Mental abacus: the soroban method with the soroban taken away
Mental abacus — anzan in Japanese — is not ordinary mental arithmetic with a memory trick bolted on. It is the same soroban method run on a picture of the frame: the same complements, the same rods, the same order of moves, with nothing under your hands. This walkthrough removes the instrument in three stages — frame and digits, frame alone, then nothing at all — and grades you at each one. Nine chapters, twenty-four steps, nothing timed.
What this page asks of you
Every chapter is a frame with an explanation beside it, and the last third hands the beads over. Two things about the stage are worth knowing first. The reading under the frame always names the value, even on steps where the digit row is switched off — so those steps are a self-check rather than a test: read the beads by their shape, then look down and see whether you were right. And on the mental steps the frame really is empty, so the reading says zero while the equation line beside it counts. That gap between the two is the lesson, not a fault.
Mental abacus is what Intermediate B is about, the sixth rung of the nine-level ladder: three-digit work, and the frame beginning to move into the head. Small friends and big friends are prerequisites rather than alternatives — every mental route on this page is one of those two rules with the beads taken away.
What is the mental abacus (anzan)?
There is no new arithmetic here. Picture the frame, move the beads in the picture in the same order your hands would move them — highest place first, complement before carry — and read the shape at the end. What makes that work is that a soroban number is a picture rather than a string of digits: a rod holding six is one bead above the bar and one below it, and a shape is easier to hold through a chain of additions than a word is.
The instrument does not go away for good. Mental abacus is built on the physical frame and stays anchored to it — the frame comes back at the end of this walkthrough, and calculators who work entirely in their heads still practise on beads. What is being trained is the picture, and the picture only holds steady once the real thing is automatic.
Move the beads yourself
Loading abacus…
The frame is showing 7.
The whole lesson, written out
Act I — taking the instrument away
Beads, with a digit underneath. Seven on the ones rod: heaven bead down, two earth beads up, and the digit row underneath confirming it. This is where a learner stands at the end of Elementary B — the beads do the arithmetic and the digits check it.
Digits off. The shape has to say it. The same seven, with the digit row switched off. Nothing about the beads changed; the reading of them is now yours to do. One bead above the bar and two below is 5 + 2, and that is what the shape of seven looks like.
And now the frame is empty. One sweep and there is nothing on it. Everything after this happens on the frame you just watched, held in mind — which is why clearing is a real move on a soroban rather than a reset. Mental abacus is that picture, with the beads still moving on it.
Twelve. One earth bead up on the left rod, two earth beads up on the right, no heaven bead anywhere: 10 + 2. Reading a rod by its shape instead of a printed digit is the one skill this technique cannot be done without, so it comes before any arithmetic. The line under the frame tells you whether you read it right.
Forty-six. Four earth beads and no heaven bead on the tens rod is 40. Heaven bead down with one earth bead up on the ones rod is 5 + 1. You are reading two different shapes at once, which is exactly what a two-digit number asks of you once the digits are gone.
Eighty. Heaven bead down and three earth beads up on the tens rod — 50 + 30 — and an empty ones rod. An empty rod is a zero and has to be read as deliberately as any other digit: a rod you do not notice is a place value you have dropped.
Act II — one kind of sum, at three removals
Seven, and you are asked for eight more. No rod can show 15, so this is a big friend: the partner of 8 is 2, and the move is take two here, add ten on the left. Nothing about the arithmetic is new — the point of this chapter is what the move feels like while everything is still in front of you. 7 + 8 = ?
Take the two. Two raised earth beads drop and the ones rod reads 5, heaven bead still down. Both beads were already on the side they needed to be, so this half is a plain subtraction inside the rod. 7 − 2 = 5
Add the ten. One earth bead rises on the tens rod and the frame reads 15. Hold onto the shape it makes — one bead on the left rod, one bead above the bar on the right. That shape is the thing you will be picturing shortly. 5 + 10 = 15
Thirty-four, with nothing to read it for you. Three earth beads on the tens rod, four on the ones rod. The complement is the same one as the last chapter on purpose: the arithmetic is not the new thing here, the missing digit row is. Partner of 8 is 2, so take two here and add ten there. 34 + 8 = ?
