i always thought each bead on an abacus represented one.
and you could count from zero to one hundred and back again by moving each bead along.
but last week, when i watched george do his math, and he was using the abacus, i almost asked "why are you using an abacus? you are working a problem with 943 and 487 in it? neither of those is less than 100!?!"
and i learned from him. he used the beads on the 5th and 6th rungs as 100s. each bead represented 100. he used the beads on 3rd and 4th rungs as 10s. and he used beads on top two rungs as ones.
so to subtract 487 from 943 he first moved 9 100s beads over. then he traded one 100s beads for 10 10s beads. he went further and traded one 10s bead for 10 ones beads- but he still had 943 represented. then he began to take away 487.
i never knew abacuses were used this way. i feel like i'm just broadcasting my ignorance. but i never learned this in school! so there has got to be just a few people in this boat with me.
but i think what is most curious is, where did he learn it? i've asked and he says he just made it up.
so maybe this isn't the correct way rouse an abacus? but it makes sense! and shows he grasps borrowing on a tangible level.
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