All Object Lessons
Mathematics & Number

The Quipu: Knotted Cords That Ran an Empire

⏱ 45 minutes 🎓 Primary & Secondary 📚 mathematics, history, geography, language, ethics
Core question How did the largest empire in pre-Columbian America keep records of millions of people without writing — and what does that tell us about what counts as 'writing'?
An Inca quipu, made of dyed cotton cords. Each colour and each knot carried meaning. With these, the Inca state ran an empire of millions of people without writing as we know it. Photo: bobistraveling / Wikimedia Commons / CC BY 2.0
Introduction

Imagine running a country of about 12 million people, stretched across high mountains, deep valleys, deserts, and coast. You have to know how many people live in each village, how much food each region grows, how many soldiers each town owes the army, and how taxes are paid. You have to send and receive messages over thousands of kilometres of difficult country. Now imagine you do all of this without writing — at least, not the kind of writing students learn at school. The Inca empire, which ruled much of western South America from the 1400s to the 1500s, did exactly this. They used a tool called the quipu — a bunch of coloured cords with knots tied along them. Officials called quipucamayocs, or 'knot-keepers', could read and write quipus. The system was so accurate that the Inca state could track its 12 million people in detail. When the Spanish arrived in the 1530s, they were amazed — and then they burned most of the quipus, calling them idols. About 1,500 survive. Some can be partly read; most cannot. This lesson asks how a few cords could run an empire, and what we lose when one way of recording the world is destroyed.

The object
Origin
The Andes mountains of South America, in what is now Peru, Bolivia, Ecuador, and Chile. Used by the Inca empire and earlier Andean cultures.
Period
From at least 200 CE to about 1600 CE — over 1,400 years. A few are still made today.
Made of
Cotton, sometimes the wool of llamas, alpacas, or vicuñas, dyed in many colours. The knots and the cord positions carry the meaning.
Size
Vary widely. Small quipus have a few cords and fit in a hand. Large ones have hundreds of cords and are bigger than a person.
Number of objects
About 1,500 quipus survive today, mostly from after about 1400 CE. Many more were destroyed by Spanish conquerors in the 1500s, who saw them as 'idols'.
Where it is now
Most surviving quipus are in museums in Peru, Chile, Germany, and the United States. A few villages in the Andes still make and use simpler quipus today.
Before you teach this — reflect

Questions for you

  1. Most students think of writing as letters on a page. The quipu is a different kind of system. How will you stretch their idea of what 'writing' means without confusing them?
  2. The Spanish destroyed most quipus deliberately. How will you teach this honestly, as part of the story of colonisation, without making the lesson only about loss?
  3. Quipus are mathematical objects, but also something more. How will you do justice to both the maths and the cultural meaning?

Common student difficulties — tick any you have noticed

Discovery sequence
1
Imagine you have to remember three numbers — say, 47, 132, and 8. You have no paper. You have no phone. But you have a piece of string. You tie a knot for each unit. So 47 might be 4 knots high up the string, then a gap, then 7 knots lower down. Now you have remembered the number, just by tying knots in a special pattern. Is this writing?
Points to consider (for the teacher)

This is the start of the quipu idea. The Inca system used the same logic — knots in different positions on cords meant different numbers. They had a base-10 number system, like ours: a knot in the top section of a cord meant hundreds, a knot in the next section meant tens, a knot in the bottom section meant ones. So 47 had four knots in the tens position and seven knots in the ones position. By making cords hang from one main cord, a quipu could store many numbers at once. The full system had different kinds of knots — single knots, long knots, figure-of-eight knots — for different things. The colour of the cord, the way it was twisted, where it was attached, all carried meaning. Some scholars argue the quipu was a writing system. Others say it was a record-keeping system, like a spreadsheet but in cord. The honest answer is that it was both, and probably more. Students should see that 'writing' as we know it — letters in lines on a page — is just one way to record information. The quipu was another way, and a very powerful one.

2
The Inca empire stretched along the Andes from what is now Colombia to central Chile — a strip of land over 4,000 kilometres long. About 12 million people lived in it. The Inca state collected taxes, organised armies, ran storage warehouses, and kept census records of every village. Quipus did all of this. Trained officials called quipucamayocs (or khipu kamayuq) could read and write them. Why did the Inca choose cords over paper?
Points to consider (for the teacher)

This is a useful question because it gets students past the assumption that writing on paper is the obvious answer. The Andes did not have paper, but they had something even better: huge amounts of cotton and wool, plus thousands of years of weaving expertise. Cord was available, durable, and easy to carry. A quipu could be rolled up like a scroll and tucked into a bag. Two quipus could be compared by laying them side by side. They could be copied carefully when they wore out. They could be made by anyone with weaving skills, which in the Andes meant most people. Cords also work in three dimensions, while paper works in two — a quipu could store more types of information at once. Students should see that the Inca did not 'lack' writing. They had a record-keeping system perfectly adapted to their materials, their landscape, and their economy. The fact that it looks strange to us is about us, not about them. Many cultures have made similar choices — using knots, beads, sticks, or wood instead of paper. They are not failed attempts at writing. They are different inventions.

