# Open Resources for Community College Algebra

Portland Community College Faculty

Copyright Year: 2018

Publisher: Portland Community College

Language: English

## Conditions of Use

Attribution

CC BY

## Reviews

This text covers all areas and ideas that make up the scope of a developmental college algebra curriculum. It also provides basic skills review in the appendices and opens with fundamental knowledge so that readers are aware of the background... read more

This text covers all areas and ideas that make up the scope of a developmental college algebra curriculum. It also provides basic skills review in the appendices and opens with fundamental knowledge so that readers are aware of the background knowledge needed to successfully use this resource. There were a few topics I was surprised not to see, such as polynomial and synthetic division and systems of inequalities, but these are not necessarily crucial to every college algebra course. The index (which also serves as the glossary) is clear and easily accessible from any section. The index is extremely effective because of its interactive features that allow you to expand an information box to get a brief summary, definition, etc. or to view the material in its original context/section.

I have found no content errors or inaccuracies in this book. In both the theoretical principles discussed and the concrete problems presented, I felt that everything was accurate and appropriate for the related content. Accurate content is, in my opinion, a large part of the foundation of a solid and dependable text, and this book has a strong foundation.

Overall, this text is relevant to current audiences and is sustainable for years to come. The mathematics in each section will stand the test of time moving forward. Technology is incorporated throughout this text both in demonstrating mathematical applications in technology and teaching readers how to use technology as a tool to solve mathematical problems. The authors go beyond referencing just a standard calculator, but instead integrate online graphing tools, interactive images and examples, and specific connections between math and technology. As we live in a technology dependent and advancing world, it was refreshing to see a text that embraced and reflected that world. The only content updates I would foresee would be for contextual and real-world application examples/problems. While some of these problems involve data that is still pertinent (within the last 5-10 years), this data will need to be updated to maintain relevance to future students. I am in agreement with other reviewers that as modern technology continues to develop, more relevant application problems will need to be added to support students’ investment in an algebra course and mathematics in general. The text itself reads much easier than traditional mathematics textbooks, and the language used demonstrates the authors’ intentional choice of words and arrangements to make this text not only accessible, but also appealing, to 21st century learners.

This text is clear, focused, and accessible to students with varying confidence levels in mathematics. As mentioned in the Relevance/Longevity section, this text reads much easier than traditional math texts and that is largely due to the authors’ intentional language choices that communicate the material extremely clearly. The authors were able to strike a productive middle ground between being overly technical and not technical enough. As vocabulary is crucial to understanding any mathematics branch, especially in algebra, the authors’ vocabulary features throughout the text are a major contribution to the overall clarity. Whenever key terms are used, whether it be from the last section or 10 sections ago, readers can click on the highlighted term to open an information box containing a brief reminder definition or pertinent facts for the technical term being used. All of the information boxes I viewed provided enough detailed information to be an effective reminder, and if readers need further explanation, a simple click of a button in the box will bring them back to the term’s original context pages. Also, any worked out examples are easy to follow and incorporate different colors, bolding, or italics for emphasis to enhance clarity. The clarity of this text is heightened by the resources and features in each section that allow for students of varying learning styles/preferences to access the material in a suitable way and reinforce the material in multiple ways. For example, the alternate videos in most sections benefit students who prefer to learn by auditory means, while the worked out solutions and interactive checkpoints cater to more visual and kinesthetic learners. Any graphs or images in this text are also very clear and supported by context – they have a clear purpose for being included where they are. My only suggestion would be to include a vocabulary list at the beginning or end of each section to further reinforce the technical terminology.

The consistency of this text is extremely strong. The three separate parts/books that make up the entire text are formatted in the exact same clear way. Whether you use just one part or all three, you will not find any deviations in the framework. This is a positive especially for students who may use this text over the course of multiple semesters. The consistency of this text is heightened by features within the framework. For example, each section consists of a brief introduction paragraph of what was recently covered and where students are headed in the section, an alternative video when applicable, definitions and examples using the same headings and formats each time, regular checkpoint exercises, and closing independent exercises. There are no surprises when you “turn the virtual page”. Another feature of this text that bolsters its consistency is the interactive elements of key words, facts, and examples. Throughout the text, these key words, facts, and examples are clickable so that when a student clicks on one, a relevant definition, reminder note, or other reference expands from previous pages without having to leave the current page (and if they need more information than this reminder provides, they can easily click to go back to the original section). This is clear evidence that the terminology in this text is consistent through all three parts.

The text is clearly broken down into three separate main parts and is appropriately further divided into chapters and sections within those chapters. Each of these sections consists of multiple subsections that each focus on a very specific skill or piece of content, making the text more reader-friendly and easily allowing instructors to omit or rearrange subsections to fit their course curriculum. There are no overwhelming amounts of text or content in any section. The text is designed to avoid large blocks of text in any given subsection by using definitions, a mix of static and active examples, checkpoint problems, and authors’ warnings or remarks throughout as to not overwhelm readers with too much content at one time.

