not blend in with the questions, and 6) refer to specific figures and tables as “Figure 3” and “Table 2,” for example, rather than “Figure” and “Table.”

Grammatical Errors rating: 4

The errors are relatively minor, and might not be an issue for most students and instructors. There are many missing and misplaced commas, quotation marks that need to be fixed, and errors in spacing throughout the book. There are periods on phrases, and there are some awkwardly worded sample questions. There are a few missing words, as well. With that said, the book is pretty well written, and only needs minor edits throughout. I would definitely use the book as-is, but a polished version would be nice.

Cultural Relevance rating: 3

- I appreciate the variety of names in the application problems. The applications themselves are everyday tasks, not tasks unique to specific cultures. - There are far more males represented in the application problems than females. Unfortunately, the problems that involve females include them buying a dress, a pair of shoes, a purse, and painting a nursery. - There seem to be many questions that deal with separating people into groups of boys and groups of girls. I am sure there are better, and more interesting, ways to group people.

I believe this textbook is a quality resource for learning and teaching mathematics. In my review, I am making recommendations for making the text a little better, but as is, the text is a solid tool for learning and teaching mathematics. I appreciate those who made it available free of charge to students.

Reviewed by Sandra Sze, Assistant Professor, LaGuardia Community College on 2/1/18

The book covers topics. The contents of the book fits into a prealgebra curriculum. read more

The book covers topics. The contents of the book fits into a prealgebra curriculum.

There is a list of errata online, but the book covers the material well.

This book definitely is relevant, using contemporary examples like miles per gallon in cars.

I like the way the book is written. It is clear.

The book is consistent. Each chapter has an introduction and then a more in depth coverage of the material with some exercises within the text. The chapters end with a glossary of terms students should know, along with review exercises.

The text is easy to read and the sections of the chapters are of perfect length.

The topics are presented in a clear logical manner.

The text is easy to read, the images are good and the external links work.

Grammar is good.

I did not find any offensive content in the book.

Reviewed by Virginia Petitt, Math Instructor, Rogue Community College on 8/15/17

The book includes all topics commonly covered in Math 20 (Pre-Algebra) and also includes units on polynomials and graphing. The readiness quiz at the beginning and self-check at the end of each sub-section of each unit provide strong support for... read more

Comprehensiveness rating: 3 see less

The book includes all topics commonly covered in Math 20 (Pre-Algebra) and also includes units on polynomials and graphing. The readiness quiz at the beginning and self-check at the end of each sub-section of each unit provide strong support for learning.

It would be beneficial to have more practice problems for mastery of the content. Although there is a glossary at the end of each sub-section in each chapter, it often omits terms introduced in the text that would be useful in supporting the study of concepts, eg variable and factor, mathematical properties such as Identity Property and Commutative Property, and PEMDAS. An index would also be useful.

While there are several videos linked within most Sections to support learning, there are too few for a fully online class.

In online format, some Practice Exercises have a useful “Show/Hide Solution” capability, although a step-by-step solution is not always provided. This would be especially useful in Sections such 4.3, Multiplying and Dividing Complex Fractions.

Both content and spelling are very accurate. Problems sampled at random had correct answers.

The material is presented with up-to-date pop-culture references, eg the number of calories in a caramel macchiato, and uses up-to-date instructional strategies such as fraction blocks. Although a wide variety of contexts for application problems are used, additional cultural references within application problems would be beneficial.

Concepts and instructions are well-written at an appropriate reading level for the audience. Flesch-Kincaid reading-level checks computed via Microsoft Word averaged high 8th grade level. It would be helpful to have a more complete glossary, as well as increased use of boldface text and highlighted blocks of content for emphasis.

The layout and framework of the textbook are consistent throughout.

While each unit in the book could be taught as a stand-alone set of lessons, each Section within units is multiple pages long, both in the online and pdf versions, making it difficult to divide into smaller sections and reorganize or repurpose.

Organization/Structure/Flow rating: 4

Learning objectives are present, but are labeled as “Summary” at the beginning of each section and require users to click a down arrow in the online version. This is not necessarily intuitive for learners new to online textbooks or curriculum. However, learning objectives show up automatically in the pdf version.

Topics seem to flow well from one to the next, in a logical sequence.

Practice exercises are not numbered, which would make them difficult to discuss as a class.

Navigation is generally straightforward and consistent, with the exception of the learning objectives issue mentioned above. More use of color for emphasis and interest would be helpful, as would additional images to help make application problems relevant.

Numbering practice exercises would make navigation less awkward when assigning the problems or discussing them with a class.

Spelling and grammar are accurate. Occasional use of contractions such as “we’d” are a bit awkward.

Cultural references consist primarily of a variety of names used within application problems. Additional cultural references within application problems would be beneficial.

This OER has several useful additional resources including an Instructor Getting Started Guide, Instructor Answer Guide, Sample Syllabus Language, and PowerPoint slide decks that provide accompaniment for each chapter. Also helpful is a publication titled, “Errata Release Notes,” which appears to be updated annually by Rice University, as well as suggested workarounds for each error.

Another separate and useful resource is the “Manipulative Mathematics for the Teacher” which provides a few games, worksheets, as well as links to teacher-created videos, which are of good quality though not overly engaging.

While the foundational concepts shared in this text are strong and well presented, the missing details such as the amount of practice exercises, the absence of numbering of problems, and the need for an index and stronger vocabulary support make this textbook more useful as supplementary material, since it would require a significant amount of additional work on the part of the teacher to be used as a primary text.

