Activities/Abacus

Where to get Abacus

Activity | Source

About Abacus

Abacus lets the learner explore different representations of numbers using different mechanical counting systems developed by the ancient Romans and Chinese. There are several different variants available for exploration: a suanpan, the traditional Chinese abacus with 2 beads on top and 5 beads below; a soroban, the traditional Japanese abacus with 1 bead on top and 4 beads below; the schety, the traditional Russian abacus, with 10 beads per column, with the exception of one column with just 4 beads used for counting in fourths; and the nepohualtzintzin, a Mayan abacus, 3 beads on top and 4 beads below (base 20).

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  suanpan (Chinese)

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  soropan (Japanese)

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  schety (Russian)

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  nepohualtzintzin (Mayan)

How to use an abacus

Clear the abacus

Before you start an arithmetic operation, you need to "clear" the abacus. The upper beads should be positioned against the top of the frame and the lower beads should be positioned against the bottom of the frame. This is the default position for the abacus when you launch the activity. (Note that the schety does not have any upper beads. All of the beads in the schety should start in the down position.)

Reading the abacus

In each column, the bottom beads represent 1s and the top beads represent 5s. (The exception is the column in the schety with only 4 beads. These are 1/4 each.) So for each bead you raise up from the bottom in a column add 1 and for each bead you lower from the top in the same column, add 5.

The columns themselves represent decimal positions from right to left, e.g., 1s, 10s, 100s, 1000s, etc. (There are two exceptions: (1) the nepohualtzintzin uses base 20, e.g., 1s, 20s, 400s, 8000s, etc.; and (2) on the schety, the beads to the right of the column with just four beads are 0.1s, 0.01s, 0.001s, and 0.0001s.)

The current value is always displayed on the frame. Experiment and you will quickly learn to write and read numbers.

Examples: In the gallery below, several simple examples are shown. In the gallery of images above, the number 54321 is shown on each of the different abaci.

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  1 bottom bead is up, corresponding to 1 unit

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  1 top bead is down, corresponding to 5 units

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  5 bottom beads are up, also corresponding to 5 units

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  1 bottom bead is up and 1 top bead is down, corresponding to 6 units

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  5 bottom beads are up and 1 top bead is down, corresponding to 10 units (time to "carry" to the left)

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  This 10 is equivalent to...

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  ... this 10

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  54321

Note: The display always assumes a fixed unit column, but you can override this choice.

TODO: add an indicator for assigning the unit column.

Addition

To add, simply move in more beads to represent the number you are adding. There are two rules to follow: (1) whenever you have a total of 5 units or more on the bottom of a column, cancel out the 5 by sliding the beads back down and add a five to to the top; and (2) whenever you have a total of 10 units or more in a column, cancel out the 10 and add one unit to the column immediately to the left. (With the nepohualtzintzin, you work with 20 rather than 10.)

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  4

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  +3 (5–2=3)

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  +5

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  carry 5s to next column

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  +19 (20-1=19)

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  +24

• Abacus-55,png

  4+3+5+19+24=55

Subtraction

Subtraction is the inverse of addition. Move out beads that correspond to the number you are subtracting. You can "borrow" from the column immediately to the left: subtracting one unit and adding 10 to the current column.

TODO: Add instructions for multiplication and division.