The topics in this text are very much presented in a clear and logical manner that still allows for flexibility. The structure is straightforward and easy to follow. The authors took an interleaving approach to the text which is evident in how the topics build off of each other and are consistently revisited. This strongly supports student learning and mathematical thinking because it encourages them to continually think about topics and how they connect rather than just checking off a box when they have reached a satisfactory level. The National Council of Teachers of Mathematics (NCTM) explains some effective practices to be those that “use and connect mathematical representations” and this interleaving approach encourages those connections. Also, many of the sections don’t start by just listing definitions or facts like many traditional texts do. Instead, most sections begin by offering a real-world problem or scenario related to the coming content for students to consider or by explaining a concept in general terms before diving into the mathematical jargon. Structuring the text this way encourages students to actually conceptualize and deeply understand the material rather than just memorizing terms and formulas. Another effective practice from NCTM is to “build procedural fluency from conceptual understanding,” and I think beginning the sections in this way when applicable is fostering exactly that. My only neutral comment is that I found Chapter 8 (Quantities in the Physical World) to be a little out of place in the overall flow of the chapters, but the organizational flexibility of the text makes this trivial.

For the most part, the text is free of significant issues, distortions, or distractions. The interactive HTML version is user friendly and its interactive nature made the HTML version more beneficial to me as a reader in comparison to the PDF or hard copy versions. The calculator, which also comes with extensive graphing tools and other features, is easily accessible by clicking the calculator button and it is not a distraction when it is not needed as the reader has the option to have it on screen or not. My only issues with the interface of this text are that I could not find a search function to aid in navigation, and the answers to the odd-numbered exercises were difficult to locate. In the front matter, the authors noted that the answers to the odd-numbered exercises were located in an appendix. However, on the side menu, under Appendices, only Appendices A, B, and C are listed, none of which are the answers to the exercises. Now if you click on the general Appendices header in the menu, the corresponding page lists Appendices A, B, C, and D with D containing the answers to the exercises. For students who wish to check their answers, navigating to this page may cause some confusion. Further, when I got to the answers page, it appeared that the majority of the odd-numbered answers are not listed. Only a few exercises in the occasional section have an answer attached, which could be frustrating to students trying to check their work.

No grammatical errors found.

This resource does not appear to have any content, wording/phrases, or examples that are culturally insensitive or offensive. Any cultural references are found in word problems throughout the text, and it is clear that the authors thoughtfully designed these problems for students from a variety of backgrounds. While I believe that there is always room to increase diversity and cultural responsiveness, I think this book does a good job of making the material accessible and relevant to several cultures.

Overall, this resource is high quality and both instructor and student friendly. It is clear that the authors kept their audience in mind by making it interactive and relevant to today’s students and by providing a curricular foundation for instructors that still leaves room for flexibility. As someone who works in a university math support center, I believe that this is the kind of resource that many of our students need.

This book is excellent with regards to comprehensiveness. As part of the "ORCCA" series, this book is divided into 3 parts: Part 1 (chapters 1, 2, 3, 4), Part 2 (chapters 5, 6, 7, 8, 9) and Part 3 (chapters 10, 11, 12, 13). Every chapter... read more

This book is excellent with regards to comprehensiveness. As part of the "ORCCA" series, this book is divided into 3 parts: Part 1 (chapters 1, 2, 3, 4), Part 2 (chapters 5, 6, 7, 8, 9) and Part 3 (chapters 10, 11, 12, 13). Every chapter provides multiple sub-sections and within each section are several example problems clearly showing how to solve the different types of problems, in detail, showing all the steps. Within each section are also "checkpoints" where the students can try example problems on their own and if they make a mistake they are shown all the steps needed to solve it and arrive at the correct answer, so they know where they went wrong. The Exercises (practice problems) at the end of each section cover a variety of different questions that allow for a thorough understanding of all the topics presented within that section. *At the end of Part 3, after Chapter 13, there are also Appendices titled, "Basic Math Review," "Unit Conversions," and "Course Content and Outcome Guides for MTH 60, 65, and 95."

I have been teaching mathematics for 15 years and this is the most accurate textbook I have every used. I don't recall finding any errors in any of the problems from ANY of the books: Part 1, Part 2, or Part 3. The sections that include graphs and charts are clear and easy for students to understand (no errors in presentation). The myriad of word problems through this book series demonstrate how students can apply what math they're learning to real-world concepts and applications. These word problems are entirely unbiased and free of any inappropriate content.