Reviewed by Donna Parrish, Adjunct Instructor, Rogue Community College on 8/15/17

The book has 1146 Pages and covers most topics typically taught in a transition to algebra class. read more

The book has 1146 Pages and covers most topics typically taught in a transition to algebra class.

I found no errors

The content in the book is standard math content that does not change much so the book can be used for a long time. The examples were rather traditional - same problems I solved decades ago.

The text is written in a straight forward way.

No problems noticed.

Like most math books, this one was broken into logical small sections

Very traditional

I noted nothing that was confusing or distorted

I noticed no problems

I just found this book boring. The type face and the page set-ups were not interesting. The strongest part of the book was the video links on each lesson. The videos are very well done without razzle-dazzle or goofiness. On the first chapter I was excited to read and see examples of modeling, but that disappeared, It was disappointing not to see things like an area model for multiplication of whole numbers, decimals, common fractions, polynomial, and so on.

Reviewed by Moreland Smith, Adjunct Professor, Rogue Community College on 4/11/17

This text is very comprehensive on typical Math 20 topics(through 8th grade math). Also, is a very good introduction and more on Algebra concepts. Also includes some Algebra II concepts. Great integration of Geometry concepts. read more

This text is very comprehensive on typical Math 20 topics(through 8th grade math). Also, is a very good introduction and more on Algebra concepts. Also includes some Algebra II concepts. Great integration of Geometry concepts.

Book is very accurate and typo free. Has some unique approaches to the presentation of some topics. For example, teaches decimals by starting with fractions!

The material is presented in a nearly timeless fashion. But, still has some connections to today. Should be a long time before it becomes dated.

This book is the clearest math book I have ever seen. The visual learner will love this book. The learn differently student should find this book helpful. Problems are solved with all steps filled in -- no gaps in problems. Yet the book is a reasonable thickness!

The layout and terminology is very consistent throughout the book.

The modules are based on the real number system -- whole numbers, integers, rationals, etc.

Again, organized around the real number system. Best flow I have seen in a Math 20 book. Best geometry integration I have ever seen.

The book has a high degree of clarity in the presentation of topics and attention to detail.

As a math person, I am very comfortable with the grammar in the text!

The book has diversity in its presentation. The diversity is gentle in character and - not - beat the reader over the head level!

Best Math 20 book I have seen in my career. I hope to teach out of it in the future.

One gripe, does not use PEMDAS or GEMDAS to describe order of operations -- although it describes the steps without the acronym.

Reviewed by Griffin Colegrove, Adjunct Instructor, Rogue Community College on 4/11/17

Prealgebra is comprehensive and includes a table of contents, tables and formulas, and an index. Does not include a glossary but has vocabulary defined and referenced throughout the book. The scope of the units of the book is beyond the the text... read more

Prealgebra is comprehensive and includes a table of contents, tables and formulas, and an index. Does not include a glossary but has vocabulary defined and referenced throughout the book. The scope of the units of the book is beyond the the text that we are currently using in our Pre Algebra classes. Prealgebra includes Solving Linear Equations, Math Model and Geometry, Polynomials, and Graphs. Most of these are beyond the level of our currently adopted Pre Algebra book.

The book seems accurate from the selection of pages and problems that I reviewed (book is 1000+ pages long). Any possible errors can be submitted to OpenStax for occasional updates of the online edition.

The content of the book is relevant and up-to-date, but not overly specific to its 2017 copyright date. The examples make sense now and should still be relevant for many years to come.

Prealgebra is very clear and in written in a way that is easy to comprehend. Any new terminology is introduced in the unit it pertains to allowing students to gain vocabulary as they work through the text. The vocabulary is not listed in the introduction.

The book seems consistent in its terminology and framework. Each chapter and its sections are set up consistently.

Prealgebra has helpful and obvious page and section breaks that make it easy to use and follow. It is a little difficult to know which section of the chapter you are in after the opening page because the section is not listed on the top or bottom of the page. This means you must flip forward or backward to the beginning or end of the section to be sure which section it is.

While long, this textbook has nice flow that leads easily from one unit to the next. The chapter review exercises are also logical and clear. Each section usually includes learning objectives, readiness quizzes, vocabulary, "How To:" steps, examples, links to manipulative models, visuals (when appropriate), and exercises. The answers for most questions are included in the Answer Key at the end of the book.

Interface rating: 2

The online version is easy to read. The printed version, however, is difficult to read. Much of the printed text is italicized or colored differently and printed too lightly. Also, the margins of the printed version seem to small and do not take advantage of enough of the page. This may be to be more efficient with ink, but seems to waste space on each page.

I did not notice any grammatical errors as I was reviewing this textbook. The publishers also revise it occasionally and any errors can be submitted to OpenStax.

Prealgebra seems to be culturally relevant and inclusive.

The book is long, but very thorough. Each section includes learning objectives, readiness quizzes, and has multiple examples, explanations, and visuals (when possible) to describe the new content. It also includes great resources that are accessible to students and instructors. Once instructors make a free online account, they can access additional materials. My instructor account is in the process of being verified by OpenStax, but some books have online homework assignments that can be created. I am hoping this is true of Prealgebra. This book seems to be a wonderful, free resource that should be implemented in more of our community college to keep classes affordable for students, keep the book relevant (instead of being used once and being obsolete due to a one-time access code), and protect our natural resources by minimizing printing and using books many times.

