Sometimes the simplest advice is the best. That’s often the case with math.
The single best math tip I ever received came in high school freshman algebra. The teacher compared an algebraic equation to one of those balance scales with an equal number of apples in the tray on each side.
The “equal” sign must always be obeyed — the equation always must be a true statement. The left side always must equal the right. In solving the equation, look to the scale. If you add an apple to one side, you must also add one to the other. Subtract from one side, subtract the same from the other. The scale must always balance.
How does this work in practice? Consider the simple equation: X + 10 = 20
To solve, subtract 10 from both sides so that the X sits alone on the left — the scale stays balanced and you get: X = 10.
Now for an actual formula: D = V x T, where D is distance, V is velocity and T is time.
Here’s a simple problem: How long would it take you to drive 100 miles at 10 miles per hour?
D (100 miles) = V (10 miles/hour) x T
Divide both sides by 10 so that the T stands alone on the right — the scale stays balanced and you get 10 = T.
All right, I know, that’s as basic as it gets, but the scale/balance analogy helped me a lot in my algebra studies. And a great many water and wastewater math problems involve algebra.
Now, here are some more advanced resources that can help you hone your industry-specific math skills.
Algebra I for Dummies. I know, you’re not a dummy, but the “For Dummies” book series does explain topics in ways designed to be especially easy to understand. This book, while not specific to water and wastewater, gives you simple, plain-English guidance that can improve your skill in solving those vexing exam problems. It includes practical examples in line with the methods math teachers use today.
Math for Wastewater Operators. This free training video from the U.S. EPA isn’t just for exam preparation. It provides an overview of basic wastewater math concepts and you can use the various formulas to optimize plant operations and reporting. Concepts include pump math, area and volume conversions, velocity and flow calculations, and much more. It’s not just a cursory overview — it runs to about 90 minutes. You could view it in half-hour intervals. Visit epa.gov/compliance/math-wastewater-operators.
Wastewater Treatment Math Study Guide. This free publication from the Kentucky Division of Compliance offers two sets of 20 multiple choice math problems (Class I and II and Class III and IV), along with answer keys, and at the end, for each problem an explanation of how to solve it. It’s a great resource for exam practice. You can easily search it up online.
American Water College. This organization provides high-quality training, including math, to water and wastewater pros. The college offers a YouTube channel with free math-related instructional videos: youtube.com/@americanwatercollege/featuredvideos.
Wastewater Treatment Facility Operator’s Math. This comprehensive guide from the Minnesota Pollution Control Agency starts with a review of basic math concepts and adds a Solving Math Problems Checklist. It also includes an Essential Math Refresher section followed by almost 90 pages of how-to’s on industry-specific calculations. Visit https://www.pca.state.mn.us/sites/default/files/wq-wwtp8-02.pdf.
Wastewater Guru. This vendor offers a series of Wastewater Operator Practice Exams covering different levels of licensing. Each guide includes 500 practice questions, plus 21 bonus math questions. The questions aligned with the latest need-to-know requirements. The company says the guides prepare users not just for exams but for real-world treatment operations. Visit wastewater.guru.
I hope you find these resources helpful. If you have a favorite item of math advice to share with TPO readers, send it to me at editor@tpomag.com, and I will mention it in a future column.
