What Is Anzan? Mental Math with an Imaginary Abacus

You have probably seen the videos: a child watches numbers flash on a screen — 47, 82, 15, 93 — faster than an adult can read them, then says the total. No pen, no calculator, no visible effort. That skill has a name: Anzan (暗算), Japanese for "mental calculation", and it is the reason abacus classes exist.

Anzan is not a memory trick and it is not a gift. It is what happens when a child has moved abacus beads so many times that they can see the abacus in their mind and move the imaginary beads instead.

From beads to pictures

Every abacus learner goes through the same stages:

1. Physical abacus. The child sets numbers and moves beads by hand, learning how to read a rod and then the Small Friend and Big Friend formulas.
2. Fingers in the air. Around this stage children start "playing" the abacus on the table or in the air while looking at a problem. Teachers encourage it — it is the picture forming.
3. Semi-Anzan. The abacus is still on screen, but it moves by itself. The child watches the beads update and keeps the running total in their head — the picture is being handed over.
4. Full Anzan. No abacus at all. Numbers flash on screen one at a time. The child holds the imaginary abacus, moves the imaginary beads, and reports the total.

The remarkable thing is that the method never changes. A child doing full Anzan on 47 + 82 is performing exactly the Big Friend moves they learned on real beads. The beads have simply become invisible.

500

50

5

100Hundreds

10Tens

1Ones

47

Why visualising beads works

Ordinary mental arithmetic asks a child to hold digits in verbal memory — "seven plus five is twelve, carry the one…" — and verbal memory is small and slow. Anzan moves the work to visual-spatial memory, which is much larger and much faster. Instead of remembering words about the number, the child holds a picture of the number.

Two other things make it efficient:

• Every move is local. On an abacus you only ever touch one or two rods at a time, so the mental picture only has to update in one place.
• There are no special cases. After Level 2 there are exactly two ideas — Small Friend and Big Friend — that handle every digit. There is nothing to "look up" mid-calculation.

How long does it take?

Honest answer: months of short, regular practice, not weeks. The bead picture forms from repetition, and there is no shortcut around the repetition. What can be shortened is the boring part — which is why the app generates fresh problems every time and wraps speed work in timers, streaks and games.

A typical path for a child who starts around six: Level 1 in a few weeks, Level 2 formulas over a few months, and the first real Anzan moments — answering without looking at the abacus — somewhere in the first year. From there, speed grows as long as practice continues.

How Abacus Kids trains Anzan

Level 3 of the Learning Path is built around the four stages above, in five modes:

• Guided Series — numbers appear one by one and the child follows along on the abacus (or lets it move automatically).
• Semi-Anzan — the abacus updates by itself while the child calculates the total mentally.
• Full Anzan — numbers flash on screen with no abacus — pure mental calculation.
• Speed Drill — equations one after another for 30, 60 or 90 seconds, a point per correct answer.
• Flash Challenge — rapid-fire numbers in four tiers, from Starter (3 slow single-digit numbers) to Master (10 two-digit numbers at blazing speed).

Before each round you choose how many numbers (3, 5, 7 or 10), one- or two-digit, and the flash speed — Slow, Normal, Fast or Blazing — so the difficulty grows with the child.

For children who want to go further, Custom Challenge Mode lets you set up your own workout: 5 to 20 questions, 1 to 4 digit numbers, flash gaps from 0.5 to 3 seconds, numbers spoken, shown, or both — the closest thing to an abacus competition on a phone.

Is it worth it if they'll have a calculator anyway?

Yes — and not mainly because of speed. A child who can do Anzan has a rock-solid, physical sense of what numbers are: what 10 is made of, why carrying happens, how 47 and 82 fit together. That understanding is what makes fractions, algebra and estimation feel reasonable later. The speed is the visible part. The number sense underneath is the point.