Reviewed by Kevin Brewer, Instructor, Chemeketa Community College on 2/8/17

Chapters 1 through 8 make a great textbook. They cover all the elements I am looking for in prealgebra. Chapters 9-11 are like bonus chapters for me. They delve into concepts from the beginning of algebra and geometry classes. These are helpful... read more

Chapters 1 through 8 make a great textbook. They cover all the elements I am looking for in prealgebra. Chapters 9-11 are like bonus chapters for me. They delve into concepts from the beginning of algebra and geometry classes. These are helpful chapters to have included to offer material for the advancing student or even class. Different teachers and programs like to have some of these concepts in their prealgebra. For some of us who also help GED students, those three chapters allow this entire book to meet their needs.

I noticed no errors. All of the problems I calculated were accurate, including the solutions that were worked out. There is no loss of credibility in this area.

The content has many generic examples. What I mean by that are examples dealing with furniture or cars or telephones. These are staples, cutting across all generations, ethnicities, socio-economic (in so far as students taking this class will be concerned). Though not "cutting edge" with flashy questions about Twitter or Snapchat or the latest news from the Kardashians may be missing, it is nonetheless able to avoid becoming outdated.

The language used to explain concepts was solid. The explanations are fairly concise, leading quickly into examples. Applications are not overly emphasized, but that is fine, applying concepts should be placed more on the teacher. This also keeps the book more current and needing less updating. Students at this level will be able to understand what is being said.

The terms remained constant throughout the book, as far as I could tell. Pre-algebra defines many of the basic categorizations of the number system and basic rules. These are applied, but not in an overwhelming way. Vocabulary was defined at appropriate times using previously defined concepts in a fairly traditional way.

The book does appear to have flexibility, even as evidenced by it's ability to be in PDF or online versions. One can scroll down for "quite a while" until reaching the bottom of the lesson. Options to deal with this are available using different technologies and preferences. An instructor might find sections able to be combined or skipped entirely, or if desired and with work, they could be rearranged some; the danger is ensuring stream of development of some definitions and conceptual understanding.

Nothing appeared "out of order", it had a nice flow along the way, though it did have some concepts in different locations than the books I use. It was interesting to see solving equations for addition/subtraction was in a different chapter than solving equations with multiplication/division. I would like to see how that affects student learning. It makes me wonder if there were other concepts in a different order than my experience; maybe they flowed in a way that it did not trip me up.

Some of the answers when clicking on "Show the Answers" in the Online Version were tiny. I have several students each term who complain already about small print. Using a tablet can help that, however it is then larger making navigation more cumbersome. Otherwise, the layout was great, white space is very much appreciated, and having answers hidden worked very well. I especially liked how the first one or two answers for a question type gave the worked-out solution, even with coloring and explanations.

No issues with grammar.

The book did very well in this respect. They mixed in names and information globally. I appreciated that this was not a book that overplayed the multicultural in a tacky way. Some books seem like they just write a math problem then throw in the most popular name from a random country. In general, the book is not trying to be a flashy textbook with teenager lingo, but tries to just focus on concepts that many people can relate to. This will allow the Rural Teacher and the Urban Teacher both to be able to modify to their classroom cultures. I appreciate this.

Reviewed by John Czaplewski, Assistant Professor, Winona State University on 8/21/16

This text details all of the selected topics well. The index is as to be expected. There is not a glossary, per se, but there is a list of key terms after each section. Additionally, there are numerous helpful appendices to asset comprehension. read more

This text details all of the selected topics well. The index is as to be expected. There is not a glossary, per se, but there is a list of key terms after each section. Additionally, there are numerous helpful appendices to asset comprehension.

There were no issues with accuracy that I came across.

With the basis of this text being that of pre algebra concepts, the material will not be out-of-date. The notation is consistent with traditional learnings, so students will not have new jargon to familiarize themselves.

Content is quite clear. Processes are explained in detail, so that students can easily understand the flow of thinking. There was careful thought given to the examples to be utilized as a reference for the students.

There are no issues with consistency.

The design of this textbook makes it adaptable so that sections and/or chapters can be arranged and omitted as needed.

There are numerous examples in each section provided. This comes after well-defined objectives for each section. Included are self-assessments for the students to utilize in their learning process. Nothing is taken for granted, so students are able to experience success in mathematics. Throughout the text are link to video explanations and applications; the mathematics is made meaningful for the students.

I did not encounter any issues with outside sources nor within the text itself.

I did not encounter any grammatical errors.

There were no observable concerns regarding cultural relevance.

Having the objectives stated at the beginning of each lesson is helpful. Students need to know what they should be experiencing. The use of outside resources is beneficial, providing assistance to students in manner that is not purely text-based. Ample answers provided to aid in checking understanding.

Reviewed by Brenda Bradley, Instructor, Portland Community College on 8/21/16

While this Prealgebra text does cover most of the traditional topics, (Whole Numbers, Integers, Rational numbers, Decimals, Percents, Solving Linear Equations up to multi-step equations and graphs), it does so in a non-traditional order by... read more

While this Prealgebra text does cover most of the traditional topics, (Whole Numbers, Integers, Rational numbers, Decimals, Percents, Solving Linear Equations up to multi-step equations and graphs), it does so in a non-traditional order by focusing on whole numbers and basic operations first. The table of contents is thorough and there is an index to locate concepts and vocabulary. This book not only provides a PDF version, but also an online version that has interactive components for the students. There is even the option to use WebAssign for online homework assignments.