Content in this book is up-to-date and very clearly presented in a way that makes it easy for students of various backgrounds and skill levels to comprehend. Part 1 (chapters 1, 2, 3, 4) is what I used to teach MTH 60, Part 2 (chapters 5, 6, 7, 8, 9) is what I used to teach MTH 65, and Part 3 (chapters 10, 11, 12, 13) is what I used to teach MTH 95 and the content within the chapters is arranged in the most straightforward way for teaching. In many of the other textbooks I've used throughout my career as a Mathematics educator I've chosen to teach the material in a different order than how it was presented in the book, but when I used this particular textbook series, I didn't feel the need to change a single thing! *See "Organization" part of this Review for a complete layout of how the topics are arranged.*

This textbook is exceptional with regards to clarity. All of the example problems within the sub-sections of each chapter show step-by-step solutions with all of the new vocabulary terms shown in bold print with clear definitions and explanations as to how they are incorporated within the problems. The wording throughout the book flows smoothly and is easy to read. Italicized wording is used to show emphasis associated with a specific rule or to show the importance of remembering the sequence of steps when calculating the solutions. All graphs, charts, and diagrams not only show a comprehensive way for students to analyze data, but they also provide an additional way of finding solutions for students who are "visual learners" and find it challenging to follow along with logistical problem-solving methods.

Part 1, Part 2, and Part 3 of this textbook provide consistency with regards to wording, explanations, visual representations, and the layout of all numerical problems and concepts. Once you read through chapter 1, you know what to expect for all subsequent chapters - the formatting doesn't change at all throughout the book. Consistency is important in order for students to feel comfortable with learning new topics. It has been my experience as an educator that if students know what to expect as they journey through a math textbook (in other words, there are no "surprises") then it helps ease their anxiety related to the subject material.

In order to explain how excellent the modularity is within this textbook, I'll use one chapter as an example. Chapter 10 title: "Factoring" Sec. 10.1 - Factoring out the Common Factor 10.1.1 - Motivation for Factoring 10.1.2 - Identifying the Greatest Common Factor 10.1.3 - Factoring out the Greatest Common Factor 10.1.4 - Visualizing with Rectangles 10.1.5 - More Examples of Factoring out the Common Factor 10.1.6 - Reading Questions 10.1.7 - Exercises Sec. 10.2 - Factoring by Grouping (includes sub-sections similar to Sec. 10.1) Sec. 10.3 - Factoring Trinomials with Leading Coefficient = 1 (includes sub-sections similar to Sec. 10.1) Sec. 10.4 - Factoring Trinomials with Leading Coefficient not equal to 1 (includes sub-sections similar to Sec. 10.1) Sec. 10.5 - Factoring Special Polynomials (includes sub-sections similar to Sec. 10.1) Sec. 10.6 - Factoring Strategies (includes sub-sections similar to Sec. 10.1) Sec. 10.7 - Solving Quadratic Equations by Factoring (includes sub-sections similar to Sec. 10.1) Sec. 10.8 - Factoring Chapter Review (includes sub-sections similar to Sec. 10.1)

All topics throughout this textbook are presented in a clear, logical fashion, and are arranged as the following: Chapter 1 "Linear Equations and Lines" (topics include evaluating expressions, combining like terms, solving equations, modeling with equations, and algebraic properties) Chapter 2 "Linear Equations and Inequalities" (topics include isolating linear variables, solving inequalities, and special solution sets) Chapter 3 "Graphing Lines" (topics include cartesian coordinates, finding Slope, graphing 3 forms of a line, and parallel vs perpendicular lines) Chapter 4 "Systems of Linear Equations" (topics include substitution, elimination, and graphing) Chapter 5 "Exponents and Polynomials" (topics include adding, subtracting, multiplying and dividing polynomials, along with exponent rules for both positive and negative exponents) Chapter 6 "Radical Expressions and Equations" (topics include square root properties, solving radical equations, and rationalizing denominators of fractions) Chapter 7 "Solving Quadratic Equations" (topics include solving by using square roots, completing the square, and using the Quadratic Formula . . . "Factoring" is introduced later in chapter 10) Chapter 8 "Quantities in the Physical World" (topics include scientific notation, unit conversions, and a variety of geometry applications) Chapter 9 "Topics in Graphing" (topics include graphing quadratic equations and key features of parabolas) Chapter 10 "Factoring" (topics include factoring by GCF, grouping, trinomials, and perfect squares) Chapter 11 "Functions" (topics include function basics, interval notation, and domain and range) Chapter 12 "Rational Functions and Equations" (topics include complex fractions, solving rational equations, and the addition, subtraction, multiplication and division of rational expressions) Chapter 13 "Graphs and Equations" (topics include vertex form vs standard form for quadratic equations, solving absolute value equations, and compound inequalities)

This textbook, in its entirety, is free of any interface issues, navigation problems, distortion of images, and any other features that could possibly cause confusion to the reader. The wording is presented in a font that is big enough to read clearly but not so big that it seems unusual or distracting. Same is true for the size and clarity of all graphs, charts, diagrams and other images throughout. Any new concept or terminology is introduced in a way that shows its connection to previous topics presented in earlier chapters (when applicable) as well as the material in the current chapter.

