The soroban (算盤) is Japan's refined version of the Chinese suanpan abacus, developed during the 16th century and perfected over the following two hundred years. Unlike digital calculators, the soroban demands active participation from the human brain — each operation is a physical gesture, and repeated practice forges strong mental arithmetic pathways that remain long after the instrument is set aside.
Research conducted at universities in Japan and Taiwan has consistently found that children trained on the soroban develop superior working memory, spatial reasoning, and concentration. Soroban practitioners often reach a stage called anzan (暗算) — mental abacus — where they visualize a soroban in their mind and manipulate imaginary beads at remarkable speed.
Core philosophy
The soroban is not a shortcut — it is a physical encoding of thought. Every bead movement maps directly to an arithmetic rule. Teach the rules by teaching the movements, and the two will reinforce each other for life.
Why teach soroban at Prime Montessori Academy?
The Montessori method prizes concrete, hands-on learning before abstract notation. The soroban is an ideal Montessori material: it makes the abstract concept of place value visible and tangible. Every digit a student sets is a physical movement they can feel and see, grounding their understanding in genuine comprehension rather than rote procedure.
Chapter two
Anatomy of the soroban — 13 rods explained
The standard soroban used in Japanese schools and competitions has 13 rods. This allows it to display numbers from 0 up to 9,999,999,999,999 (just under ten trillion). Each rod holds one decimal digit.
How many rods?
The standard modern soroban has 13 rods (1 heaven bead + 4 earth beads per rod = 5 beads per rod × 13 = 65 beads total). The rightmost rod is always the units column — exactly as numbers are written on paper, with ones on the right.
The 13-rod soroban — cleared (all zeros). Rightmost rod = units.
Fig. 1 — A fully cleared soroban. Small dots on the beam mark the units, thousands, millions, billions and trillions columns — just like commas in written numbers. All rod labels shown below, digit values above (all zero).
Inactive bead — resting away from beam, not counted Active bead — touching the beam, counted
The 13 rods and their place values
Rods are numbered right to left, matching how we read place value in written numbers.
Position
Place name
Place value
Max contribution
Rightmost (rod 1)
Units
× 1
9
Rod 2
Tens
× 10
90
Rod 3
Hundreds
× 100
900
Rod 4
Thousands (1K) ●
× 1,000
9,000
Rod 5
Ten-thousands (10K)
× 10,000
90,000
Rod 6
Hundred-thousands (100K)
× 100,000
900,000
Rod 7
Millions (1M) ●
× 1,000,000
9,000,000
Rod 8
Ten-millions (10M)
× 10,000,000
90,000,000
Rod 9
Hundred-millions (100M)
× 100,000,000
900,000,000
Rod 10
Billions (1B) ●
× 1,000,000,000
9,000,000,000
Rod 11
Ten-billions (10B)
× 10,000,000,000
90,000,000,000
Rod 12
Hundred-billions (100B)
× 100,000,000,000
900,000,000,000
Leftmost (rod 13)
Trillions (1T) ●
× 1,000,000,000,000
9,000,000,000,000
● = column marked by a dot on the beam
Key components
The frame (枠)
The outer rectangular border, traditionally lacquered hardwood, holds all rods under tension.
The beam (梁)
A horizontal bar dividing each rod into two zones. A bead is counted only when it is touching the beam.
Heaven bead — 上珠 (kami dama)
One bead per rod, living above the beam. Push it down to the beam → active, worth 5. Push it back up → inactive, worth 0.
Earth beads — 下珠 (tama)
Four beads per rod, living below the beam. Each bead pushed up to touch the beam → active, worth 1. Range: 0 to 4 earth beads active per rod.
Unit dot markers
Small inset dots on the beam mark every 3rd rod from the right — units, thousands, millions, billions, trillions — serving as visual commas in large numbers.
Chapter three
Reading bead values — digits 0 to 9
Every rod shows exactly one digit (0–9). Reading it is a single formula:
Digit value = (heaven beads active × 5) + (earth beads active × 1)
Study each digit below. Red beads are active (touching the beam). Gold beads are resting away from the beam and contribute nothing.
Digit 0 — heaven bead inactive | no earth beads active | total = 0
All 13 rods showing digit 0. Calculation: 0 + 0 = 0. The rightmost rod is units; this is how 0 appears on any rod.
Digit 1 — heaven bead inactive | 1 earth bead active (= 1) | total = 1
All 13 rods showing digit 1. Calculation: 0 + 1 = 1. The rightmost rod is units; this is how 1 appears on any rod.
