Math for Everyone — 50 free lessons, kindergarten to trigonometry

Learn Math, Your Way

Free, plain-language math lessons for kids, teens, and adults — now covering the full arc from counting to trigonometry. Every lesson has graded practice questions that check your answers and interactive diagrams you can read at a glance. There is no single "right" way to work a problem — we teach both directions of arithmetic so you can learn the method that matches how your brain works.

Browse by grade

Early years (K–2)

Adding & taking away
Place value
Counting to multiplying

Upper primary (3–5)

Times tables & division
Fractions & decimals
Perimeter & area
Factors & primes

Middle years (6–8)

Negative numbers & PEMDAS
Variables & equations
Ratios & percents
Angles, triangles & circles
Statistics basics

High school (9–12)

Graphs, systems & quadratics
Polynomials & factoring
Pythagoras & trigonometry
Probability & counting

Teens & adults

Mental math both directions
Estimation & word problems
Binary, floats & modular math

Arithmetic — both directions

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, explained step by step. Subtraction — left to right Count down by chunks, or work the 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.

Algebra

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. (Interactive graph!) Systems of equations Substitution, elimination, and where lines meet. Quadratic equations Parabolas, zero-product, and the formula that always works.

Geometry

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. (Diagrams!) 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. (Interactive!) 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.

Numbers & structure

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, adding/subtracting, why neg×neg = pos. Order of operations PEMDAS honestly — including the famous ambiguous case. Factors & primes Divisibility tricks, prime factorization — and why primes protect every password you type.

Ratios, data & chance

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.

Trigonometry

sin, cos, tan SOH-CAH-TOA on right triangles — sides and angles. The unit circle (cos, sin) as a point — and the free identity. (Interactive!)

Thinking skills

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.

Math in science & computing

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.

Logic & computation

Lambda calculus The language with one rule — three kinds of expression that compute anything. Lambda syntax Variables, abstraction, application — and reading λ-terms without drowning. Beta reduction The single rule of computation, step by step. (Interactive reducer!) Church numerals Numbers conjured from functions — "three" means "do it three times." Booleans & pairs True and false as chooser functions — logic and data from nothing. Recursion & Y Loops without loops — fixed points and the Y combinator.

Two directions, same answer

Most schoolbooks only show the right-to-left method — start with the ones column and carry to the left. But skilled mental calculators around the world often work the other way: biggest place value first. Neither is better; they are the same arithmetic seen from different ends. Our articles teach each convention on its own page, and every page links to its mirror so you can compare.

Why two methods? Research on how children actually calculate shows that invented left-to-right strategies are common and often lead to better place-value understanding. See further reading & research for the papers behind this approach.

📚 Research & further reading — real papers and books, with links.

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