Medium Articles

Medium is a publishing platform where anyone can create an account and write articles for other people to read. You can read 3 articles a month for free. A monthly fee of $5 gets you unlimited reading. A portion of the fee pays the authors you read.

Here are the math related articles I've written for Medium. I've sorted them by subject matter. The pictures don't always match the subject matter as there aren't very many visually interesting pictures related to division or fractions, so I just picked a picture that struck my fancy at the time.

Articles on Basic Ideas

Reuse/Recycle Your MathI’ve found a lot of my math hacks by being lazy. I don’t want to use any more effort than I have to to get an answer. One of the first…

A(B+C) = AB + ACThe basis of many simplifications.

Breakin (Numbers) Up Ain’t Hard to DoDon’t take your ones, away from me

Articles on Adding Subtracting Multiplying and Dividing

Mental Math: AddingHow to add in your head.

Mental Math: SubtractionEasy Ways to Subtract Numbers in Your Head

Subtracting Without BorrowingI suck at borrowing. I always try to do math in my head and borrowing introduces extra numbers that prevent that. (Why is it called…

5 Ways to Subtract Without BorrowingIt’s difficult to subtract using borrowing in your head. Here’s what I do instead.

Mental Math: The Multiplication TableI’m going to be honest here…I suck at memorizing things. I don’t even have the multiplication table memorized. So, what do I do if I need…

Mental Math: Multiplying Larger NumbersIn the last article, Mental Math: Multiplication Table…

Can I Divide by…?I’m always telling my students to simplify, simplify, simplify. However, most people don’t know how to tell when something is evenly…

Mental Math: DivisionI’m going to start out with a short digression. I was searching for a picture to go with this subject and despite searching multiple…

Divide FirstI always encourage my students to work with the simplest numbers possible. Doing so not only reduces the chances for error but often makes…

Taking the “Long” out of Long DivisionI was working with some students, teaching them how to divide any number by 2, when a student asked if the method works with all numbers. I…

Divide Any Number by 2 in Your HeadDividing by 2 is something we do A LOT, thus it’s practical to be able to do it in your head. It’s easy to divide even numbers, such as…

Articles on Averaging

Averaging Using ComparisonsWhen we take averages, we rarely do it in isolation. Whether finding batting averages or averaging data, we usually take more than one…

Finding the Not-So-Mean MeanEveryone knows how to find a mean value: we add up the numbers and divide by the number of numbers. While not difficult, that’s not the…

Simplifying the MeanWhen we say the word “average” we usually are referring to the mean rather than the median or mode. That’s the “add them all up and divide…

Averaging with PacketsI was working on my book the other day (Yes, I’m writing a book with all my math tricks in it. The first volume should be out in about 3…

Articles on Measurements

Subtracting with Multiple Units: Borrowing at the EndWhen working with multiple units, be they inches and feet, pounds and ounces, or fractions and whole numbers, we have an option when…

Cups, Pints, Quarts! Oh My!I’ve always had a problem keeping pints and quarts straight and doing conversions using Imperial units. When I had to teach these…

Simplifying RatiosRatios are handy for scaling things up or down. It’s best when we can see a clear relationship in the numbers, however, sometimes the…

Articles on Fractions

Adding/Subtracting Fractions and Whole Numbers Like Inches and FeetAs I’ve mentioned in the past, I teach a remedial math class for the Army. I finished the unit on measurement and conversions today and…

Subtracting Mixed Numbers.This week’s math hack is a trick to make things simpler when you’re subtracting mixed numbers. First, I always treat the whole part and the…

Simplifying Fractions GraphicallyI teach remedial math for the Army (adult learners). Since most people are visual learners, and fractions are where many of them have…

Using Fractions to Solve Percentage ProblemsThere are three ways to solve percentage problems: 1) treat it like a ratio, 2) the 10% method and 3) substitute in a fraction. Today I’d…

New, Easy Way to Divide Fractions and Mixed NumbersI’m SO excited. (I know you guys will understand — my husband just looked at me.) I did something by accident today, and when I thought…

Dividing Mixed Numbers By Whole Numbers.I like efficiency. Though I like math, I don’t like doing math I don’t need to. That’s why the traditional way of dividing mixed numbers by…

Multiplying Large Mixed Numbers by FractionsThe standard method of multiplying a mixed number by a fraction is to convert the mixed number to an improper fraction, multiply straight…

Fractions: Changing a Subtraction Problem with Borrowing into a Basic Addition ProblemI encourage my students to share the tricks they’ve figured out with me. A couple years back, I had a student who told me that when they…

Invert and Multiply: What’s Happening Physically When We Divide by a FractionMy background is in physics, so I believe that math describes physical processes. When I teach math, I illustrate with physical things so…

Multiplying 2 Mixed NumbersMultiplying a fraction or a whole number times a mixed number is easy: You break the mixed number apart and multiply the fraction or whole…

Articles on More Complex Ideas

Working with Negative SpacesFirst, what do I mean by negative spaces? Negative spaces are places where things aren’t, but yet kinda are. For example, if we look at the…

Expanding the FOIL methodMost of us learned the FOIL method as a way to multiply algebraic expressions. FOIL stands for First, Outer, Inner, and Last, which is how…

Understanding Calculus in 4 MinutesCalculus is the bane of many people. Much of that is the approach taken when teaching it. It’s taught using mathematical theorems and…

Dealing with Math AnxietyMath Anxiety is a problem that many people face, and whether you are looking for a way around it yourself or you’re teaching someone who’s…

Articles on Teaching Math

The Least Efficient Way to Teach MathThe US ranks 30th in the world for math1. I’m not surprised as I teach a remedial math class to people in the Army (soldiers need to pass a…

Are We Teaching Math Wrong?I don’t have to repeat any statistics regarding America’s math scores; we all know they’re bad. I sometimes hang out on Quora and there are…

Why We Should Value That Loud Dumb KidAs a teacher, we all fantasize about teaching the perfect class. We come in ready, with lesson plans and examples. The lecture smoothly…

Teaching Math: Tools VS MethodsI’ve written several articles critical of how math is taught, but saying that something is wrong isn’t helpful unless you also tell what…

Seeing the ForestMath is the study of patterns - let’s teach it that way.

Math: How We Teach It V.S. How We Do ItI came to teaching in an unusual route: I got my Ph.D. in Space Physics before becoming a teacher of remedial math for the army. This means…

Dumb Math Teacher TricksAs a physicist, I’ve had A LOT of math classes. As a math teacher, I try very hard not to do the same dumb tricks that frustrated me as a…

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