Monday, October 31, 2011

The Soroban Abacus


Today we made a Soroban (a Japanese abacus).
And we learned how to use it.

Here's how it works.

First of all, the one we made will go up to 999.  If you need a larger number, into the thousands, then add another column, making four, or however many you'd like.

I decided upon making a temporary, out of a paper box, to start with (if it gets played with often, then I'll commit one of our wooden boxes, or make a frame).  Elsewise we used three bamboo skewers (strong string will also work), fifteen beads, and something sharp or pokey for a piercing tool.

We found 12 natural beads, and three blue beads.  (If you don't have any large beads, why not make some out of paper or clay?)
Using something that will poke through (I used a upholstery needle, a nail will work - just use a slim one so your skewers are snug in the holes), poke holes at one end of your paper box, or if you think you'll use this often, drill holes in a wooden box.

Insert skewers through on end (or you can use string if you like), and in order, add one heavenly and four earthly beads upon each stick.

After drilling or poking the other side of the box, put the other end of the skewer through the hole.

Push the heavenly beads away from you, and the earthly beads toward you, and mark the center point between the two on your skewers or string.  This is where your active beads will be placed. 

I trimmed off the points and excess length of the skewers.

The upper beads are called "heavenly beads".  The lower beads are called "earthly beads".  We made our "heavenlies" blue, and chose natural brown for the "earthlies" (earth and sky seemed logical).
Heavenly beads have a value of 5, earthly beads have the value of 1.

Thus, numbers are represented accordingly:

zero          -          one          -          two          -          three          -          four          -          five


six         -         seven         -         eight         -         nine         -         ten         -         twenty


fifty       -       sixty       -     seventy     -       seventy-five       -       one hundred seventy-five

So.  You see how that works.

Let's take 137,

and add 54.

fifty gets added first


and then two (of the four)


carry over one to the tens column (this adds the third of four)


the ones go back to zero since we've made ten, 
and have added one to the tens column


and add in the last one (the fourth) of the fifty-four.


and we have 191.

Of course I just had to know how to subtract, as well, so did some research on that.

Let's begin again with 137 again, and subtract 54, this time.


We can't automatically subtract fifty from these three (thirty),


so we'll have to take one away from the column to its left,


and add back in five

(because 10-5=5.  If we were subtracting 80, we'd add back in 2.  If we were sutracting 60, we'd add back in 4.)

We can't take away four "ones" (singles) from our last column, so we'll take out the five,


and add one to make four.

 There.  137 - 54 = 83!
See?  That's not so bad!  :)

Some shopkeepers in China and Japan still use an abacus to calculate what their customers owe... they can do it is quickly as they could on an electronic calculator!

I beleive that, for I've already started getting the hang of this machine!
Happy playing.


This was our first project from our book Amazing Math Projects You Can Build Yourself.

4 comments:

  1. honto kakuiiiiii! what a great project! thanks for sharing:)

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  2. Debbie and CLZ - I'm super excited to have learned... I've been wondering how it works forever, and it seemed so hard! Am glad to have learned it! :)

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  3. very cool. I love math and have never taken the time to figure out how these work. Now I get it!

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Thanks so much for sharing your thoughts!