The Singapore approach to primary maths: fewer topics a year, each one taken further before the next one starts.
A number splits into two parts, and the two parts make it again. Addition and subtraction are then the same picture read two ways, rather than two things to memorise separately.
8 + 5 becomes 10 + 3. Moving to the nearest ten first is the habit that makes mental arithmetic quick later, and it is practised long before it is needed.
Every idea is met with objects, then drawn as a bar or a bond, and only then written as numbers. The drawing is what carries a child through word problems.
A ten is traded for ten ones and a hundred for ten tens — the same value, counted differently. Naming it as an exchange is why regrouping across a zero stays sensible instead of becoming a rule about crossing out digits.
Adding 99 by adding 100 and giving one back comes before adding it in columns. A child who can already do it in their head knows what the written method should produce, so a wrong answer looks wrong.
Multiplication starts as equal groups and arrays, and division as sharing and grouping — both meanings, before any fact is memorised. The tables of 2, 5 and 10 then land on an idea that is already there.