The text problems and exercises appear to be accurate, and there is a link provided to reference an Errata list.

Content appears to be up-to-date, prices of materials, etc, The text is also adaptable to instructor's needs.

The text uses accessible prose and is easily understood. There could be more instructions added to the examples, however, when solving problems. The problems seem to "skip" simplifying steps, which might confuse students.

Consistency rating: 4

Different fonts are used throughout the text, which is somewhat uncomfortable, as are different methods of explaining processes. Overall, though, each chapter is consistent with an introductory summary, readiness quizzes, Try-it sections, etc.

This text is divided up in a reasonable manner, consistent with most math textbooks.

The topics of the book are presented in a standard format for prealgebra courses. I like that the authors took effort to focus on fundamentals in the first section so that students can start learning the course confidently.

The PDF text file, when downloaded, has many places where formatting is a problem. For example, in Chapter 1, the header for Example 1.3 is at the bottom of page 21, but the actual problem is at the top of page 22. There are many places where pagination needs to be corrected to reduce student's confusion. Also, the page numbers in the index of the pdf version do not match up with the page numbers of the text. If you type in "10" to go to "number line" in the text the pdf actually takes you to page 4. The online version does not appear to have this problem.

There appears to be relatively few grammatical errors. There is an Errata list provided on the website.

The text is fairly culturally sensitive, using examples of several races, ethnicities and backgrounds in word problems and introductory segments.

This book has many helpful features for instructors and students, including Manipulative Mathematics worksheets, links to extra resources inserted directly into the text, and an online homework partner, WebAssign. There are also active components for students in the online version to practice the lesson and then reveal the hidden answers.

Reviewed by Julie Pfaff, Instructor, Lane Community College on 8/21/16

This text covers a range of topics typical of a prealgebra-level text, focusing primarily on arithmetic skills, equations, and graphing. I found the content emphasis somewhat uneven. Most of the content in the first eight chapters focuses on... read more

This text covers a range of topics typical of a prealgebra-level text, focusing primarily on arithmetic skills, equations, and graphing. I found the content emphasis somewhat uneven. Most of the content in the first eight chapters focuses on "pre-algebra" skills. A chapter each is devoted to whole numbers, fractions, decimals, percents, and integers. The second chapter addresses variables and expressions but also covers arithmetic topics such as multiples and factors, and the seventh chapter explains number properties and the distributive property but also includes systems of measurement. Another chapter covers problem solving applications and area /surface area/ volume problems. Overall, I felt that the pacing and depth of this section of the book was appropriate for students preparing for algebra. The final three chapters of the book, however, do not match this pacing and depth. The first of these chapters introduces solving linear equations, moving from solving one-step equations to multi-step equations and equations with fraction or decimal coefficients. Another chapter focuses on polynomial operations, including multiplying binomials and factoring. The last chapter, on graphing, introduces the coordinate plane, graphing with intercepts, and the concept of slope. I would have preferred to see more emphasis placed on graphing (perhaps an explanation of slope-intercept form) and the connection between equations and graphs, and less emphasis on polynomials. Moving so quickly from arithmetic to advanced skills such as mutlitplying binomials seems a rather large leap for students.

The content in this text seems to be very accurate. I have not found any errors in explanations nor in the examples or problem sets.

Explanations of mathematical concepts are consistent with current standards. Examples and problem scenarios are realistic, relevant to adult learners, and reference situations that will be familiar to most students. Word problems could be easily adapted for variety and context.

This is a highly readable math text, appropriate for lower-level readers. Concepts are explained in a clear, straightforward manner. Mathematical vocabulary is introduced and used throughout, but explanations are given in a conversational tone. Diagrams and graphics enhance the explanations and examples. Connections are made to previously covered concepts, as are analogies to non-mathematical situations. The text also does a nice job of making formulas accessible to students by clearly defining variables and breaking down the parts of the formula.

With the exception of the previous comment on the somewhat uneven difficulty level of the text, the presentation of content is consistent throughout. The tone and language is consistent throughout the book, regardless of chapter topic. Chapters follow a standard pattern of introduction/explanation/examples/practice. Each section and chapter feels like a part of a whole rather than disjointed, stand-alone modules.

While the text functions well as a whole, individual sections are complete within themselves and could be used individually and/or rearranged to fit the needs of a particular class. Links are used (in the online version) to reference material covered in other sections of the book; these are infrequent and generally not required for understanding of the topic being explained. Review and summary of precursor skills is included in many sections. Chapters are divided into 5-9 subsections; each subsection is clearly divided into subtopics.

Organization/Structure/Flow rating: 3

Within chapters and sections, the organization aids the reader in accessing the content. The table of contents, internal links and references, and section headings make the book highly navigable. The organization of the text as a whole might feel jumpy to students (moves from whole number skills to basic algebra concepts, then back to decimals/fractions/percents, then to properties of real numbers, then geometry...). This makes sense as a progression from concepts that can be learned and practiced with only whole numbers, to concepts requiring facility with fractions and decimals, etc. but this might not be evident to students. In particular, I might move the geometry chapter so that it "bridges" the arithmetic and algebra sections.