Digit 2 — heaven bead inactive | 2 earth beads active (= 2) | total = 2
All 13 rods showing digit 2. Calculation: 0 + 2 = 2. The rightmost rod is units; this is how 2 appears on any rod.
Digit 3 — heaven bead inactive | 3 earth beads active (= 3) | total = 3
All 13 rods showing digit 3. Calculation: 0 + 3 = 3. The rightmost rod is units; this is how 3 appears on any rod.
Digit 4 — heaven bead inactive | 4 earth beads active (= 4) | total = 4
All 13 rods showing digit 4. Calculation: 0 + 4 = 4. The rightmost rod is units; this is how 4 appears on any rod.
Digit 5 — heaven bead active (= 5) | no earth beads active | total = 5
All 13 rods showing digit 5. Calculation: 5 + 0 = 5. The rightmost rod is units; this is how 5 appears on any rod.
Digit 6 — heaven bead active (= 5) | 1 earth bead active (= 1) | total = 6
All 13 rods showing digit 6. Calculation: 5 + 1 = 6. The rightmost rod is units; this is how 6 appears on any rod.
Digit 7 — heaven bead active (= 5) | 2 earth beads active (= 2) | total = 7
All 13 rods showing digit 7. Calculation: 5 + 2 = 7. The rightmost rod is units; this is how 7 appears on any rod.
Digit 8 — heaven bead active (= 5) | 3 earth beads active (= 3) | total = 8
All 13 rods showing digit 8. Calculation: 5 + 3 = 8. The rightmost rod is units; this is how 8 appears on any rod.
Digit 9 — heaven bead active (= 5) | 4 earth beads active (= 4) | total = 9
All 13 rods showing digit 9. Calculation: 5 + 4 = 9. The rightmost rod is units; this is how 9 appears on any rod.
Reading summary
Digit
Heaven bead
Earth beads active
Calculation
0
Inactive (resting up)
0
0 + 0 = 0
1
Inactive
1
0 + 1 = 1
2
Inactive
2
0 + 2 = 2
3
Inactive
3
0 + 3 = 3
4
Inactive
4
0 + 4 = 4
5
Active (pushed down)
0
5 + 0 = 5
6
Active
1
5 + 1 = 6
7
Active
2
5 + 2 = 7
8
Active
3
5 + 3 = 8
9
Active
4
5 + 4 = 9
Chapter four
Place value and rod hierarchy
The value of any bead depends entirely on which rod it occupies. One earth bead on the units rod = 1. That same bead on the thousands rod = 1,000. This is the whole secret of the soroban.
The golden rule
Each rod to the LEFT is worth exactly 10× the rod to its right. Reading right to left: units → tens → hundreds → thousands → and so on.
All ten digits active at once — 9,876,543,210
9,876,543,210 — a different digit on each rod
Reading right to left: 0 (units) · 1 (tens) · 2 (hundreds) · 3 (thousands) · 4 (ten-thousands) · 5 (hundred-thousands) · 6 (millions) · 7 (ten-millions) · 8 (hundred-millions) · 9 (billions). The three leftmost rods are zero.
Chapter five
Setting numbers: from units to trillions
Setting a number means arranging beads to display that value. Always work left to right — from the highest occupied place value down to units. The red digit above each rod confirms what that rod is contributing.
Finger technique
1
Thumb pushes earth beads UP (adding 1–4)
2
Index finger pulls earth beads DOWN (removing 1–4)
3
Index finger pushes heaven bead DOWN (adding 5)
4
Index finger pushes heaven bead UP (removing 5)
Number hierarchy — all place values illustrated
Every number below is shown on the full 13-rod soroban. Active rods are highlighted; inactive rods are dimmed. The caption explains the digit breakdown.
3 — Single digit — units rod only
Breakdown: 3 in units. Set these rods left to right, highest digit first.
31 — Two digits — tens and units
Breakdown: 3 in tens + 1 in units. Set these rods left to right, highest digit first.
107 — Three digits — hundreds, zero tens, units
Breakdown: 1 in hundreds + 7 in units. Set these rods left to right, highest digit first.
134 — Three digits — hundreds, tens, units
Breakdown: 1 in hundreds + 3 in tens + 4 in units. Set these rods left to right, highest digit first.
672 — Three digits — note 6=5+1 (heaven+1 earth) on hundreds
Breakdown: 6 in hundreds + 7 in tens + 2 in units. Set these rods left to right, highest digit first.
1,024 — Four digits — thousands, zero hundreds, tens, units
Breakdown: 1 in thousands + 2 in tens + 4 in units. Set these rods left to right, highest digit first.
