# Numbers get ‘Knotty’

Minutes until the bus comes, amount of money leftover for ice-cream, number of homework assignments due before Tuesday. . . Every day we have plenty of things to count and keep track of. Good thing we have numbers and paper to help us. But what about a society that had NO symbols to represent numbers? How would they keep track?

Rewind about 800 years and take a trip to the Inca Empire. These people had no way to write down numbers– no paper– and no symbols to represent numbers yet. The emperor of the time lived in the capital city of Cuzco. His huge empire, called Tahuantinsuyu (TA-wan-tin-suyu), was connected by a system of roads that joined the four quarters of the empire. The emperor and his family were very rich because they collected taxes from the people who lived throughout this empire. But how could the tax-collectors keep track of all that money they collected with no written numbers?

In Mesopotamia (Modern day Middle East), people at first used pebbles to represent numbers, and then later clay tablets with number symbols carved onto them. They could carry these tablets with them to keep track of the amounts of things.

In the Inca Empire, it was a long way from each of the quarters of the empire to the capital city. It would be hard to carry around all those heavy clay tablets. What do you think the Inca people used to keep track instead?

Introducing the QUIPU!

There are plenty of llamas in South America, right? Instead of using clay tablets, the Inca people used what was readily available: wool from all those llamas. Now, this quipu might look like a mop, but it was actually an elaborate system of knots to represent numbers. Here’s how it worked:

First, several strings were tied to a top cord. A group of knots were tied in the cord at various positions to represent numbers. The placement of the knots was important. For example, the knots on the bottom of the string represented units (ones) and the next highest cluster of knots meant tens. Next was the hundreds place and so on. In the example here, the number is 586. That is, a cluster of 6 knots in the ones place, a group of 8 knots in the tens place and 5 knots together in the hundreds place.

Like our own numbers, the Inca people used a system where the position of the knots made a difference in what number was represented. (We call this a positional number system)

Can you create your own quipu?

What to Do:

Lay a sturdy cord horizontally on a flat surface. (Give yourself plenty of room)

Tie 3 or 4 pieces of string so that they are perpendicular (vertical) to the top cord. Start at the bottom. Tie a few knots closely together. These are your ones. Leave an inch or two and tie another cluster of knots closely together. These are your tens. Finally, leaving another inch or two of space, tie a third cluster of knots. These will represent the hundreds.

What knotty number did you create?

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