Compared to some other open textbooks, I'm pleased with the interface of this text. Many math texts look cluttered, busy, and, frankly, boring. This text is clean, uses minimal but effective color, and includes simple but effective graphics. There is sufficient white space on the page so that students can break down and focus on individual sections without distraction. The style and layout of headings, text, and graphics are consistent throughout the text. Both the online and print copies of this text are visually inviting to the reader.

I have not found any grammatical errors in this text.

Examples and application problems are appropriate and relevant for adult learners. "Characters" in word problems have names that reflect a variety of ethnic groups, and problem situations will be familiar for most adults (basic banking, making measurements of a room, etc). Though some specific cultural references are made (Sudoku, Girl Scouts, and others) they generally reference widely known things, and are not essential to understanding the problem.

This book is a much-needed resource for adult basic skills. There are not many open resources available and appropriate for this level, so this book will meet a great need.

Reviewed by Jessie Antonellis-John, Part-Time Math Instructor, Southwestern Oregon Community College on 8/21/16

This textbook is a very comprehensive pre-algebra text. It contains all the topics typically covered in pre-algebra - from basic arithmetic to decimals, fractions, and percents – as well as several chapters that go beyond the scope of the average... read more

This textbook is a very comprehensive pre-algebra text. It contains all the topics typically covered in pre-algebra - from basic arithmetic to decimals, fractions, and percents – as well as several chapters that go beyond the scope of the average pre-algebra course. This text introduces early algebra topics such as integers, polynomials, and graphing, as part of an overall approach that develops math literacy as students progress through the chapters. While the order in which topics are presented is non-traditional – for instance, variables, integers and equations are introduced prior to fractions and decimals – the material is customizable for different courses, and with eleven chapters, could potentially be taught across more than one term.

This text has been well vetted. Aside from the occasional typo or missing period, it is very accurate and free of major errors.

The book is relevant to modern life, with story problems in which people make purchases, categorize objects, are concerned about their course grades, and the like. The examples used are likely to be relevant in the future as well, with minor adjustments such as updating prices and statistics.

The tone is conversational and is thus easily accessible to students, even if they struggle with reading or are English language learners. New concepts are introduced one at a time, making a simple task of parsing new vocabulary.

This text is highly internally consistent. The authors have worked deliberately to build a foundation for math learning that is holistic and logical, and the topics and sequence used to create that foundation were developed with obvious care.

Individual sections of the text are brief and easily digestible, and all follow a similar format that makes their parts easy to recognize once students have the hang of it. Although the sequence is logical as is, it would be easy to select and rearrange sections to suit other approaches.

Although the logic of the sequence is such that students learn prerequisite skills before they need to apply them in later sections, what is sometimes lacking is an explanation of why a topic is being introduced at a given point. Often the topic’s relevance isn’t obvious (to students) until a later section. However, this can be managed with instructor input; even though the sequence is unusual, one who has taught such a class previously will understand why certain topics come before others.

Overall, the interface is really nice, in both the online and PDF versions of the text. The images and figures are clear and external resources are linked in-text and thus apply directly to the topic at hand. The PDF and online versions have different benefits; it is easier to navigate in the online version, but the PDF version has distinct pages and looks more like a traditional text.

Aside from unavoidable mechanical errors and typos, the grammar of this text is free of substantial errors.

An effort has been made to include names from a variety of ethnicities for the story problems, and the characters are involved in the kinds of activities that any American might do, such as taking care of their homes, going shopping, and opening a bank account. However, the activities are somewhat gendered; the female characters are more likely to buy skirts, wear jewelry, carry purses, and be on a diet, while the male characters engage in more “neutral” activities. There is also some emphasis on dividing groups by gender (e.g. counting the number of boys and girls in a classroom). Most notably, some of the very earliest real-world examples used in the text involve large price tags, such as $500,000 dollar houses or $75,000 annual incomes, which may be unrealistic or alienating to some students.

Pedagogically, this textbook is very well crafted and is fantastic for developing conceptual understanding and math literacy. The modeling of concepts is excellent, as is the emphasis on recognizing patterns. Students are shown how to extend from the concrete to the abstract, and the authors have structured the sequence so that students experience success right off the bat and can grow their confidence as they proceed through the text. The introduction to solving word problems in Chapter 9, which begins with promoting a positive attitude, is especially nice. The manipulatives that accompany the models used in the text are well worth purchasing for classroom use, or recreating with simple materials (for some models). At the end of the book are self assessments that students can take for each section that allow them to build metacognition of what they know and what they need to work on. All in all, this is a great text for early algebra.

Table of Contents

• 1 Whole Numbers
• 2 The Language of Algebra
• 4 Fractions
• 7 The Properties of Real Numbers
• 8 Solving Linear Equations
• 9 Math Models and Geometry
• 10 Polynomials

Ancillary Material

About the book.

Prealgebra 2e  is designed to meet scope and sequence requirements for a one-semester prealgebra or basic math course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

The second edition contains detailed updates and accuracy revisions to address comments and suggestions from users. Dozens of faculty experts worked through the text, exercises and problems, graphics, and and solutions to identify areas needing improvement. Though the authors made significant changes and enhancements, exercise and problem numbers remain nearly the same in order to ensure a smooth transition for faculty. 

The first edition of Prealgebra by OpenStax is available in web view in the ancillaries.

