Maths

Maths has a particular way of going wrong for people. You are shown a rule, you practise it on twenty near-identical questions, and it works — until a question is phrased slightly differently and the whole thing collapses. What was missing was never effort. It was the structure underneath the rule: what the pieces are, how they relate, and why the steps happen in that order rather than some other order.

That structure is what this subject is built around. Every concept here starts as an interactive playground rather than an explanation. You get a handful of labelled pieces on a canvas — numbers, families, steps, units — and your job is to connect them the way they actually relate. Get it wrong and you find out immediately, and working out why the connection does not fit is where the understanding forms. The written explanation, a real-world example, and a short quiz come afterwards, once you have something to hang them on.

Because of that, the topics chosen here are the structural ones rather than drills. Sorting a number into the family it belongs to, seeing why a digit changes value when it moves, working out why one operation has to happen before another, converting between a fraction and a percentage and a decimal — these are all ideas with a shape you can see. Arithmetic practice is easy to find elsewhere; understanding what you are practising is the harder gap to fill.

Three categories are live. Numbers and Arithmetic is where anyone should start, whatever their age or background: number families, place value, the order of operations, how numbers divide into and multiply out of each other, and the single most useful skill in everyday maths — recognising that one amount can be written as a fraction, a decimal or a percentage, and moving between them at will. Algebra makes the jump to letters, which is where most people lose the thread, by explaining what a letter actually stands for before asking you to solve anything. Measurement is the most immediately practical of the three, and the one whose mistakes cost the most in real life. Each of these is a domain rather than a topic: they will keep gaining tracks as the subject grows. Nothing here assumes a maths background, and nothing here needs a calculator.