Interactive walkthroughs
Each walkthrough states one rule, works it in full, then hands you the abacus and asks you to make the frame read a number. Nothing is timed and nothing is scored — this is the part that comes before the drills.
A soroban rod holds one heaven bead worth five and four earth beads worth one each, so a single rod can only ever show 0 to 9. The two complement walkthroughs exist because of that limit: the number you want to add is bigger than the beads you have free to move. When that happens you do not count your way out — you make a bigger move and correct it in the same breath.
Small friends is that trade inside one rod. When you cannot add three earth beads, you take the whole five and give two back, because 3 and 2 make 5. Big friends is the same trade across two rods. When even the five is not enough, you take ten from the rod on the left and give the difference back on the right, because 3 and 7 make 10.
That is why the order is not a preference. Big friends nests small friends inside itself: adding 7 to 6 means carrying a ten and then taking 3 off a 6, and taking 3 off a 6 is a small-friend move. A learner still thinking about the first rule cannot see the second one happening. Work the small friends walkthrough until the trade feels automatic, then come back for the big ones — and only then the three above them, which all use complements as the small change of a larger move: mental abacus runs them with the frame taken away, while multiplication and division keep the arithmetic unchanged and add one question each, namely which rod a digit belongs on.
Kani Math teaches on a nine-level program ladder. Level is a placement, never an age: a seven-year-old and an adult beginner start on the same rung. Five rungs are links, and each goes to the walkthrough for the technique that rung is about — small friends at Elementary A, big friends at Elementary B, mental abacus at Intermediate B, multiplication at Higher A, and division where Higher B runs into Grand Level.
The remaining four rungs have no walkthrough yet. They are listed anyway, because the shape of the program is the honest answer to "where does this go" — and five lessons out of nine is a very different picture from five lessons out of five.
Foundation · 19 chapters · 43 steps
Every number from 0 to 99, built from six moves. Where the earth beads run out, why four plus one means moving five beads, and what really happens at nine — then the beads are yours against a target.
Start counting to 99Elementary A · 9 chapters · 22 steps
The trade inside a single rod. Why the rule exists, the two pairs that make five, one worked addition, two worked subtractions — and then four steps where the beads are yours to move against a target.
Start the small friends walkthroughElementary B · 9 chapters · 26 steps
The trade across two rods: the carry, the borrow, and the combined move where a big friend and a small friend fire on the same problem. Same shape — read, watch, then move the beads yourself.
Start the big friends walkthroughIntermediate B · 9 chapters · 24 steps
The instrument removed in three stages: full frame, then the digit row switched off, then nothing at all. The same complements, run on a picture — and the mental steps are graded too, because the checkpoint in the middle of a sum is what proves the route.
Start the mental abacus walkthroughHigher A · 9 chapters · 22 steps
One rule: multiply the digit on rod i by the digit on rod j and the answer lands on rod i + j. Four pictures of the rule, three worked problems ending with the one that spills onto a rod already in use, then six graded steps where you place the partial products yourself.
Start the multiplication walkthroughHigher B into Grand Level · 9 chapters · 26 steps
Dividend on the right, divisor on the left, and each digit of the answer written two rods left of the digit it came from. Worked once exactly and once with the placement correction the method really demands — including the one frame on the site that is wrong on purpose.
Start the division walkthroughSeveral other places on this site cover the same ground, and each does a different job from a walkthrough. Pick the one that matches what you actually want right now.