About the Contributors

Lead Authors, Senior Content Experts

Lynn Marecek , Santa Ana College

MaryAnne Anthony-Smith , Santa Ana College

Contribute to this Page

Prealgebra is a term commonly used to refer to the level of mathematics a student studies before moving on to algebra and/or geometry . Prealgebra is difficult to define precisely other than "the math taken before algebra" because of the broad number of subjects that various prealgebra curriculums use.

A typical prealgebra curriculum more-or-less consists of:

• Arithmetic with the natural numbers and integers .
• An introduction to fractions and decimals .
• An introduction to the basics of number theory ( prime factorization , multiples , least common multiple , greatest common divisor , etc.)
• An introduction to the basics of statistics .
• Exponents , the root operation , and scientific notation .
• Solving linear equations , inequalities , and modeling word problems using variables.
• Ratios , computing simple conversions and rates .
• Percentages .
• An introduction to geometry (computing area, perimeter, angles, etc.).
• the Art of Problem Solving: Prealgebra by David Patrick (Details) .

AoPS Classes

The AoPS classes for prealgebra are a good starting point for those who finished up Beast Academy 's curriculum or have a working understanding of simple arithmetic. Note that AoPS's classes are quite challenging as each class is considerably more in-depth and problem-solving-oriented compared to the equivalent typical school course in prealgebra which focuses more on rote memorization.

• Prealgebra 1
• Prealgebra 2
• Introductory Mathematics Topics

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Liphontcta Art of Problem Solving Prealgebra Textbook and Solutions Manual 2-Book Set Paperback – January 1, 1965

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About the author

Richard rusczyk.

Richard Rusczyk founded Art of Problem Solving (AoPS) in 2003 to create interactive educational opportunities for avid math students. Richard is one of the co-authors of the Art of Problem Solving classic textbooks, author of Art of Problem Solving's Introduction to Algebra, Introduction to Geometry, and Precalculus textbooks, co-author of Art of Problem Solving's Intermediate Algebra and Prealgebra, one of the co-creators of the Mandelbrot Competition, and a past Director of the USA Mathematical Talent Search. He was a participant in National MATHCOUNTS, a three-time participant in the Math Olympiad Summer Program, and a USA Mathematical Olympiad winner (1989). He graduated from Princeton University in 1993, and worked as a bond trader for D.E. Shaw & Company for four years. AoPS marks Richard's return to his vocation: educating motivated students.

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Welcome to Prealgebra , an OpenStax resource. This textbook was written to increase student access to high-quality learning materials, maintaining highest standards of academic rigor at little to no cost.

About OpenStax

OpenStax is a nonprofit based at Rice University, and it’s our mission to improve student access to education. Our first openly licensed college textbook was published in 2012, and our library has since scaled to over 20 books for college and AP ® Courses used by hundreds of thousands of students. Our adaptive learning technology, designed to improve learning outcomes through personalized educational paths, is being piloted in college courses throughout the country. Through our partnerships with philanthropic foundations and our alliance with other educational resource organizations, OpenStax is breaking down the most common barriers to learning and empowering students and instructors to succeed.

About OpenStax Resources

Customization.

Prealgebra is licensed under a Creative Commons Attribution 4.0 International (CC BY) license, which means that you can distribute, remix, and build upon the content, as long as you provide attribution to OpenStax and its content contributors.

Because our books are openly licensed, you are free to use the entire book or pick and choose the sections that are most relevant to the needs of your course. Feel free to remix the content by assigning your students certain chapters and sections in your syllabus, in the order that you prefer. You can even provide a direct link in your syllabus to the sections in the web view of your book.

Instructors also have the option of creating a customized version of their OpenStax book. The custom version can be made available to students in low-cost print or digital form through their campus bookstore. Visit your book page on openstax.org for more information.

All OpenStax textbooks undergo a rigorous review process. However, like any professional-grade textbook, errors sometimes occur. Since our books are web based, we can make updates periodically when deemed pedagogically necessary. If you have a correction to suggest, submit it through the link on your book page on openstax.org. Subject matter experts review all errata suggestions. OpenStax is committed to remaining transparent about all updates, so you will also find a list of past errata changes on your book page on openstax.org.

You can access this textbook for free in web view or PDF through openstax.org.

About Prealgebra

Prealgebra is designed to meet scope and sequence requirements for a one-semester prealgebra course. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

Students who are taking Basic Mathematics and Prealgebra classes in college present a unique set of challenges. Many students in these classes have been unsuccessful in their prior math classes. They may think they know some math, but their core knowledge is full of holes. Furthermore, these students need to learn much more than the course content. They need to learn study skills, time management, and how to deal with math anxiety. Some students lack basic reading and arithmetic skills. The organization of Prealgebra makes it easy to adapt the book to suit a variety of course syllabi.

Coverage and Scope

Prealgebra follows a nontraditional approach in its presentation of content. The beginning, in particular, is presented as a sequence of small steps so that students gain confidence in their ability to succeed in the course. The order of topics was carefully planned to emphasize the logical progression throughout the course and to facilitate a thorough understanding of each concept. As new ideas are presented, they are explicitly related to previous topics.

Each of the four basic operations with whole numbers—addition, subtraction, multiplication, and division—is modeled and explained. As each operation is covered, discussions of algebraic notation and operation signs, translation of algebraic expressions into word phrases, and the use the operation in applications are included.

Mathematical vocabulary as it applies to the whole numbers is presented. The use of variables, which distinguishes algebra from arithmetic, is introduced early in the chapter, and the development of and practice with arithmetic concepts use variables as well as numeric expressions. In addition, the difference between expressions and equations is discussed, word problems are introduced, and the process for solving one-step equations is modeled.

