Kani Math
Cosmic Abacus
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Three-digit mental math practice

The abacus goes away and the image stays. Three-digit columns worked entirely on a soroban the learner can only see.

  • 5 rows × 3 digits, add & subtract
  • About 10 min
  • Free, no account

Sample problems

Real problems from this drill, with answers. Nothing to install, no account, no email — work them on paper, on a physical abacus, or in your head.

  1. 1
    726
    + 403
    + 457
    + 923
    + 693
    ?
  2. 2
    413
    + 572
    + 749
    − 955
    + 778
    ?
  3. 3
    481
    + 693
    + 315
    + 386
    + 621
    ?
  4. 4
    777
    − 328
    + 903
    + 377
    − 665
    ?
  5. 5
    978
    − 859
    + 607
    − 337
    + 717
    ?
  6. 6
    611
    + 687
    − 673
    + 811
    + 899
    ?
  7. 7
    891
    + 391
    − 858
    + 978
    + 914
    ?
  8. 8
    600
    + 621
    + 895
    − 190
    + 548
    ?
  9. 9
    609
    − 428
    + 324
    − 269
    + 169
    ?
  10. 10
    593
    + 197
    + 426
    + 715
    − 215
    ?
Full answer key
  1. 726 + 403 + 457 + 923 + 693 = 3202
  2. 413 + 572 + 749 − 955 + 778 = 1557
  3. 481 + 693 + 315 + 386 + 621 = 2496
  4. 777 − 328 + 903 + 377 − 665 = 1064
  5. 978 − 859 + 607 − 337 + 717 = 1106
  6. 611 + 687 − 673 + 811 + 899 = 2335
  7. 891 + 391 − 858 + 978 + 914 = 2316
  8. 600 + 621 + 895 − 190 + 548 = 2474
  9. 609 − 428 + 324 − 269 + 169 = 405
  10. 593 + 197 + 426 + 715 − 215 = 1716

This page is one drill. The app is the whole programme.

Kani Math is a full mental-arithmetic course, not a single exercise. Free to start, no signup, and it runs on the web, Android and iPhone.

It also delivers the numbers for you — flashed on screen or read aloud, with the speed, digit count and number of rows under your control. That is the one thing a printed page cannot do.

  • ✓Nine levels, from the first bead to division
  • ✓Guided lessons that teach the technique, not just drills
  • ✓Flash, listening and abacus drills at a speed you set
  • ✓Versus matches against friends or the computer
  • ✓Say your answers out loud — the app listens and marks them
  • ✓Streaks, coins and badges, with parent and teacher views

Want to stay here? The demo further down runs right on this page.

Launch App →Try the demo ↓

Practise it now

The same drill, live in your browser, with a virtual soroban and instant marking.

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Loads a full interactive drill right here on the page. It never asks who you are.

No signup. Nothing saved unless you ask.

Explore the free virtual abacus →How to use an abacus →Mental Math Drill →

About this drill

This is the transition the whole method exists for. Up to now the beads did the remembering; from here the learner holds the bead image in working memory and moves it there. Three digits is the standard width to start — wide enough that written arithmetic would be slower, narrow enough that the mental image stays stable across five rows.

Expect accuracy to drop sharply when the physical abacus is withdrawn, and expect it to come back within a few weeks. That dip is the point of the exercise, not a sign of going too fast. The drill below presents each row briefly so there is no time to fall back on written methods.

How to practise it

  1. 1Put the physical abacus out of reach — not just out of use.
  2. 2Picture the rods left to right, and keep the image in one fixed place.
  3. 3Move the imagined beads; do not add the numbers arithmetically.
  4. 4Answer out loud before writing anything down.
Where this sits

Level 6 — Intermediate B

3-digit operations and the start of mental visualization.

Teaches: 3-digit operations, transition to mental abacus visualization (Anzan)

Find your level with the free placement exam →

Questions

What is anzan?
The Japanese term for calculating on a mentally visualized abacus. It is not a memory trick or a set of shortcuts — it is the same bead procedure, run on an image instead of an object.
Why did my child get slower?
Because the beads are gone. The image has to be built and held, which costs working memory at first and almost none after a few weeks of daily practice.
Should we go back to the physical abacus?
Only for new techniques. Going back for practice the child can already do mentally re-establishes the dependency this level is designed to remove.
Is three digits the ceiling?
No, it is the starting width. Competitive anzan runs to six or seven digits, but width should only grow once accuracy at the current width is near perfect.
Learn the techniqueMental abacus (anzan)Walk through it on the beads →