1,757 — Four digits — mixed heaven and earth beads
Breakdown: 1 in thousands + 7 in hundreds + 5 in tens + 7 in units. Set these rods left to right, highest digit first.
15,574 — Five digits — ten-thousands range
Breakdown: 1 in ten-thousands + 5 in thousands + 5 in hundreds + 7 in tens + 4 in units. Set these rods left to right, highest digit first.
234,567 — Six digits — hundred-thousands range
Breakdown: 2 in hundred-thousands + 3 in ten-thousands + 4 in thousands + 5 in hundreds + 6 in tens + 7 in units. Set these rods left to right, highest digit first.
1,000,000 — Seven digits — exactly one million
Breakdown: 1 in millions. Set these rods left to right, highest digit first.
9,999,999 — Seven digits — maximum 7-rod value
Breakdown: 9 in millions + 9 in hundred-thousands + 9 in ten-thousands + 9 in thousands + 9 in hundreds + 9 in tens + 9 in units. Set these rods left to right, highest digit first.
123,456,789 — Nine digits — hundred-millions range
Breakdown: 1 in hundred-millions + 2 in ten-millions + 3 in millions + 4 in hundred-thousands + 5 in ten-thousands + 6 in thousands + 7 in hundreds + 8 in tens + 9 in units. Set these rods left to right, highest digit first.
9,999,999,999,999 — Thirteen digits — maximum soroban value
Breakdown: 9 in trillions + 9 in hundred-billions + 9 in ten-billions + 9 in billions + 9 in hundred-millions + 9 in ten-millions + 9 in millions + 9 in hundred-thousands + 9 in ten-thousands + 9 in thousands + 9 in hundreds + 9 in tens + 9 in units. Set these rods left to right, highest digit first.
Common mistake
Never use the middle, ring, or little finger. Students who develop this habit become significantly slower at advanced levels. If needed, lightly tape the non-working fingers during drill sessions until the correct habit forms.
Chapter six
Addition with visual examples
Addition is performed left to right — highest place value first. This is the opposite of written column addition, which is why soroban users can announce answers before finishing the calculation.
Add n directly if beads allow · otherwise use complementary pair
Complementary pairs
Type
Pairs
When to use
5-complement
1↔4 2↔3
Adding would cross the 5 boundary — set heaven bead, remove complement
10-complement
1↔9 2↔8 3↔7 4↔6 5↔5
Sum exceeds 9 — remove complement on this rod, carry 1 to left rod
Example: 23 + 15 = 38 (Simple — no carry)
1
Set 23 on the soroban (2 earth beads on tens rod, 3 earth beads on units rod).
2
Add 1 to tens rod → tens shows 3.
3
Add 5 to units: push heaven bead down → units shows 8.
4
Read result: 38.
Start: 23
+
Adding: 15
=
Result: 38
Example: 47 + 38 = 85 (10-complement carry)
1
Set 47.
2
Add 3 to tens: 4+3=7 → tens shows 7.
3
Add 8 to units: 7+8=15, exceeds 9. Remove (10−8)=2 from units, carry 1 to tens. Units=5, tens=8.
Subtract 3 from tens: tens=0, borrow. Add 7 to tens, subtract 1 from hundreds. Hundreds=2, tens=7.
4
Subtract 7 from units: units=0, borrow. Add 3 to units, subtract 1 from tens. Tens=6, units=3.
5
Read result: 263.
Start: 500
−
Subtracting: 237
=
Result: 263
Practice problems
#
Problem
Answer
Technique
1
85 − 32
53
Direct removal
2
73 − 46
27
Borrow from tens
3
500 − 237
263
Multi-step borrow chain
4
4,021 − 1,876
2,145
Extended borrow
Chapter eight
Multiplication
Multiplication uses the standard long-multiplication algorithm, with partial products accumulated directly on the soroban. The multiplication table (1×1 through 9×9) must be memorized first.
Example: 6 × 8 = 48 (Single digit × single digit)
1
Recall: 6 × 8 = 48.
2
Set product 48 on product rods: 4 on tens, 8 on units.
3
Read result: 48.
Multiplicand: 6
×
Multiplier: 8
=
Product: 48
Example: 23 × 5 = 115 (Two-digit × one-digit)
1
Multiply tens digit: 2×5=10. Set 10 on product (hundreds=1, tens=0).
2
Multiply units digit: 3×5=15. Add 15 to product starting at tens: tens 0+1=1, units=5.
3
Read result: 115.
