The Inca, whose empire ran along the Andes of South America, kept records on khipus (quipus, from the Quechua word for knot): a main cord with many cords hanging from it, sometimes hundreds. Numbers were tied in base ten, the way we write them. The ones sit at the bottom of a cord, the tens above them and the hundreds above that. In the tens and hundreds a cluster of single knots gives the digit; in the ones place a long knot with 2 to 9 turns gives the digit and a figure-eight knot means 1; a place with no knot is zero. Some top cords hold the sum of the cords in their group, a check on the record. Khipu keepers (khipukamayuq) used them for counts of people, harvests, herds and storehouses. The knot rules on these pages follow Marcia and Robert Ascher's study of hundreds of surviving khipus; the village counts are made up.
Five pages of 2nd and 3rd grade place value on khipu cords, each with a key to the knots at the top. Page 1 reads eight cords and writes each number. Page 2 ties eight numbers on empty cords, with a dashed zone for each place. Page 3 reads two cords, adds them and ties the sum. Page 4 has two groups with top cords: one top cord to find, and one missing cord to work out from its top cord. Page 5 reads a khipu of five villages into a place value table and answers three questions. The first problem on pages 1 to 3 is a worked example.
Tie a real khipu with yarn first: a long main cord and a few short ones, with single knots for tens and a long knot (wrap the yarn round several times before pulling it through) for ones. Ask why the ones need a different knot from the tens (a long knot of one turn would look like a single knot, so 1 is a figure eight).
Tie your family's ages or your house number on a piece of string, then swap strings and read each other's.
This pack supports the following Common Core State Standards for Mathematics:
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Place value on the khipu (quipu), the knotted cords the Inca of the Andes kept their numbers and records on. Students read and tie hundreds, tens and ones as knots, add two cords, find a top cord's sum and fill in a village record table.
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