This activity is based on an example in this text. In pre-colonial Western Africa, the Yoruba people lived in what is now southern Nigeria. This group of people organized their numbers around groups of 20, and had a sophisticated mathematical system for buying and selling using small cowry shells as currency. Both men and women were merchants; let’s pretend we are watching a woman selling goods in the market.

Our merchant is calculating . She begins by setting out 20 groups of 20 cowrie shells. Let’s call this “Step 1”. We will draw small circles to represent the shells.

She first rearranges the shells by moving one shell from each of the groups into a new group she is forming. We’ll show this in the next picture and call this “Step 2”.

Finally, she rearranges the shells from Step 2, removing two more shells from one group and placing them in two of the groups of to make groups of . Let’s draw this in the next picture and call it “Step 3”.

(a)
Which part of the diagram shows , and how do you know?
(b)
How many shells are in the diagram all together, and how do you know?
(c)
How could the merchant use mental math or properties of multiplication to find the solution to from the Step 3 picture? What is the final answer?
Marcus thinks that is the same as . How could you use the pictures above to help Marcus understand why this thinking is incorrect?
Parsa thinks that should be equal to . Use the pictures above or draw a new picture to help Parsa understand why this thinking is incorrect.
How could you use a similar method (with a different picture) in our base ten system to solve ?
2025-10-03 13:20:28