PROJECT THREE: THE YORUBA NUMBER SYSTEM

The Yoruba people currently number over 15 million. According to their legends, they came from the East, to settle in what is now Nigeria, Togo, and the Republic of Benin (Dahomey). Many historians believe that the Yoruba migrated to their present home from Upper Egypt, between 600 and 1000 A.D. They are city-dwellers. Their ancient cities of Ife and Oyo were founded between 800 and 1000 A.D.

The Yoruba have always had a monarch, whom they believe to be descended from their gods. However, the Yoruba government and social structure is not dictatorial. Responsibilities are shared. Although recognition and respect for rank is evident, there is also the possibility of moving up in rank through hard work. In fact, the Yoruba describe their culture as "a river that is never at rest".

The Yoruba were great traders. The city of Oyo, founded by a group of traders, was positioned to control trade routes all the way to the coast. They traded gold, slaves, and cocoa.

THE YORUBA NUMBER SYSTEM

In her book, Africa Counts, Claudia Zaslavsky describes the Yoruba number system as a complex system based on 20 (vigesimal) that uses subtraction to express numbers. For example,

35 = (2 x 20) - 5; 47 = (3 x 20) - 10 - 3; 51 = (3 x 20) - 10 + 1;

55 = (3 x 20) - 5; 67 = (4 x 20) - 10 - 3; 73 = (4 x 20) - 10 + 3;

86 = (5 x 20) - 10 - 4; 117 = (6 x 20) - 3

According to the Yoruba system, the numbers from 1 to 10 have unique names. The numbers 11, 12, 13, and 14 are written additively (i.e., 11 = 10 + 1, 12 = 10 + 2, 13 = 10 + 3, 14 = 10 + 4). But the numbers from 15 through 19 are written using subtraction from 20. The numbers 21, 22, 23, and 24 are also written additively. The numbers 25 -29 are written as subtractions from 30. Each number after 30 is written as a multiple of 20 plus or minus tens and units. This pattern is repeated for numbers up to 200. After 200, the system becomes irregular. The number 20 and its multiples are considered special to the Yoruba. Here are some of their Yoruba names.

20 = ogun; 40 = ogun meji; 200 = igba; 400 = irinwo.

Although this number system seems very difficult and abstract to westerners, it is perfectly natural to the Yoruba and is still used today.

YORUBA CURRENCY

Until recently, cowrie shells were the basic unit of currency in Africa. Cowries were either counted in groups of 5 or pierced and threaded in strings of 40. According to the Yoruba system for counting cowries,

40 cowries = 1 string; 2000 cowries = 1 head or 50 strings;

20,000 cowries = 1 bag or 10 heads.

As part of their trading commerce, the Yoruba had to count huge numbers of cowries. When a cowrie counter had to count thousands of shells, he would empty the bag onto the floor and start counting 20s by making 4 groups of 5 shells each. Then the counter would make 5 groups of 20 to make 100. Then 2 groups of 100 would be pushed together to make the important 200. The subtractive principle developed from counting in this manner. The Yoruba also learned to estimate well when counting large quantities of cowrie shells.

MATHEMATICS ACTIVITIES

1. Put about 200 counters of uniform size all together on a table or the floor. Some examples of counters are M&Ms, pennies, chips, cookies, lima beans, macaroni, or peanuts. Begin separating the counters as the Yoruba would, into groups of 5, 20, and 100. Using your counters, show each of the following amounts: 25, 46, 72. Explain how the Yoruba system of subtraction developed from counting cowries.

2. Express each of the following numbers according to the Yoruba number system:

a.   37       b.   62       c.  108

3. Explain the Yoruba number system in your own words.

4. Why do you think the system becomes unpredictable for numbers larger than 200. Provide an example with your explanation.

5. How does the Yoruba system compare to Roman Numerals? What are some similarities and differences?

CONNECTIONS TO CHILDREN'S LITERATURE

Wood-Hoopoe Willie by Virginia Kroll is the story of an African-American family observing Kwanzaa. Their African musical legacy is interwoven into the story.

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