Articles
Guides and resources about math education.
Standard Deviation and Variance: Measuring the Spread
The average tells you where the data is centered; the spread tells you how wide it wobbles. Meet the recipe behind variance and standard deviation — why we square the distances, what n minus 1 is doing, and how one number becomes a ruler for spotting unusual results.
Expected Value: The Number That Predicts Luck
Expected value is how you price luck: weight every outcome by its chance, add the results, and you get a forecast no gut feeling can match. Learn the formula, why it is not the same as an average, and how casinos, insurance, and everyday “should I?” decisions quietly lean on it.
Counting: The Multiplication Principle and Combinations
Count options without listing them. Meet the multiplication principle (multiply the choices), the order matters vs. order doesn't decision, and the combination formula that divides out the repeats — the counting shortcuts the probability guides lean on.
Probability Rules: And, Or, and Why Odds Change
Two rules run almost every probability question: AND multiplies, OR adds. Meet the formulas, see why a deck that 'remembers' makes odds change, and learn the independent-vs-mutually-exclusive trap that separates good answers from guesswork.
Probability Trees: Mapping Every Possible Outcome
A probability tree turns a messy 'what could happen?' into a tidy map of every possible outcome. Learn the two drawing rules — branches at a fork add to 1, multiply along a path — and how the tree itself does the probability work for you.
Quadratics and Parabolas: The Letter U of Algebra
A parabola is the letter U of algebra: the curved graph that appears in every thrown ball and fountain. Meet the smile-and-frown rule that 'a' controls, the vertex turning point, the mirror line, and the three places a parabola can land relative to the floor.