Before you print
Little friends: the first genuine soroban technique
Twenty four addition problems inside 9. Several of them need the classic little friends trick, the pairs that make five, which is the first point where soroban stops being careful counting and becomes a method. It works as a pencil sheet or alongside a real abacus.
The skill this sheet trains
The four pairs are 1 and 4, 2 and 3, 3 and 2, 4 and 1. Their use is not obvious until you look at the rod. To add 4 to a rod already showing 4, there is no fifth lower bead to raise. So instead of adding 4, the child brings the five bead down and takes away 1, because 1 is what 4 needs to reach five. Nothing is being approximated; the answer is exact. What has changed is that a movement which was impossible has been swapped for two movements that are both possible. That substitution is the mental habit the whole discipline runs on, and every later formula is the same idea applied to a bigger number.
Using the sheet
Do not time this one. The problems are deliberately mixed, so some can be solved by moving beads directly and some cannot, and the useful work is deciding which is which before the hand moves. Twenty four problems takes most children twelve to twenty minutes on a first pass. Finished looks like every answer correct, with the complement problems taking visibly longer than the direct ones. That gap is expected and it narrows on its own over a fortnight of short sittings.
What to watch for
Watch for the child who gets the right answers but never touches the five bead, reaching the total by counting on in their head and then setting the result. The answers will be correct and the technique will be absent, which is the one failure mode this sheet is designed to expose. Ask them to show you 4 plus 4 on the beads. If the five bead does not come down, go back and rehearse the four pairs on their own before returning to the sheet.
Where it sits in the course
The five complements are the substance of Level 2 in some syllabuses and the tail of Level 1 in others. In our graded course they sit at the join between the two, taught once direct movement is secure and before the ten complements arrive. Compare this against the full curriculum.
If the four pairs are new to you as well as to your child, our step-by-step guide to how the little friends work on a soroban shows the substitution being made bead by bead.
What to print next
The same trick, one order of magnitude up, is what crossing ten needs: Abacus Level 2 Worksheets.
Little Friends Addition
Addition within 9, including the five-complement pairs
Improver · Ages 6 to 9
Name: ______________________
Date: ______________________
- 1.4 + 3 = ______
- 2.3 + 4 = ______
- 3.2 + 4 = ______
- 4.4 + 4 = ______
- 5.1 + 4 = ______
- 6.3 + 3 = ______
- 7.4 + 2 = ______
- 8.2 + 3 = ______
- 9.5 + 3 = ______
- 10.6 + 2 = ______
- 11.5 + 4 = ______
- 12.7 + 2 = ______
- 13.6 + 3 = ______
- 14.2 + 2 = ______
- 15.3 + 5 = ______
- 16.1 + 8 = ______
- 17.4 + 5 = ______
- 18.2 + 6 = ______
- 19.3 + 6 = ______
- 20.1 + 3 = ______
- 21.4 + 1 = ______
- 22.2 + 7 = ______
- 23.1 + 7 = ______
- 24.3 + 2 = ______
Answers: 1) 7 · 2) 7 · 3) 6 · 4) 8 · 5) 5 · 6) 6 · 7) 6 · 8) 5 · 9) 8 · 10) 8 · 11) 9 · 12) 9 · 13) 9 · 14) 4 · 15) 8 · 16) 9 · 17) 9 · 18) 8 · 19) 9 · 20) 4 · 21) 5 · 22) 9 · 23) 8 · 24) 5