The curriculum

Fifteen skills: twelve bead skills (S0 to S11) and three mental skills (A1 to A3). Each has a lesson, a drill generator that only produces items exercising its rule, and a difficulty ladder (crates/abax-core/src/curriculum.rs, generator.rs).

The graph

Nothing is locked. The prerequisites below are the suggested path, not a gate.

A skill’s prerequisites count as met when every one of them has a knowledge estimate of at least 0.80 (see the scheduler). That threshold drives three things:

• The suggested next lesson. The lesson list marks one lesson next, and Home’s Continue opens it: the first skill, in the order of the table, whose prerequisites are met and which you have neither practised nor marked as known. It does not wait for the prerequisite to be mastered.
• The “builds on” note. Open a lesson whose prerequisites are not met yet and a small line under its title names them, for example Builds on: S10 Multiplication, each a link to that lesson. It appears once.
• A light review in planned sessions, described under the session planner.

Skipping what you know

Every lesson has I know this already at the top right. It marks the skill as known, sets its knowledge estimate to 0.80 (never lowering a higher one) and moves on to the suggested next lesson. A known skill counts as met and is mixed into focus drills and cool-downs like any practised skill.

A lesson you marked shows Reset this skill in the same place; Settings → Data → Reset one skill does the same for any skill. A reset puts that one skill back to new, as if never met; your history in Stats is kept. When the skill has real practice behind it, the reset asks for a second tap.

Moves below use the notation from Finger rules: +3 is three earth beads up (thumb), −2 two earth beads down (index), +5 and −5 the heaven bead down and up (index), +1 left a carry onto the next rod.

Ladders

Each skill climbs a ladder of steps, raising one thing at a time: first the number of operands, then digits, then time pressure. “Gentle” timing allows 2.0 times your typical time per operand, “tight” 1.3 times, never less than 1.2 s per operand.

For multiplication “3×2” means a 3-digit multiplicand times a 2-digit multiplier; for division “4÷2” a 4-digit dividend and a 2-digit divisor.

S0: Reading and setting numbers

Teaches the rods, the beam, the values of the beads and the unit dots. Drills “Set this number” and “Read this soroban”, half each, with 1 to 5 digits. Set 7 is +5, +2 (one pinch); set 406 is +4 on the hundreds, then +5, +1 on the units.

S1: Adding without complements

Rule: when the beads you need are free, push them to the beam. The thumb pushes earth beads up, the index finger brings the heaven bead down; for 6 to 9 both move together. Drills chains of one-digit additions in which no complement is ever needed. Examples from the lesson: 2 + 2 is +2; 3 + 5 is +5; 1 + 6 is +5, +1 in one pinch; 12 + 36 is +3 on the tens, then +5, +1 on the units.

S2: Subtracting without complements

Rule: move beads away from the beam with the index finger; for 6 to 9, earth beads first, then the heaven bead. Drills one-digit subtraction chains with no complement. Examples: 4 − 3 is −3; 8 − 5 is −5; 9 − 7 is −2, −5; 87 − 52 is −5 on the tens, −2 on the units.

S3: Adding with the five-complement

Rule: when the earth beads you need are not free, add 5 and take away the “small friend” (the number that makes 5 with it: 1 and 4, 2 and 3). Heaven bead first, then the earth beads, both with the index finger. Drills addition chains that must use the five-complement at least once and never need a carry. Examples: 1 + 4 is +5, −1; 3 + 3 is +5, −2; 4 + 2 is +5, −3; 23 + 34 is +5, −2 on the tens and +5, −1 on the units.

S4: Subtracting with the five-complement

Rule: when the earth beads to take are not at the beam, take 5 away and give back the small friend: earth beads up with the thumb first, then the heaven bead up with the index finger. Drills subtraction chains that use it. Examples: 6 − 4 is +1, −5; 5 − 2 is +3, −5; 7 − 3 is +2, −5; 65 − 42 is +1, −5 on the tens and +3, −5 on the units.

S5: Adding with the ten-complement

Rule: when the sum would pass 9, take away the “big friend” (the number that makes 10: 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5) on this rod, then carry 1 onto the rod to the left. Drills addition chains that need a carry at least once (five-complements may appear too). Examples: 4 + 8 is −2, +1 left; 9 + 1 is −4, −5, +1 left (taking away 9, the friend of 1); 5 + 5 is −5, +1 left; 38 + 27 is +5, −3 on the tens (a five-complement), then −3 on the units and +1 left, giving 65.