While introducing the basic operations with negative numbers, students continue to practice simplifying, evaluating, and translating algebraic expressions. The Division Property of Equality is introduced and used to solve one-step equations.

Fraction circles and bars are used to help make fractions real and to develop operations on them. Students continue simplifying and evaluating algebraic expressions with fractions, and learn to use the Multiplication Property of Equality to solve equations involving fractions.

Basic operations with decimals are presented, as well as methods for converting fractions to decimals and vice versa. Averages and probability, unit rates and unit prices, and square roots are included to provide opportunities to use and round decimals.

Conversions among percents, fractions, and decimals are explored. Applications of percent include calculating sales tax, commission, and simple interest. Proportions and solving percent equations as proportions are addressed as well.

The properties of real numbers are introduced and applied as a culmination of the work done thus far, and to prepare students for the upcoming chapters on equations, polynomials, and graphing.

A gradual build-up to solving multi-step equations is presented. Problems involve solving equations with constants on both sides, variables on both sides, variables and constants on both sides, and fraction and decimal coefficients.

The chapter begins with opportunities to solve “traditional” number, coin, and mixture problems. Geometry sections cover the properties of triangles, rectangles, trapezoids, circles, irregular figures, the Pythagorean Theorem, and volumes and surface areas of solids. Distance-rate-time problems and formulas are included as well.

Adding and subtracting polynomials is presented as an extension of prior work on combining like terms. Integer exponents are defined and then applied to scientific notation. The chapter concludes with a brief introduction to factoring polynomials.

This chapter is placed last so that all of the algebra with one variable is completed before working with linear equations in two variables. Examples progress from plotting points to graphing lines by making a table of solutions to an equation. Properties of vertical and horizontal lines and intercepts are included. Graphing linear equations at the end of the course gives students a good opportunity to review evaluating expressions and solving equations.

All chapters are broken down into multiple sections, the titles of which can be viewed in the Table of Contents.

Accuracy of Content

We have taken great pains to ensure the validity and accuracy of this text. Each chapter’s manuscript underwent rounds of review and revision by a panel of active instructors. Then, prior to publication, a separate team of experts checked all text, examples, and graphics for mathematical accuracy. A third team of experts was responsible for the accuracy of the Answer Key, dutifully re-working every solution to eradicate any lingering errors. Finally, the editorial team conducted a multi-round post-production review to ensure the integrity of the content in its final form.

Pedagogical Foundation and Features

Learning objectives.

Each chapter is divided into multiple sections (or modules), each of which is organized around a set of learning objectives. The learning objectives are listed explicitly at the beginning of each section and are the focal point of every instructional element.

Narrative text

Narrative text is used to introduce key concepts, terms, and definitions, to provide real-world context, and to provide transitions between topics and examples. An informal voice was used to make the content accessible to students.

Throughout this book, we rely on a few basic conventions to highlight the most important ideas:

• Key terms are boldfaced, typically when first introduced and/or when formally defined.
• Key concepts and definitions are called out in a blue box for easy reference.

Each learning objective is supported by one or more worked examples, which demonstrate the problem-solving approaches that students must master. Typically, we include multiple Examples for each learning objective in order to model different approaches to the same type of problem, or to introduce similar problems of increasing complexity.

All Examples follow a simple two- or three-part format. First, we pose a problem or question. Next, we demonstrate the Solution, spelling out the steps along the way. Finally (for select Examples), we show students how to check the solution. Most examples are written in a two-column format, with explanation on the left and math on the right to mimic the way that instructors “talk through” examples as they write on the board in class.

Prealgebra contains many figures and illustrations. Art throughout the text adheres to a clear, understated style, drawing the eye to the most important information in each figure while minimizing visual distractions.

Supporting Features

Four small but important features serve to support Examples:

Be Prepared! Each section, beginning with Section 1.2, starts with a few “Be Prepared!” exercises so that students can determine if they have mastered the prerequisite skills for the section. Reference is made to specific Examples from previous sections so students who need further review can easily find explanations. Answers to these exercises can be found in the supplemental resources that accompany this title.

A “How To” is a list of steps necessary to solve a certain type of problem. A "How To" typically precedes an Example.

A “Try It” exercise immediately follows an Example, providing the student with an immediate opportunity to solve a similar problem. In the PDF and the Web View version of the text, answers to the Try It exercises are located in the Answer Key.

The “Media” icon appears at the conclusion of each section, just prior to the Section Exercises. This icon marks a list of links to online video tutorials that reinforce the concepts and skills introduced in the section.

Disclaimer: While we have selected tutorials that closely align to our learning objectives, we did not produce these tutorials, nor were they specifically produced or tailored to accompany Prealgebra .

Section Exercises

Each section of every chapter concludes with a well-rounded set of exercises that can be assigned as homework or used selectively for guided practice. Exercise sets are named Practice Makes Perfect to encourage completion of homework assignments.

• Exercises correlate to the learning objectives. This facilitates assignment of personalized study plans based on individual student needs.
• Exercises are carefully sequenced to promote building of skills.
• Values for constants and coefficients were chosen to practice and reinforce arithmetic facts.
• Even and odd-numbered exercises are paired.
• Exercises parallel and extend the text examples and use the same instructions as the examples to help students easily recognize the connection.
• Applications are drawn from many everyday experiences, as well as those traditionally found in college math texts.
• Everyday Math highlights practical situations using the math concepts from that particular section.
• Writing Exercises are included in every Exercise Set to encourage conceptual understanding, critical thinking, and literacy.