Take the two. Two of the four raised earth beads drop and the ones rod reads 2. Say the whole number to yourself off the shape — three beads left, two beads right, thirty-two — before you look at the line underneath. 34 − 2 = 32
Add the ten. One free earth bead rises on the tens rod. Three were already up, so there was exactly one left to move, and the frame reads 42. The reading underneath is your check, not your source. 32 + 10 = 42
Clear the frame, and leave it cleared. From here the beads do not move. The frame in front of you is empty and stays empty, so the reading underneath will say zero the whole way through while the line above it counts. That contradiction is not a bug — it is the entire technique, stated by the page itself. 26 + 47 = ?
Set twenty-six in the picture. Two earth beads on the tens rod; on the ones rod, heaven bead down with one earth bead up. Build that shape in your head and hold it. Do not hold the words twenty-six — hold the beads, because every move you are about to make is a move on beads. 26
Highest place first: add the forty. Adding 4 to the tens rod would want four free earth beads and only two are free, so it is a small friend: add five, take one back. In tens that is plus fifty, minus ten. The picture passes through 76 and settles on 66 — heaven bead down and one earth bead up on each rod. The order is not optional: a soroban is driven from the highest place, so the picture has to be driven the same way. 26 + 50 − 10 = 66
Then the seven, with one rule inside another. Adding 7 to a rod holding 6 would need 13, so it is a big friend: take three, add ten. But taking three from six wants three raised earth beads and only one is raised, so the taking is itself a small friend: take five, give back two. Heaven bead up to 61, two earth beads up to 63, one earth bead on the tens rod for the carry, 73. Three complements in a row, on a frame with nothing on it. 66 − 5 + 2 + 10 = 73
Now look. The beads are back, showing 73: heaven bead and two earth beads on the tens rod, three earth beads on the ones rod. This is a check and not a demonstration — you already had the answer. Seeing it as a shape is what ties the picture in your head back to the instrument it came from. 26 + 47 = 73
Act III — your turn, at all three
Take the big friend of eight. The ones rod reads 7 and the beads are live. Drop two earth beads so it reads 5, and stop there. Doing both halves at once would prove nothing about which route you took, which is why the carry is a step of its own. 7 − 2 = 5
Now the carry. The frame reads 5. Raise one earth bead on the tens rod so it reads 15. The place labels are switched on for this step: the bead you want is on the second rod from the right. 5 + 10 = 15, so 7 + 8 = 15
The same move, without the digit row. The frame reads 34 and the digits are off. Drop two earth beads on the ones rod so the frame reads 32. Read the shape and decide before you look down — the line under the frame will confirm it either way, so nobody gets stuck here. 34 − 2 = 32
And the carry, still by shape. Raise one earth bead on the tens rod so the frame reads 42. Three beads were already up there, so there is exactly one left that can move — a thing you can see without reading a single digit. 32 + 10 = 42, so 34 + 8 = 42
Run the tens work in the picture, then set the result. The frame opens cleared, so there is nothing here to push around. Add 26 and 40 in the picture first — plus fifty, minus ten — and only then set what you got. The checkpoint is 66, the running total halfway through, and it is deliberately not the answer: if you solve the whole sum in one go and set 73, this step says no. Run the route, then confirm it here. 26 + 40 = 66
Now finish it with your hands. The frame hands you 66 on real beads. Add seven: heaven bead up on the ones rod, two earth beads back up, then one earth bead on the tens rod for the carry, and it reads 73. The same three moves you just made in your head, made with your fingers, so the picture and the instrument stay tied to each other. 66 + 7 = 73, so 26 + 47 = 73
Five rods, no target. Wider than either complement sandbox, because this technique is drilled on chains rather than single sums. Set a number, add another, add another, and let the frame carry the running total. Then run the same chain with your hands still and the frame only in your head, and see how far you get before the picture slips. That distance is the thing the technique grows.
Where to go from here
Same subject, four different jobs. This page was the walkthrough; these are the others, and none of them replaces it.