Multiplication is lots of little times-table answers, each added onto exactly the right rod.
Updated · 2 min read
What you need first
Two things: confident addition with little and big friends, because every partial product is added onto the board; and the times tables up to 9 × 9. Shaky complements show up here first.
Setting up the board
Set the number being multiplied (the multiplicand) towards the right, its last digit on a unit rod.
Set the number you are multiplying by (the multiplier) to its left, leaving two empty rods between them as a gap.
The answer grows in the empty rods to the right of the multiplicand.
Put the smaller or simpler number on the left as the multiplier: there is less to keep track of.
Where each little product goes
Start with the multiplicand's last digit. Multiply it by each multiplier digit in turn, from left to right. The first little product puts its tens digit on the rod immediately to the right of the multiplicand digit, and its ones digit on the rod after that. Each further multiplier digit shifts one more rod to the right. Add each one onto whatever is already there, with the usual complements.
When a multiplicand digit has been multiplied by every multiplier digit, clear it. Then move one digit left and repeat.
Worked example: 23 × 3
Worked example: 23 × 3 = 69
1Move 1. Set 3 on the left, leave two empty rods, then set 23. Put 9 onto the two rods just right of the 3 — the 0 here and the 9 next door. 9 = 5 + 4. Big bead down and 4 up together. 👍 thumb + ☝️ index finger, together2Move 2. This digit is finished, so wipe it off. That is what keeps the board honest. Index finger down 3 beads. ☝️ index finger3Move 3. Put 6 onto the two rods just right of the 2 — the 0 here and the 6 next door. 6 = 5 + 1. Big bead down and 1 up together. 👍 thumb + ☝️ index finger, together4Move 4. This digit is finished, so wipe it off. That is what keeps the board honest. Index finger down 2 beads. ☝️ index finger✓Answer: 69, read from the rods to the right of the gap
Worked example: 46 × 3
This time the little products overlap, so the second one is added on top of the first — watch the carry.
Worked example: 46 × 3 = 138
1Move 1. Set 3 on the left, leave two empty rods, then set 46. Put 18 onto the two rods just right of the 6 — the 1 here and the 8 next door. Thumb up 1 bead. 👍 thumb2Move 2. 8 = 5 + 3. Big bead down and 3 up together. 👍 thumb + ☝️ index finger, together3Move 3. This digit is finished, so wipe it off. That is what keeps the board honest. 6 = 5 + 1. Big bead up and 1 down together. ☝️ index finger4Move 4. Put 12 onto the two rods just right of the 4 — the 1 here and the 2 next door. Thumb up 1 bead. 👍 thumb5Move 5. Thumb up 2 beads. 👍 thumb6Move 6. This digit is finished, so wipe it off. That is what keeps the board honest. Index finger down 4 beads. ☝️ index finger✓Answer: 138, read from the rods to the right of the gap
Two-digit multipliers: 46 × 23
With 23 on the left and 46 on the right, each digit of 46 is multiplied by 2 and then by 3, each little product shifting one rod further right:
46 × 23, one little product at a time
Step
Little product
Answer rods show
1
6 × 2 = 12
12
2
6 × 3 = 18, then clear the 6
138
3
4 × 2 = 8
938
4
4 × 3 = 12, then clear the 4
1,058
Zeros in the multiplier
A zero in the multiplier still takes up its place. When multiplying by 503, after the 5 skip a rod for the 0, and put the 3's little product two rods along from the 5's, not one.
Why clear each digit?
Clearing a finished digit tells you exactly how far you have got, stops you multiplying it twice, and keeps the board an honest running total at every step. It also means you can pause and pick up again without losing your place.