# Prealgebra

Multiple Authors, Openstax College

Pub Date: 2015

ISBN 13: 978-1-9381689-9-4

Publisher: OpenStax

## Conditions of Use

Attribution

CC BY

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 … read more

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.

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.

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

Fine

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.

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. … 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.

Prealgebra is comprehensive and includes a table of contents, tables and formulas, and an index. Does not include a glossary but has vocabulary … 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.

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.

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. … 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.

While this Prealgebra text does cover most of the traditional topics, (Whole Numbers, Integers, Rational numbers, Decimals, Percents, Solving Linear … 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.

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.

This text covers a range of topics typical of a prealgebra-level text, focusing primarily on arithmetic skills, equations, and graphing. I found the … 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.

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.

This textbook is a very comprehensive pre-algebra text. It contains all the topics typically covered in pre-algebra - from basic arithmetic to … 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.

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 … 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.

## Table of Contents

## About the Book

*Prealgebra* is a textbook for a one-semester course that serves as a bridge between arithmetic and algebra. It can be used in courses named “Basic Mathematics,” “Introductory Algebra,” “Fundamentals of Algebra,” and so on. The organization makes it easy to adapt the book to suit a variety of course syllabi.

The philosophy of this book is to strengthen students’ arithmetic skills and introduce the fundamental concepts and vocabulary of algebra in a nurturing, non-threatening environment while addressing the needs of students with diverse backgrounds and learning styles. *Prealgebra* addresses a variety of unique challenges by guiding math students as they learn study skills and time management, while helping them overcome math anxiety. All procedures and strategies as results of complete explanations and examples. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. Deliberate attention is paid to ensure all students are fully prepared to progress toward higher mathematics. The result is a supportive, memorable learning experience that students can carry with them as a foundation for further learning and careers.

OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.

## About the Contributors

### Author(s)

**Lead Authors, Senior Content Experts**

Lynn Marecek, Santa Ana College

MaryAnne Anthony-Smith, Santa Ana College