This text contains no grammatical errors that I am aware of.

The wording of the explanations throughout this textbook along with the wording within the word/story problems for each section do not contain anything that may be interpreted as culturally insensitive or offensive. It is not one-sided or biased with regards to race, ethnicities, or backgrounds. This book was clearly designed by professionals who are passionate about the subject of mathematics, and it does not deviate from the material being taught within each section/chapter.

Using this textbook will help make your job as a mathematics instructor easier and less stressful with regards to lesson planning and how to implement the material within your class. It will also make learning these math concepts easier and less stressful for the students and help them to realize that math can be FUN !

This textbook is a comprehensive collection of beginning through intermediate algebra topics often covered in community college developmental courses. There is an excellent index and glossary of terms for locating material. There are a few... read more

This textbook is a comprehensive collection of beginning through intermediate algebra topics often covered in community college developmental courses. There is an excellent index and glossary of terms for locating material. There are a few topics included that I would consider to be "extra" such as rationalizing the denominator and absolute value inequalities.

Having read through the majority of the text, I did not find any errors or content that was inaccurate. I am very pleased with this aspect of the text, considering that other OERs I have read are not always up to the standard hoped for.

The language of the explanatory text is easy to read and written with a modern voice. There are not a lot of data or applied context problems/examples, but those that are given are well done and up to date with data from up to 2015/16. This will need to kept up to date, but as the data is localized, that should not be difficult. I would like to see more applied problems and examples throughout the text, as the relevance of mathematics to the modern student is an important aspect in the motivation for study.

The written language of the text is well done, using proper mathematical language without being overly technical. The writers did a good job of keeping their audience in mind. There are also instructional videos imbedded in the online textbook. These are clear and of a decent quality, however I found them to be slightly boring and not overly creative.

The text is internally consistent and includes links that refer back to definitions and concepts. I love the feature in the online book where a term can be clicked on, and without taking the reader back to the original context, a reminder of the meaning displays.

The textbook is divided into sections that make sense, and has a flow that is easily followed. I also appreciated that each chapter includes a summary review at the end, so that if I don't want to cover the entire section in a course, I could use the review to remind students of pre-requisite knowledge. The content is such that moving sections or omitting them would not be a problem. Each section of the online text does include the Portland Community College (home institution of the authors) course objectives. While these might not apply to my institution's objectives, it helps make clear what are the intended outcomes for each section.

The book flows well and has good organization. There may not be a lot of creativity or freshness to the approach, but it is a clear and thorough text which could be supplemented well.

The text is ADA compliant and works well on both computer and mobile devices. My only complaint is that I found the left-hand menu to be a little difficult to deal with when scrolling around. The menu sometimes jumps and I could not figure out how to collapse the menu once it was expanded.

I found no grammatical errors.

The book was in no way culturally insensitive and there was evidence of some effort to use a variety of names from different cultural contexts. Again, there are not a large amount of applied context questions, which addition of could increase the cultural relevance of the textbook.

Overall I this this a great product and very well done. The authors should be proud of their work and I look forward to thinking about how to use these materials in my developmental algebra courses.

## Table of Contents

- Chapter 1: Variables, Expressions, and Equations
- Chapter 2: Linear Equations and Inequalities
- Chapter 3: Graphing Lines
- Chapter 4: Systems of Linear Equations
- Chapter 5: Exponents and Polynomials
- Chapter 6: Radical Expressions and Equations
- Chapter 7: Solving Quadratic Equations
- Chapter 8: Quantities in the Physical World
- Chapter 9: Topics in Graphing
- Chapter 10: Factoring
- Chapter 11: Functions
- Chapter 12: Rational Functions and Equations
- Chapter 13: Graphs and Equations
- Appendix A: Basic Math Review

## Ancillary Material

## About the Book

Open Resources for Community College Algebra (ORCCA) is an open-source, openly-licensed textbook package (eBook, print, and online homework) for basic and intermediate algebra. At Portland Community College, Part 1 is used in MTH 60, Part 2 is used in MTH 65, and Part 3 is used in MTH 95.

## About the Contributors

### Author

**Portland Community College Faculty**

**Project Leads**: Ann Cary, Alex Jordan, Ross Kouzes**Technology Engineer**: Alex Jordan**Contributing Authors**: Ann Cary, Alex Jordan, Ross Kouzes, Scot Leavitt, Cara Lee, Carl Yao, and Ralf

Youtz**WeBWorK Problem Coding**: Chris Hughes, Alex Jordan, Carl Yao**Other Contributors**: Kara Colley