Chapter Review Features

The end of each chapter includes a review of the most important takeaways, as well as additional practice problems that students can use to prepare for exams.

• Key Terms provides a formal definition for each bold-faced term in the chapter.
• Key Concepts summarizes the most important ideas introduced in each section, linking back to the relevant Example(s) in case students need to review.
• Chapter Review Exercises includes practice problems that recall the most important concepts from each section.
• Practice Test includes additional problems assessing the most important learning objectives from the chapter.
• Answer Key includes the answers to all Try It exercises and every other exercise from the Section Exercises, Chapter Review Exercises, and Practice Test.

Additional Resources

Student and instructor resources.

We’ve compiled additional resources for both students and instructors, including Getting Started Guides, manipulative mathematics worksheets, Links to Literacy assignments, and an answer key to Be Prepared Exercises. Instructor resources require a verified instructor account, which can be requested on your openstax.org log-in. Take advantage of these resources to supplement your OpenStax book.

Partner Resources

OpenStax Partners are our allies in the mission to make high-quality learning materials affordable and accessible to students and instructors everywhere. Their tools integrate seamlessly with our OpenStax titles at a low cost. To access the partner resources for your text, visit your book page on openstax.org.

About the Authors

Senior contributing authors.

Lynn Marecek and MaryAnne Anthony-Smith have been teaching mathematics at Santa Ana College for many years and have worked together on several projects aimed at improving student learning in developmental math courses. They are the authors of Strategies for Success: Study Skills for the College Math Student, published by Pearson HigherEd.

Lynn Marecek, Santa Ana College Lynn Marecek has focused her career on meeting the needs of developmental math students. At Santa Ana College she has been awarded the Distinguished Faculty Award, Innovation Award, and the Curriculum Development Award four times. She is a Coordinator of Freshman Experience Program, the Department Facilitator for Redesign, and a member of the Student Success and Equity Committee and the Basic Skills Initiative Task Force. Lynn holds a bachelor’s degree from Valparaiso University and master’s degrees from Purdue University and National University.

MaryAnne Anthony-Smith, Santa Ana College MaryAnne has served as department chair, acting dean, chair of the professional development committee, institutional researcher, and faculty coordinator on several state and federally-funded grants and was a member of AMATYC’s Placement and Assessment Committee. She is the community college coordinator of California’s Mathematics Diagnostic Testing Project.

Tony Ayers, Collin College Preston Ridge Campus David Behrman, Somerset Community College Brandie Biddy, Cecil College Bryan Blount, Kentucky Wesleyan College Steven Boettcher, Estrella Mountain Community College Kimberlyn Brooks, Cuyahoga Community College Pamela Burleson, Lone Star College University Park Tamara Carter, Texas A&M University Phil Clark, Scottsdale Community College Christina Cornejo, Erie Community College Denise Cutler, Bay de Noc Community College Richard Darnell, Eastern Wyoming College Robert Diaz, Fullerton College Karen Dillon, Thomas Nelson Community College Valeree Falduto, Palm Beach State Bryan Faulkner, Ferrum College David French, Tidewater Community College Stephanie Gable, Columbus State University Heather Gallacher, Cleveland State University Rachel Gross, Towson University Dianne Hendrickson, Becker College Linda Hunt, Shawnee State University Betty Ivory, Cuyahoga Community College Joanne Kendall, Lone Star College System Kevin Kennedy, Athens Technical College Stephanie Krehl, Mid-South Community College Allyn Leon, Imperial Valley College Gerald LePage, Bristol Community College Laurie Lindstrom, Bay de Noc Community College Jonathan Lopez, Niagara University Yixia Lu, South Suburban College Mikal McDowell, Cedar Valley College Kim McHale, Columbia College of Missouri Allen Miller, Northeast Lakeview College Michelle Moravec, Baylor University TX/McLennan Community College Jennifer Nohai-Seaman, Housatonic Community College Rick Norwood, East Tennessee State University Linda Padilla, Joliet Junior College Kelly Proffitt, Patrick Henry Community College Teresa Richards, Butte-Glenn Community College Christian Roldan-Johnson, College of Lake County Community College Patricia C. Rome, Delgado Community College, City Park Campus Kegan Samuel, Naugatuck Valley Community College Bruny Santiago, Tarrant College Southeast Campus Sutandra Sarkar, Georgia State University Richard Sgarlotti, Bay Mills Community College Chuang Shao, Rose State College Carla VanDeSande, Arizona State University Shannon Vinson, Wake Technical Community College Maryam Vulis, Norwalk Community College Toby Wagner, Chemeketa Community College Libby Watts, Tidewater Community College Becky Wheelock, San Diego City College

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Access for free at https://openstax.org/books/prealgebra/pages/1-introduction

• Authors: Lynn Marecek, MaryAnne Anthony-Smith
• Publisher/website: OpenStax
• Book title: Prealgebra
• Publication date: Sep 25, 2015
• Location: Houston, Texas
• Book URL: https://openstax.org/books/prealgebra/pages/1-introduction
• Section URL: https://openstax.org/books/prealgebra/pages/preface

© Feb 9, 2022 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

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