S6: Subtracting with the ten-complement

Rule: when the rod does not hold enough, borrow 1 from the rod on the left first, then add the big friend on this rod. Drills subtraction chains that need a borrow. Examples: 11 − 7 is −1 left, +3; 10 − 1 is −1 left, +5, +4; 15 − 8 is −1 left, +2; 62 − 38 is +2, −5 on the tens, then −1 left, +2 on the units, giving 24.

S7: Combined complements

Rule: the ten-complement’s own move on the rod sometimes cannot be made directly and needs a five-complement inside it. 7 + 6: taking away 4 (the friend of 6) from 7 is impossible with two earth beads up, so take 4 through 5: +1, −5, then +1 left, giving 13. In subtraction, 12 − 7: borrow (−1 left), then add 3 to the 2 on the units rod, which needs the small friend: +5, −2, giving 5. Drills mixed chains that must contain a combined move. Other lesson examples: 6 + 8 is +3, −5, +1 left; 13 − 6 is −1 left, +5, −1.

Exactly these one-rod additions are combined: 5 + 6 to 5 + 9, 6 + 6 to 6 + 8, 7 + 6, 7 + 7 and 8 + 6. (8 + 7 is not: 8 has three earth beads up, so −3, +1 left works directly.)

S8: Multi-digit addition

Rule: nothing new. Add each digit on its own rod, from the left; carries travel left, so they never land on a rod you still have to visit. Drills chains of 2- and 3-digit numbers, 2 to 10 operands, any complement allowed. Example: 478 + 365. Hundreds: 4 + 3 is +5, −2. Tens: 7 + 6 is the combined move +1, −5, then +1 on the hundreds. Units: 8 + 5 is −5, then +1 on the tens. Result 843. And 1999 + 1, where one carry ripples across three rods: −4, −5 on the units, tens and hundreds in turn, then +1 on the thousands.

S9: Mixed addition and subtraction

Rule: every operation lands on the running total, so plus and minus mix freely. Before a subtraction, look left to see where a borrow will come from. Drills mixed chains of multi-digit numbers. Example: 843 − 599. Hundreds: −5. Tens: 4 − 9 borrows 1 from the hundreds and adds 1 to the tens, which on a rod showing 4 is +5, −4. Units: 3 − 9 borrows from the tens (5 − 1 is +4, −5), then adds 1 on the units. Result 244.

S10: Multiplication

Method: Kojima’s standard method. Set the multiplier on the left and the multiplicand to its right with two empty rods between. Multiply the rightmost digit of the multiplicand by each multiplier digit from left to right. Each two-digit partial product goes with its tens on the first rod to the right of the multiplicand digit being used, and each next one shifts a rod further right. Clear the multiplicand digit, move to the next one to the left. The product’s units end up (digits of the multiplier + 1) rods to the right of the multiplicand’s units. Drills products from 1 × 1 digits up to 3 × 2 digits; you type the answer and can step through the worked procedure.

Abax’s own walk-through of 23 × 12:

1. Set the multiplier 12 on the left.
2. Set the multiplicand 23 with its units on the unit rod, two empty rods after the multiplier.
3. 3 × 1 = 03: add it with its tens on the first rod right of the 3.
4. 3 × 2 = 06: add it one rod further right.
5. Clear the 3.
6. 2 × 1 = 02, tens on the first rod right of the 2; 2 × 2 = 04 one rod further right.
7. Clear the 2 and read 276, three rods right of where the multiplicand’s units were.

S11: Division

Method: the standard method (商除法, shōjohō). Set the dividend with its units on a unit rod and the divisor on the left, four empty rods away. Compare the divisor with the leading digits of the dividend and guess a quotient digit; it goes two rods left of the dividend’s leading digit when the divisor goes into that one digit, one rod left when two digits are needed. Subtract quotient × divisor digit by digit. If a partial product cannot be subtracted, the guess was too large: lower it by one and add back what was already taken. If what remains is still at least the divisor, the guess was too small: raise it and subtract once more. Drills exact divisions from 2-digit ÷ 1-digit up to 4-digit ÷ 2-digit.

Abax’s walk-through of 391 ÷ 17 revises twice: try 3 (from 3 ÷ 1), find 3 × 7 cannot be taken, revise to 2 and take 2 × 7; then try 5, revise to 4, then to 3, and take 3 × 7. The quotient 23 is read three rods left of the dividend’s units.

A1: Anzan, the mental soroban

Teaches calculating on a soroban you picture. The start of each item is set on the beads, the beads fade to glass and vanish, and you add the rest in your head and type the total. Drills one-digit chains of mixed addition and subtraction with any complement, then 2-digit chains. Details in Anzan and flash anzan.

A2 and A3: Flash anzan

Teaches adding numbers that flash one after another, without beads at all. A2 uses one-digit numbers, A3 two and three digits. The ladders are in Anzan and flash anzan.