3
In 1532, Spanish soldiers led by Francisco Pizarro arrived on the Pacific coast of South America. Within a few years, they had captured the Inca emperor and taken control of much of the empire. The Spanish saw quipus everywhere. At first they used them — they realised quipucamayocs could keep accurate records. Then, in 1583, the Catholic Church declared quipus to be 'idols' and ordered them burned. Spanish priests destroyed most of the quipus they could find. About 1,500 quipus survive today. Many of them have been buried in tombs and only dug up recently. What was lost?
Points to consider (for the teacher)

A huge amount. Each destroyed quipu was a record — a census, a story, a tax record, a history, a family tree. We will never know how much was burned. Modern scholars can read the numerical information on some surviving quipus, but most of the more complex meanings — the ones that probably included narrative, names, and history — are lost or only partly understood. Some scholars think quipus could record stories and chronicles, not just numbers. The Spanish destruction was not because the quipus were dangerous. It was because they did not fit Spanish ideas of what writing should look like. Anything strange enough was suspect. This is a useful lesson about colonisation: it does not just take land. It often takes ways of knowing the world. The destroyed quipus are like a library that was burned. They are also a warning. Students should see that knowledge is fragile. The same kind of loss has happened in many other places — Maya books burned by Spanish priests, Indigenous Australian knowledge suppressed, African oral histories interrupted by the slave trade. The quipu is one of the clearest examples we have.

4
For a long time, scholars thought quipus only recorded numbers. New research is changing that. Some quipus seem to encode words and names, perhaps using the colour, twist direction, and position of cords as well as the knots. A few villages high in the Peruvian Andes still make simple quipus today, mostly to track livestock — sheep, llamas, alpacas. Some elders pass the skill down to grandchildren. Does this make the quipu still alive?
Points to consider (for the teacher)

Yes, in a real sense, although the full Inca system is mostly gone. The villages of Tupicocha and a few others still use quipus in community ceremonies, though their system is simpler than the full Inca one. Scholars work with these communities — and with surviving quipus from museums — to slowly read more of what was once recorded. New techniques like 3D scanning, AI pattern matching, and careful comparison with Spanish-era documents are turning up new findings every few years. Students should see that this is a story still being written. We do not know how much of the Inca quipu system can be recovered. We do know that some of it is being recovered, and that the people doing the work are often Quechua-speaking descendants of the Inca, working with international scholars. The quipu is not an object frozen in a museum. It is a living tradition, even if only barely, and a question we have not finished answering. Some of you may be alive when more of the answer is found.

What this object teaches

A quipu is a record-keeping device made of dyed cotton or wool cords, with knots tied along them. The cords hang from a main cord, and the position, type, and colour of each knot and cord carries meaning. Quipus were used by Andean cultures for over 1,400 years, and reached their greatest development under the Inca empire from about 1400 to 1532 CE. The Inca state used quipus to record census information, taxes, military matters, and probably much more. Officials called quipucamayocs were trained to read and write them. When the Spanish conquered the Inca empire in the 1530s, they at first used quipus, then declared them idols and burned most of them. About 1,500 survive. Modern scholars, often working with Andean communities, are slowly learning to read more of them. A few villages in the Andes still make and use simple quipus today.

