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I'm going to introduce you to my favorite math puzzle. It's a doozy, and I hope you'll find it as intriguing as I do. And maybe a bit more intuitive than I did when I first encountered it.
What is the sum of the first n positive integers? Phrased mathematically: 1 + 2 + 3 … + n -1 + n = ?. The answer, it turns out, is n * (n + 1) / 2. How do we show this is true though? How do we prove this?
I always tell my students not to be afraid to ask why. In so many parts of our lives, we are asked to defend our opinions and ideas—to offer evidence and to explain our thinking or reasoning. But sometimes, it feels this is missing from math education, especially in middle school and high school. Math becomes about memorizing formulas rather than ...
How to prove the Pythagorean Theorem
The Pythagorean Theorem plays an essential role in many facets of math from Euclidean Geometry to complex numbers to trigonometry. Today we’ll explore one of its many proofs.
We’ve all been there: on a homework set or in an exam, you turn to the final page and, to your dismay, it’s a wall of text. The dreaded Word Problem. Some of the words are useful, but some of them are meant to distract. Let’s look at a strategy for answering initial value word problems.
In the year 1202, Italian mathematician Leonardo Fibonacci published the extremely influential Liber Abaci (Book of Calculations). The book's most significant contribution was to bring to Europe the Hindu-Arabic number system that we all use today. But it also contained a curious thought experiment about the reproductive patterns of rabbits, which ...
Probability is one of those topics that haunt children from grade school days, asked to determine the likelihood of picking out red marbles from a box. Even my most advanced math tutoring students sometimes feel bamboozled by it. Why? Because probability and statistics can quickly become overwhelming with the many different distributions and ...
Standardized Test Math Mechanic: SAT geometry prep
I thought that it would be fun to tackle a geometry problem on today's post. I know what you're thinking, fun and geometry – can these two words even go in the same sentence? But yes, geometry can be fun; let's see as we work together through the details of a particular problem.