Articles
Guides and resources about math education.
Distance = Rate x Time: The Formula That Moves the World
One equation, three questions, and a triangle that rearranges itself. Why the average of two speeds is usually wrong, how a fuel gauge runs this formula backwards with worse data than you have, and the two-subtraction method that solves any catch-up problem.
Converting Units: When to Divide, When to Multiply
There is no divide button and no multiply button in unit conversion. A conversion factor is just a fraction equal to 1, and the question dissolves once you write it facing the right way. Plus the three word traps that make a correct method produce a wrong answer.
Congruent vs Similar: The Same Shape or Just in Proportion
Same shape is a trap word. Congruent means every single length and angle matches with zero tolerance; similar means only the proportions match. How to tell them apart without measuring everything, why almost nothing in the real world is exactly congruent, and what engineers mean when they allow a fraction of a millimetre.
Quadrilaterals and Polygons: The Angle Family
Why a quadrilateral can never have four blunt corners: the corner budget of (n-2) x 180, why exactly three right angles is impossible but four gives you a rectangle, and how every new side buys exactly two more obtuse angles.
Triangles: The Strongest Shape and Its Angle Secrets
Why a paper square sags but a paper triangle cannot move: the three-point lock, the three name buckets, the folding proof of base angles, the outside-turn rule worth 40 plus 50, and the longest-side gate that stops a triangle from existing at all.
Tessellations and Tiling: Shapes That Fit Perfectly
A floor is a math proof you walk on. Why triangles, squares, and hexagons fill a surface with no gaps while the humble pentagon always leaves a hole — and how the 360 degree gatekeeper decides which shapes can tile at all.