QuestionWhat many people assumeWhat is actually true
Did the Inca have writing?NoThey had quipus, which could store census, tax, and probably narrative information. Whether you call it 'writing' depends on your definition.
Was the Inca empire small or large?Small and localIt had about 12 million people and stretched over 4,000 km. It was the largest empire in pre-Columbian America.
Have quipus been deciphered?Either yes or noNumerical content can be read on many quipus. More complex content is partly understood, with new findings every few years.
Why are there so few quipus?They just rotted awayMost were deliberately burned by Spanish colonisers in the 1500s, who declared them religious idols
Are quipus still made today?No, they are extinctA few Andean villages still make simple quipus, mostly for tracking livestock. The skill is being passed down.
Key words
Quipu
A record-keeping device made of knotted cords. Used by Andean cultures, especially the Inca, to store information. The word comes from Quechua and means 'knot'.
Example: A medium quipu might have 20 to 30 hanging cords, each with several knots, all attached to one main cord. Some had hundreds of cords.
Inca
The empire that ruled much of western South America from about 1400 to 1532 CE. Their capital was Cusco, in modern-day Peru. Their language, Quechua, is still spoken by about 8 million people today.
Example: The Inca empire was the largest in pre-Columbian America, with about 12 million people and over 40,000 km of paved roads.
Quipucamayoc
A trained Inca official who could read and write quipus. The word means 'keeper of the knots' in Quechua. Quipucamayocs were respected and important members of Inca society.
Example: Each Inca village had at least one quipucamayoc to keep records. The state had many more, working at every level of government.
Andes
The mountain range that runs along the western side of South America, from Venezuela to the south of Chile and Argentina. The Inca empire and many earlier cultures lived in and around these mountains.
Example: The Andes contain some of the highest cities in the world. Cusco, the Inca capital, sits at over 3,400 metres above sea level.
Quechua
The main language of the Inca empire, still spoken today by about 8 million people across Peru, Bolivia, Ecuador, and other Andean countries. Many words from Quechua have entered English — including 'quinoa', 'condor', and 'llama'.
Example: Many of the technical words used to study quipus today come from Quechua, because Quechua-speaking communities still know the most about them.
Pre-Columbian
The period in the Americas before Christopher Columbus arrived in 1492. It includes thousands of years of complex civilisations across the continent.
Example: The Inca, the Aztecs, and the Maya are three of the most famous pre-Columbian civilisations. The quipu is one of the clearest pieces of evidence of how sophisticated their record-keeping was.
Use this in other subjects
  • Mathematics: The Inca used a base-10 number system, like ours. Try reading some quipu numbers: a cord with 3 knots high up, 4 knots in the middle, and 6 knots low down means 346 (3 hundreds, 4 tens, 6 ones). Make a class quipu using string and discuss what makes our number system the same and different.
  • Geography: On a map of South America, draw the rough outline of the Inca empire — from southern Colombia down to central Chile, mostly along the Andes. Discuss what this terrain is like (high mountains, deep valleys, desert coast, jungle on the eastern side). How might governing such a country shape the records you choose to keep?
  • History: Build a class timeline showing the Inca empire (1400-1532) alongside other things happening in the world: the Ming dynasty in China, the Renaissance in Italy, the Mali Empire in Africa, the rise of the Ottoman Empire. The Inca were one of many great cultures of the time, not a 'lost' or 'isolated' civilisation.
  • Language: Discuss the difference between writing and other ways of recording information. Lists, calendars, music notation, computer code, and emoji are all systems of symbols too. Is the quipu more like writing, or more like a spreadsheet, or more like something we have not got a word for? It may be all three.
  • Art: Each student designs a small 'personal quipu' on paper or with string. The quipu must record three things about them — for example, age, number of siblings, favourite season — using only colour and knot positions. Display the quipus and try to read each other's. This is exactly what Inca officials did, but with a much wider system.
  • Citizenship: The Spanish destroyed most quipus deliberately. Discuss how knowledge can be lost on purpose, and how this has happened in many places — burned books, banned languages, lost crafts. What kinds of knowledge are we losing today, and what can we do about it?
Common misconceptions
Wrong

The Inca had no writing.

Right

The Inca had a record-keeping system, the quipu, that did almost everything writing does. Whether you call it 'writing' depends on your definition. It was certainly a sophisticated information system that could run an empire of 12 million people.

Why

'Writing' is often defined narrowly as letters on a page. By that definition, many cultures had no writing — but they all had ways to record what mattered to them. The Inca's way was knots in cords.

Wrong

The Inca empire was small and local.

Right

The Inca empire stretched over 4,000 km from north to south, with about 12 million people. It was the largest empire in pre-Columbian America, and one of the best-organised states in the world at its time.

Why

Older books often described pre-Columbian American societies as 'tribes' or 'small kingdoms'. The Inca were neither.

Wrong

Quipus only stored numbers.

Right

Numbers were one important use, but new research suggests quipus also encoded words, names, narratives, and other information. The full range of what they could record is still being worked out.

Why

Saying 'just numbers' makes the quipu sound less impressive than it is. The system was probably as flexible as writing, just in a different form.

Wrong

Quipus are mostly understood now.

