- Middle school📐Geometry🔺
Triangle area: half of the surrounding rectangle
Base × height ÷ 2: the formula comes from a rectangle cut in half. The visual proof that makes the formula obvious.
- Middle school📐Geometry🔺
A triangle's angles always sum to 180°
Why 180°? Cut the angles out with scissors — they form a straight line. Proof in 3 animated steps.
- Middle school⚡Mental math🎯
Squaring a number ending in 5, without a calculator
Multiply the left part by itself + 1, stick 25 at the end. Done.
- Middle school📐Geometry🔭
Thales' theorem: when triangles zoom
Two lines from the same point, cut by parallels. The lengths stay proportional. The key to measuring without measuring.
- Middle school📐Geometry📐
Pythagoras' theorem, without formulas: the 3-squares proof
A right triangle, three squares drawn on its sides. The visual trick that makes the formula obvious.
- Middle school🔢Arithmetic🧮
Powers of 2 to memorize (up to 1024)
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024… A short list that unlocks tons of mental math — and all of computing.
- Middle school📐Geometry🖼️
Perimeter or area? Never confuse the two
Perimeter is a length (m, cm). Area is a surface (m², cm²). A simple rule to never mix them up.
- Middle school⚡Mental math%
Percent ↔ decimal: shift the decimal point 2 places
20% = 0.20. 3.5% = 0.035. The 2-second rule that unlocks everything else (proportionality, discounts, tax).
- Middle school⚡Mental math🎩
Multiply two numbers near 100 in 5 seconds
96 × 97 = ? Two differences, one multiplication, one concatenation. The mental magician's trick.
- Middle school⚡Mental math✋
Multiply by 5: halve it, then multiply by 10
Multiplying by 5 is a classic trap: go through the half, then add a zero. Twice as fast.
- Middle school⚡Mental math💯
Multiply by 25: divide by 4, add two zeros
An ultra-efficient variant of the ×5 trick. Works for ×50, ×250 and ×2500 too.
- Middle school⚡Mental math⚡
Multiply any 2-digit number by 11 in 3 seconds
A classic but mind-blowing trick: add the two digits, slide them in the middle, done.
