50 lecciones gratuitas, desde infantil hasta trigonometría
Aprende matemáticas a tu manera
Lecciones de matemáticas gratuitas y en lenguaje sencillo para niños, adolescentes y adultos — ahora con el arco completo desde contar hasta trigonometría. Cada lección tiene preguntas de práctica calificadas que revisan tus respuestas y diagramas interactivos.
Explorar por grado
Primeros años (K–2)
- Sumar y restar
- Valor posicional
- De contar a multiplicar
- Tablas y división
- Fracciones y decimales
- Perímetro y área
- Factores y primos
- Negativos y PEMDAS
- Variables y ecuaciones
- Razones y porcentajes
- Ángulos, triángulos y círculos
- Estadística básica
- Gráficas, sistemas y cuadráticas
- Polinomios y factorización
- Pitágoras y trigonometría
- Probabilidad y conteo
- Cálculo mental en ambos sentidos
- Estimación y problemas
- Binario, flotantes y modular
Aritmética — en ambas direcciones
Addition — carry right
The classic column method: ones first, carry to the left.
Addition — biggest first
Left-to-right addition: hundreds, then tens, then ones.
Subtraction — borrow right
The standard borrowing method, step by step.
Subtraction — left to right
Count down by chunks, or biggest column first.
Multiplication — standard way
Right-to-left multiplying with carrying.
Multiplication — biggest first
Partial products left to right — the mental-math way.
Division
Long division, short division, and chunking.
Álgebra
Variables & expressions
Letters that hold numbers — evaluate and translate.
One-step equations
Undo one thing: the balance rule that starts algebra.
Two-step equations
Undo in reverse order — with step-by-step checking.
Inequalities
<, >, ≤, ≥ — and the one rule that flips the sign.
Exponents & powers
Repeated multiplication, the three rules, x⁰ and x⁻ⁿ.
Square roots
Perfect squares, estimating, and simplifying √12.
Polynomials
Terms, degrees, like terms, and distributing.
Factoring
GCF, x²+bx+c, and difference of squares.
Graphing lines
y = mx + b — slope and intercept on the plane.
Systems of equations
Substitution, elimination, and where lines meet.
Quadratic equations
Parabolas, zero-product, and the formula that always works.
Geometría
Angles & lines
Acute to straight, complements, parallel lines.
Triangles
The 180° rule, families, and why bridges trust them.
Quadrilaterals
The four-sided family tree and the 360° rule.
Circles
Radius, diameter, π — C = πd and A = πr².
Perimeter & area
Around vs inside — with unit-square grids.
Surface area & volume
Wrapping vs filling — boxes, cylinders, unit³.
The coordinate plane
(x, y) addresses, quadrants, distance.
Transformations
Slide, flip, spin, scale on the grid.
Pythagorean theorem
a² + b² = c², triples, and the distance formula.
Similarity & congruence
Same shape, different size — scale factors.
Números y estructura
Place value & bases
Why 467 means 400 + 60 + 7 — and how binary works.
Fractions
What numerator & denominator mean, adding, comparing.
Decimals & percents
Place value past the point; everyday percent tricks.
Negative numbers
The number line, and why neg×neg = pos.
Order of operations
PEMDAS honestly — including the ambiguous case.
Factors & primes
Divisibility tricks and prime factorization.
Razones, datos y azar
Ratios & proportions
Comparing quantities and cross-multiplying.
Unit rates & percents
Per hour, per dollar — and the better-deal test.
Statistics basics
Mean, median, mode, range — and when the mean lies.
Spread & deviation
Variance and standard deviation as 'typical distance.'
Probability basics
0 to 1 — favorable/total, complements, AND/OR rules.
Counting principles
Permutations, combinations, factorials.
Trigonometría
sin, cos, tan
SOH-CAH-TOA on right triangles — sides and angles.
The unit circle
(cos, sin) as a point — and the free identity.
Habilidades de razonamiento
Estimation & rounding
Front-end estimating and Fermi problems.
Word problems
Pólya's four-step method for attacking any problem.
Data, averages & graphs
Mean vs median — and how charts can politely lie.
Matemáticas en ciencia y computación
Scientific notation & SI
Writing the universe's biggest and smallest numbers.
Measurement & error
Accuracy vs precision, significant figures, honest numbers.
Math inside computers
Binary, bits, floating point — and 0.1 + 0.2 ≠ 0.3.
Binary & hexadecimal
How computers count — $FF and 0x10 explained.
Floating point
Why 0.1 + 0.2 ≠ 0.3 — and the integer-cents trick.
Modular arithmetic
Clock math — MOD, parity tests, wrap-around indexing.
Dos direcciones, la misma respuesta
La mayoría de los libros solo enseñan el método de derecha a izquierda. Pero los calculistas mentales expertos suelen trabajar al revés: primero el mayor valor posicional. Ninguno es mejor; son la misma aritmética vista desde extremos distintos.
¿Por qué dos métodos?
La investigación muestra que las estrategias de izquierda a derecha inventadas por los niños son comunes y mejoran la comprensión del valor posicional. →
📚 Investigación y lecturas — artículos y libros reales, con enlaces.