Beadbay: the soroban
Small friends and big friends on the soroban
Small friends are pairs that make five (1 and 4, 2 and 3). Big friends are pairs that make ten (1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5). When the beads you need are not free, you add or take a bigger bead and correct it with the friend.
Try them
A small friend, a big friend, then both together.
Small friends: pairs that make 5
One and four are small friends. So are two and three. When there are not enough earth beads, bring the five down and take the small friend away.
| To add | Do this | To take away | Do this |
|---|---|---|---|
| 1 | five down, take 4 | 1 | five off, add 4 |
| 2 | five down, take 3 | 2 | five off, add 3 |
| 3 | five down, take 2 | 3 | five off, add 2 |
| 4 | five down, take 1 | 4 | five off, add 1 |
Big friends: pairs that make 10
One and nine, two and eight, three and seven, four and six, five and five. When a rod is too full, take the big friend away and carry one to the left.
| To add | Do this | To take away | Do this |
|---|---|---|---|
| 1 | take 9, carry 1 left | 1 | borrow 1 from the left, add 9 |
| 2 | take 8, carry 1 left | 2 | borrow 1 from the left, add 8 |
| 3 | take 7, carry 1 left | 3 | borrow 1 from the left, add 7 |
| 4 | take 6, carry 1 left | 4 | borrow 1 from the left, add 6 |
| 5 | take 5, carry 1 left | 5 | borrow 1 from the left, add 5 |
| 6 | take 4, carry 1 left | 6 | borrow 1 from the left, add 4 |
| 7 | take 3, carry 1 left | 7 | borrow 1 from the left, add 3 |
| 8 | take 2, carry 1 left | 8 | borrow 1 from the left, add 2 |
| 9 | take 1, carry 1 left | 9 | borrow 1 from the left, add 1 |
How to tell which one you need
Look at the rod. If the answer still fits on it (nine or less) but the lower beads are in the way, it is a small friend. If the answer would be ten or more, or you are taking more than the rod holds, it is a big friend.
- Beads free: just move them.
- Fits on the rod, wrong beads free: small friend.
- Does not fit on the rod: big friend, with a carry or a borrow.
- The big friend's own move is blocked: a small friend helps it (6 + 7, 14 − 6).
Learning them
Say the pairs aloud until they are automatic, then practise sums that use one kind at a time. The app's practice remembers which pairs you find hard and brings them back until they stick.
Questions
Why are they called friends?
It is a way of teaching complements to children: two numbers that belong together because they make five, or ten.
Which should I learn first?
Small friends. They stay on one rod. Big friends come next because they bring in the rod on the left.