# Introduction

This developmental-level mathematics textbook is intended for career-technical students. It was made possible by grants from Open Oregon Educational Resources, which supports the development and implementation of high-quality materials at low or no cost to community college and university students.

# Changes from the first edition

I won’t list every detail, but here are the broad strokes.

• Added Modules 31, 32, 33, 34.
• Revised real-world data and examples from 2019 that felt outdated.
• Deleted or revised complicated explanations and examples.
• Redrew some low-resolution geometry figures.
• Cleaned up the formatting and made the online text easier to navigate.

# To the student

This textbook is designed to bring a bit of fun to what can often be a boring or intimidating subject. Many of the examples are taken from everyday life rather than the trades, which helps make the material accessible to students in any field.

There are very few step-by-step examples, because—let’s face it—does anyone ever read those? The general structure is a brief introduction of a topic followed by some practice exercises, a brief introduction of the next topic followed by more practice exercises, etc. Therefore, this book is not designed for self-study unless you already have some experience with the material and are simply looking for a refresher.

I have tried to indicate when a calculator would be appropriate, but your instructor has the final say on that. My personal philosophy is that a calculator is a useful tool, but the user needs to know enough to be able to estimate and judge whether a result is reasonable. I don’t mention calculators until we get to formulas in Module 7 because I want students to be able to work with fractions, decimals, negatives, exponents, and all that stuff without a calculator if necessary.

In most careers, nobody is going to say you cheated if you use technology such as a calculator or spreadsheet; the important thing is that you use the available technology to get the correct answer. However, you’re in school trying to obtain a degree or certificate, which means that you need to demonstrate certain knowledge and skills. Therefore, you need to show that you can (1) do the calculations without technology if necessary, and (2) determine whether an answer given by technology is reasonable or not.

One final thought about learning in general. After going through a particular topic, let’s say fractions, you may feel that you understand everything, but there is a big difference between recognizing something when it’s shown to you and actually doing it yourself. Think about learning to drive a car; your driving class has a lot of reading and videos and lectures to familiarize you with what you need to know, but it’s impossible to learn to drive a car without actually driving the car yourself. Reading about it and watching other people do it is not enough; it is crucial that you actually practice the techniques yourself to be sure that you have mastered them. (And then you need to continue practicing the techniques to maintain that mastery, but that’s another speech for another time.) Two ways to know that you’ve really and truly learned something are to either perform it yourself with no guidance or explain it to someone else. If you can follow someone else’s explanation of how to add fractions, you’re partway there. If you can explain how to add fractions to someone else, though? Now you’re in business!

I wish you the best of luck, and I hope you enjoy pictures of cats!

# To the instructor

To paraphrase the key points from above:

Many of the examples are taken from everyday life rather than specific trades. At my school, students in this course come from many different CTE programs—welding, machining, automotive, landscaping, horticulture, renewable energy—but not other programs such as nursing, electrical, or wastewater. I also have a few students in other non-CTE programs who don’t need a course in the math of CNC machining. You should of course feel free to supplement the textbook with topics you’d like to emphasize… Or heck, this is an OER with a CC-BY-NC-SA 4.0 license; you can copy, revise, and remix it however you like! The only restrictions are that you must credit the author where you use his work and you may not charge money for your product, excluding a reasonable printing cost for a print edition. If you have a Pressbooks account, you can clone the book and then start revising as needed.

There are very few step-by-step worked out examples in the textbook. I believe that they add clutter without adding value. I provide my students with a playlist of YouTube videos that I ask them to watch before class, because watching and listening to someone work a problem—with the ability to pause, rewind, replay—is generally more effective than reading a static example printed on the page. Rather than reading examples that I’ve typed out step by step, students can actively try the exercises for themselves, with guidance from you.

If you use MyOpenMath for homework assignments, I have good news! I have written and/or collected over 600 questions and organized them into assignments for each module. You can copy course #181716 and use it as you please.

I shared my personal philosophy on calculators above, but you’re the expert on your situation and what your students need. Similarly, you (or your department) will decide how students will be assessed in your course. Will students be allowed to use the textbook or their notes during exams? Will you provide formulas and other reference information? Will a calculator be allowed for some or all of each exam? Will you be giving exams or assigning some kind of mastery worksheets instead? This paragraph is getting beyond the scope of a textbook introduction, but I would ask that you think about what it’s important for your students to know how to do, with and without technology, and how they can best demonstrate that knowledge.

# To everyone

Whether you are a student or instructor, I would love to hear your thoughts on the book and whether it works well for you. Feel free to let me know about any errors you find or suggestions for improvements. In fact, the trigonometry modules were written at the request of—and in collaboration with—instructors who reached out to let me know what they needed. I had intended to include a module on arc length but ran out of time, energy, and ideas.

Special thanks go out to Bob Brown at Kishwaukee College, who provided many of the diagrams and exercises in Modules 31 & 32.

Extra special thanks go out to my Math 50 students at CCC who have given me first-hand evidence of what worked well in the first edition and what did not. 😅

Morgan Chase
Clackamas Community College
Oregon City, Oregon

morganc[at]clackamas.edu
morganchase64[at]gmail.com

March, 2024