If you want to square a two-digit number, you could just use a calculator, or you could use the traditional algorithm. I’m going to talk about a different method here, but not because I think this is a particularly useful method. The point of this discussion is to look at how numbers are interrelated; if…
Category: Mathematics
Squaring Two Digit Numbers
Math fun: If you want to square any two digit number more quickly than the traditional algorithm, here’s a strategy. It does require you to know the squares of all the single-digit numbers, as well as a bit of mental juggling. First, if the number ends in a zero, square the first digit and put…
Mathematics and Mnemonics
I’m currently reading “Why Don’t Students Like School?” (second edition) by Daniel T. Willingham. While there is a lot of good stuff in this book and I’m feeling fired out about setting my educational train back on its tracks, I winced at his cheerleading for mnemonics. And then: I reframed. He suggests the use of…
Synthetic Division
Synthetic Division is one of three common techniques for dividing one polynomial by another. The other two are long division and the box method. Of the three methods, students generally prefer synthetic division. It has the advantage of having minimal writing and being strictly algorithmic: Add, multiply, add, multiply…. First, let’s see how it works….
When Am I Ever Going To Use This?
The question is the bane of the math teacher’s existence. It probably comes up in other classes as well, but it seems to be particularly associated with mathematics. Here are two truths (and no lies): From the time I graduated from high school in 1985 to the time I started training to be a math…
Exponents: Language
Our language surrounding exponents is confusing and, I think, misleading. Power An exponential relationship involves three values. Historically, these were called the base, the exponent, and the power. On a logarithmic scale, the base represents the step size, the power represents the target value, and the exponent represents the number of steps. For instance, if…
There Is No Spoon (QF Edition)
As I was nearing the end of my article yesterday, something creeped into my head and lingered in the shadows for a while. This morning, it came into the light. The function that allows us to find the input that corresponds to the output of another function has a name: It’s the inverse function. One…
The Quadratic Formula (Vertex Form)
I really don’t like the quadratic formula. As a teacher, it feels like one of the absolute worst examples of what’s wrong with mathematics education: An arbitrary formula with weird aspects, including what is often the first appearance for students of the plus-minus sign. Sure, we can do algebraic manipulation to show why it is…
Why 0! = 1 (Set Theory Explanation)
I’ve been seeing a few videos lately explaining why 0!=1. Over my time as a teacher, I’ve seen a lot of various explanations for this equality, and they generally fall into these categories: What I don’t recall seeing is a complete explanation from the perspective of set theory, so I’ll provide that in this article….
Rough draft: Thoughts on Sets
I woke up this morning thinking about sets. I recently bought the (Canadian) French, (Mexican) Spanish, and German editions of “Dog Man”. This gave me a set of books in languages I can at least make a real effort to read, and the child already has a set of “Dog Man” books in English. Yesterday…