This lesson describes a method of addition used by the Mende people of West Africa. The method uses counting and expansion to build toward the idea of addition.
To introduce students to the concept of addition using expansion.
To reinforce the Commutative and Associative Properties of Addition.
To expose students to a mathematical process in a non-European culture.
counting
addition
base ten
base twenty
expansion
Commutative Property of Addition
Associative Property of Addition
African Mende Addition could be inserted into a basic skills mathematics, prealgebra or algebra course when reviewing or teaching the topics of whole number addition and properties of addition.
The Mende are the largest ethnic group in Sierra Leone, West Africa, with a population of over one million. They have a rich culture and excel in the traditional arts of carving, singing and storytelling. Mathematics is also a part of their traditional culture. When Mende people count, they use a method of addition - they add one to the previous number to get the next number. And when they do addition, they don’t say "five, six, seven" but rather "five oranges, six oranges, seven oranges." Mathematics is used by the Mende in their everyday lives, so they do not use numbers just as numbers, but instead must think of the numbers as being connected to something that they can count, like oranges.
To count, the Mende use a system called "puu". The word "pu" in Mende relates to the process of using two hands to scoop rice from one container and put it into another container. The two hands together have ten fingers, so we can say that the counting system used is base ten. The Mende have another way of describing counting called "nuu yila gboryongor" that relates to the fingers and toes of a person being completely counted. The fingers and toes add to twenty, so we can say that the counting system is base twenty. The word "mahu" in Mende means add to, and this word is used when counting to show that the counting process is really a system of adding to previous numbers to get the next numbers.
In the United States, we have a method of expanding numbers by using their place value. For example, the number 23,874 can be written in expanded form as
20,000 + 3,000 + 800 + 70 + 4. The Mende use a similar method of expanding numbers to perform addition. This method also uses the Commutative and Associative Properties of Addition.
Here is an example of Mende addition.
225 oranges + 112 oranges = 200 oranges + 100 oranges = 300 oranges
20 oranges + 10 oranges = 30 oranges
5 oranges + 2 oranges = 7 oranges
300 oranges + 30 oranges + 7 oranges = 337 oranges
We can re-write the problem like this:
225 + 112 = 200 + 20 + 5 + 100 + 10 + 2 Expansion
200 + 100 + 20 + 10 + 5 + 2 Commutative Property
(200 + 100) + (20 + 10) + (5 + 2) Associative Property
300 + 30 + 7 Addition
337 Addition
Here is a more challenging problem:
479 bags of rice + 264 bags of rice = 400 bags + 200 bags = 600 bags
70 bags + 60 bags = 130 bags
600 bags + 100 bags = 700 bags
(using the hundreds above and leaving 30)
9 bags + 4 bags = 13 bags
30 bags + 13 bags = 43 bags
700 bags + 43 bags = 743 bags
We can re-write the problem like this:
479 + 264 = 400 + 70 + 9 + 200 + 60 + 4 Expansion
400 + 200 + 70 + 60 + 9 + 4 Commutative Property
(400 + 200) + (70 + 60) + (9 + 4) Associative Property
600 + 130 + 13 Addition
600 + 100 + 30 + 13 Expansion
(600 + 100) + (30 + 13) Associative Property
700 + 43 Addition
743 Addition
1. Write two Mende addition problems. The numbers must have at least three digits. Remember that the Mende need to count something.
2. Solve the problems using Mende addition.
3. Re-write the solutions and state the properties and operations used.
Bockarie, Alex. (1993). " Mathematics in the Mende Culture: Its General Implication for Mathematics Teaching". School Science and Mathematics. 93(4), 208-211.