Math by topic

Each topic is a ladder. It starts with something you can play with and climbs, one step at a time, to the math taught at the end of high school. Start at the bottom, or jump in at any step that looks right.

Step	What it feels like
Play	Puzzles and things to notice. No formulas needed.
Explore	Putting what you noticed into words and numbers.
Build	The first real tools: rules, formulas, and why they work.
Master	Using the tools on harder problems.
Beyond	Where the topic leads: proofs and the math after high school.

For parents and teachers: Play suits most children from about 6, Explore from about 9, Build from about 12, Master from about 14, and Beyond from about 16. These are rough guides; curious readers ignore them.

Topics

Topic	From	To
Numbers	Counting, huge numbers and old ways to write them	Complex numbers
Patterns and sequences	What comes next?	Series, the golden ratio and proof by induction
Geometry	Shapes, tangrams and symmetry	Geometric proof and vectors
Measurement	Measuring with your body	Scale, units and accuracy
Number theory	Odd, even and rectangle numbers	Fermat's little theorem and secret codes
Counting and combinations	How many ways?	The binomial theorem and proofs by counting
Probability	Fair or unfair?	Expected value: what is a game worth?
Statistics and data	Counting, sorting and charts	Reading data honestly
Algebra	Mystery numbers and balance scales	Exponentials and logarithms
Ratio and rates	Recipes, sharing and "for every"	Growth and decay
Logic and puzzles	Riddles, clues and Sudoku	How a proof works
Change and motion	Fast and slow	Areas under curves, and the big link
Infinity and strange math	Does it ever end?	Cantor's diagonal argument and bigger infinities