You may have seen little children playing with a toy that looks like Figure 1. It has a frame in the shape of a rectangle. Several wires hold rows of beads. Children love to move the beads back and forth and hear the clacking sounds as the beads bump together. This toy is called an abacus. But it is more than just a toy.
When I visited Russia a few years ago, I saw many calculators and computers. But I was surprised to see that people were also doing calculations with the abacus. The Russians call it a scety (SCHAW-tee) and use it as a counting board. In many Russian stores a scety lay next to the cash register. Figure 2
When Napoleon invaded Russia in 1812, a mathematician traveling with the French army saw Russian people using this type of abacus. What a wonderful way to teach arithmetic, he thought. He brought a scety back to France, where it became popular. From there it spread to other European countries and to America.
Here is a scety showing the number 427.50. It may be the price of a television set or a fridge. Try to read the number. Here are some hints. Figure 3
• Count the number of beads on each wire. How many are dark? How many are light?
• Count the number of beads on the left side in each row. Write down the number for each row.
• How is the decimal point shown? How is zero shown?
• Now can you read the number 427.50 on the abacus?
You can make your own scety. Here are suggestions about the materials you will need.
• Heavy cardboard rectangle, about 8½inches by 11 inches (21 cm by 27 cm)
Figure 1
Simple abacus
Russian abacus
Figure 2
Scety showing 427. 50
Figure 3
Staple the seven strands and knot them
Figure 4a
String 10 beads and staple the end
Figure 4b
Abacus showing 6
Figure 5a
6 + 4(two ways)
Figure 5b
6 + 5
Figure 5c
• Thick string, enough to make seven rows and fasten the ends (about 7 feet, or 2 m, 10cm)
• Stapler
• Scissors
• Ruler
• 49 light-colored beads and 12 dark-colored beads (You might also use pieces of macaroni and color 12 pieces with a pen or marker.) Make sure you have enough space to move 10 beads or macaroni pieces on each string.
1. Cut the string into seven equal pieces, each a little longer than the length of the cardboard.
2. Staple one end of each piece of string to the cardboard. Knot the string at the staple. Figure 4a
3. Start with the top string. Place four light beads, then two dark beads, then four more light beads on the string. Staple the end of the string to the cardboard. Knot the end of the string around the staple. Figure 4b
4. Do the same as in step 3 for each string, except for the decimal point string, which has just one light bead (see Figure 2)
Does your scety look like the one in Figure 2?
1. Show several different numbers on your scety.
2. Think how you would use your abacus to teach a child to add. Start with small numbers; for example:
6 + 2; 6 + 4 (two ways); 6 + 5. What do you do when all 10 beads on the string have been moved to the left? You exchange those 10 beads for a single bead on the next higher strand. Then you move the 10 beads on the lower string back to the starting position and continue. Figure 5a Figure 5b Figure 5c
3. Think how you would teach a child to subtract on the abacus. Then try your method.
4. How does the abacus help children to learn arithmetic? What are the disadvantages?
5. Pretend you are a clerk in a Russian store. Use your abacus to add and subtract larger numbers, showing dollars and cents.
