Clerks Abacus Activity
Why use an abacus? This activity will teach you how to use an ancient method of calculations that was widely used during the Russian era at Metini / Fort Ross. Students today can benefit greatly by knowledge of this tool that emphasizes place value in a base ten system. This manipulative tool can be used to model/represent quantities, round quantities to a specific place value, add, subtract, multiply, and divide (including regrouping).
History of the Abacus – The term abacus is derived from the Greek word abax meaning “calculating board or table” also probably from the Phoenician word abak meaning “sand” or Hebrew word abhaq meaning “dust.” Originally, it was an adaptation of a method of counting and keeping track of quantities by moving pebbles in the sand. Over time, beads threaded onto a wooden frame replaced the stones. It is believed that the Babylonians used this first place-value number system between 1000 BC and 500 BC.
The Chinese Abacus (suan-pan – “counting tray”) – The Chinese abacus is perhaps the best known abacus in the world. The first record of the Chinese abacus is from the Yuan Dynasty (14th Century). It can be used to add, subtract, multiply, and divide as well as work on more complex problems involving fractions and square roots. The Chinese abacus is still commonly used in many Asian countries. The Chinese abacus has a horizontal center bar with rows of beads above and below (2 beads above and 5 beads below). Numbers represented are read by their relationship to the center bar. Beads below the bar (earth beads) represent ones and beads above the bar (heaven beads) represent five’s. So, if there is one heaven bead and one earth bead moved toward the center bar, the represented number is “6” – one 5 plus 1 one. Each vertical row represents place values (powers of 10). Unused beads are pushed away from the center bar.
The Russian Abacus – The “national calculator” (or s’chyoty) was used until the mid-1990’s in Russian businesses. This abacus consists of eleven wires with beads. Counting from the bottom, wires 1-3 have 10 beads, wire 4 has 4 beads, and wires 5-11 have 10 beads. For the 10 beaded wires, the first 4 beads and last 4 beads are one color and the middle 2 are a contrasting color to enable quicker, visual counting. The fourth wire seems to be a place holding wire (similar to decimal point). All wires above that represent whole number place values. Typically, the unit represented is the ruble (or Russian unit of currency). To enter the number 5874, move to the left edge in the eighth wire 5 beads, in the seventh wire 8 beads, in the 6th wire 7 beads and in the 5th wire 4 beads.
Making a S’chyoty – A combination of pony beads and 6mm pipe cleaners work well. The beads slide easily along the pipe cleaners and yet hold their position, even if the abacus is dropped. Also, the abacuses can be held upright for a quick teacher check without losing the integrity of the answer. Another aid for visual inspection of students’ understanding is to color-code the pipe cleaners and beads so that each student has the same color for each place value. In addition, the greater the contrast within the place value, the easier it is to distinguish accuracy of students’ work. For visually impaired students, try using beads with different shapes (round, square, and star, for example). Transparent beads can be used for an overhead projector version.
Adequate supplies for a classroom set of 30 abacuses costs approximately $10 to $15. In addition, using the supplies suggested, each student should be able to continue to use his/her abacus throughout the school year.
- Beads – plastic pony beads (6 x 9 mm.)
- Simple – three different colors of 8 beads each, 6 beads contrasting color
- Advanced – ten different colors of 8 beads each, 20 beads contrasting color, 1 additional color for decimal point
- Wires – 6mm pipe cleaners – various colors
- Simple – 3 each
- Advanced – 11 each
- Frame –
- Simple – bottom 2-3” of gallon milk jug (plastic) keeping bottom intact Advanced – shoebox lid
- Several Hole punchers
- Punch holes (using hole punch) on opposite sides of frame (three holes on each side for simple and 11 holes for advanced)
- Thread beads onto pipe cleaners – 4 of first color, 2 of contrasting color, and 4 more of first color
- Thread pipe cleaners through punched holes and secure. Teachers may wish to label place values for each strand of beads (using label tapes or permanent markers)
- To use, orient the abacus so pipe cleaners are vertical to the student and all beads are pushed “up.” Although the s’chyoty was traditionally oriented with horizontal beads, the vertical alignment would be easier to understand for younger users, especially while reinforcing place value concepts
- Slide appropriate beads “down” to represent specific quantities