Multiplicand: 23
×
Multiplier: 5
=
Product: 115
Example: 47 × 23 = 1,081 (Two-digit × two-digit)
1
Multiply 47 × 2 (tens digit of 23) = 94 → set 940 on product rods (shift one left).
2
Multiply 47 × 3 (units digit of 23) = 141 → add 141 to product rods.
3
940 + 141 = 1,081. Read result: 1,081.
Multiplicand: 47
×
Multiplier: 23
=
Product: 1,081
Practice problems
Problem
Answer
6 × 8
48
23 × 5
115
84 × 7
588
136 × 9
1,224
47 × 23
1,081
Chapter nine
Division
Division mirrors long division. Each partial quotient digit is estimated, the product subtracted, and the process repeated. When an estimate is too high, reduce by 1 and add the divisor back — this correction is normal even for experts.
12 ÷ 7 → estimate 1. Subtract 7×1=7 from 12, remainder 5. Working number: 56.
3
56 ÷ 7 = 8. Subtract 7×8=56. Remainder 0.
4
Read quotient: 18.
Dividend: 126
÷
Divisor: 7
=
Quotient: 18
Practice problems
Problem
Answer
36 ÷ 6
6
126 ÷ 7
18
504 ÷ 9
56
1,452 ÷ 4
363
Chapter ten
The bridge to mental arithmetic — 暗算 (anzan)
Anzan is the ultimate goal: performing complex arithmetic entirely in the mind by visualizing and manipulating an imaginary soroban. The visual-spatial nature of this skill activates the right hemisphere in ways that pure symbol-based arithmetic does not.
The four-stage progression
1
Physical soroban in hand — all operations on the real instrument, eyes open, full tactile feedback.
2
Eyes closed with physical soroban — student feels the beads and builds an internal visual image alongside the physical sensation.
3
Flash cards — photographs of bead configurations shown for 0.5 seconds; student states the value. Gradually reduce exposure time.
4
Full anzan — all arithmetic performed mentally. The student visualizes the soroban, moves imaginary beads, reads the result from their mind's eye.
Flash anzan (フラッシュ暗算)
A training method and competitive sport where numbers flash on screen for a fraction of a second each and students sum them mentally. Japanese national competitions regularly feature children adding fifteen 3-digit numbers in under two seconds.
Chapter eleven
Lesson plans and curriculum
The curriculum below follows the Japan Abacus Committee structure, adapted for Prime Montessori Academy. Each level corresponds to roughly 20–30 hours of instruction.
Level 10 — beginner
Parts and terminology
Clearing and setting
Reading digits 0–9
Addition/subtraction, 1-digit, no carry
Levels 8–9
Addition/subtraction, 2-digit
5-complement moves
10-complement (carry/borrow)
Numbers up to 9,999
Levels 6–7
Addition/subtraction, 3-digit
Multiplication 1×1-digit
Division 2÷1-digit
Introduction to anzan
Levels 4–5
Multiplication 2×2-digit
Division 3÷1-digit
Timed speed drills
Mental arithmetic basics
Levels 2–3
Multi-digit × multi-digit
Long division, 4+ digits
Decimals
Anzan: 5-number strings
Level 1 — advanced
Exam speed benchmarks
Flash anzan training
Competition preparation
Mixed operation strings
Sample first lesson — 50 minutes
Time
Activity
Goal
0–5 min
Show soroban; invite touch and exploration
Curiosity and comfort
5–15 min
Name and locate all parts; students label a diagram
Terminology
15–25 min
Practice clearing; instructor then students
Muscle memory
25–40 min
Set digits 0–9 on one rod; choral read-back
Bead ↔ digit mapping
40–50 min
Set 5 random 3-digit numbers; speed game
Confidence and fun
Chapter twelve
Teaching tips and troubleshooting
Common errors and corrections
Error
Likely cause
Correction
Losing place mid-calculation
Not tracking columns consistently
Mark the units column with a sticker; enforce left-to-right reading aloud
Off-by-one carry errors
Skipping or doubling a carry
Say "carry one left" aloud during every carry step
Wrong finger used
Casual handling habit
Tape non-working fingers during drills until the correct habit forms
Heaven bead not fully seated
Weak index-finger control
Dedicated heaven-bead drills: set and clear 5 on each rod repeatedly
Forgetting complement pairs
Incomplete memorization
Post the complement table above the workspace; oral quiz before each session
A note from Prime Montessori Academy
The soroban is among the oldest computational tools still in active use and one of the most effective. Teach it with patience and delight — the clicking of beads and the satisfaction of a correct answer arrived at through genuine understanding are pleasures that connect students to three centuries of mathematical culture.