Right

Numerical quipus can be read fairly well. More complex quipus are only partly understood, and scholars are still finding new things every few years. The story is open.

Why

Decipherment is hard, and quipus are physical objects that need careful study. Some of the work is being done by Andean communities themselves, working with international scholars.

Teaching this with care

Treat the quipu as a sophisticated record-keeping system, not as a curiosity or a 'primitive' precursor to writing. The Inca built and ran a state of 12 million people with this tool; that is a major achievement. Use the proper terms — Inca, Quechua, quipucamayoc — and pronounce them as best you can (Inca is roughly 'IN-ka', Quechua is roughly 'KETCH-wa', quipucamayoc is roughly 'KEE-poo-ka-MA-yok'). Do not call Andean cultures 'lost' or 'mysterious' — they are alive today, with about 8 million Quechua speakers across South America, and many descendants of the Inca who remain. When discussing the Spanish destruction of quipus, be honest and plain, but do not paint all Spaniards as villains or all Inca as victims; the Inca empire itself was built on conquest of other Andean peoples, and the moral history is complicated. Avoid using the word 'primitive' for any society in this story; the Inca had paved roads, suspension bridges, terraced farms, and tax records that worked across thousands of kilometres. When discussing modern villages that still make quipus, treat them with respect — these are real communities, not anthropological specimens. Finally, do not present this lesson as 'one strange object'; the quipu is one of many ways humans have recorded the world, and the lesson is bigger than the cord.

Check what students have understood

Answer each question in one or two sentences. Use what you have learned about the quipu.

  1. What is a quipu, and what was it used for?

    A quipu is a record-keeping device made of dyed cotton or wool cords with knots tied along them. The Inca used quipus to record census information, taxes, military records, and probably stories and other information.
    Marking note: Award full marks for any answer that mentions the cords, the knots, and at least one use. Specific names of parts are helpful but not essential.
  2. How big was the Inca empire?

    It stretched along the Andes for over 4,000 kilometres, from what is now southern Colombia to central Chile. About 12 million people lived in it. It was the largest empire in pre-Columbian America.
    Marking note: Strong answers will mention either the geographical reach or the population. Both is even better.
  3. How did the Inca state use quipus to run its empire?

    Trained officials called quipucamayocs read and wrote quipus. They kept records of how many people lived in each village, how much food was stored, how much was owed in taxes, and how many soldiers each town owed the army.
    Marking note: Award full marks for any answer that mentions the officials by name (or describes their role) and gives at least one specific use.
  4. Why are there so few quipus today?

    Most were destroyed deliberately by Spanish colonisers in the 1500s. The Catholic Church declared them religious idols and ordered them burned. About 1,500 survive.
    Marking note: Accept any answer that mentions the deliberate Spanish destruction. The point is that quipus were not just lost to time.
  5. Are quipus still being studied or used today?

    Yes. A few Andean villages still make simple quipus, mostly for tracking livestock. Scholars, often working with Andean communities, are slowly learning to read more of the surviving Inca quipus, with new findings every few years.
    Marking note: Award full marks for any answer that mentions either continued use, continuing research, or both. The point is that this is a live story, not a finished one.
Discuss together

These questions have no single right answer. Talk in pairs or small groups, then share your ideas with the class.

  1. Is the quipu a form of writing? Why does the answer matter?

    This is a real debate among scholars. Some say yes — quipus could encode complex information, including words and stories. Others say no — they are not phonetic, and they do not record speech the way letters do. Strong answers will see that the question depends on what 'writing' means. Push students past the obvious answer. End by asking: who decides what counts as writing? Whose definitions get to win? The quipu is a good example of why these questions matter.
  2. The Spanish burned most quipus because they did not understand them. What other kinds of knowledge might be at risk today because no one is paying attention?

    This is a hard question that connects the lesson to the present. Students might suggest endangered languages, traditional crafts, oral histories, local knowledge of plants or weather, or even the everyday memories of older relatives. The deeper point is that knowledge needs to be passed on, and when it is not, it can vanish in a generation. The quipu is one of the most dramatic examples we have.
  3. If you had to record everything important about your life on a few cords with knots, what would you record? What would you leave out?

    This is a creative question that brings the lesson home. Students may suggest birthdays, names, places they have lived, important events, or numbers like grades and scores. Push them to think about what gets left out — feelings, stories, music, smells, jokes. The deeper point is that any system of recording captures some things and not others. Writing on paper has the same limits. The quipu was a different choice with different strengths.
Teaching sequence
  1. THE HOOK (5 min)
    Without saying anything about the lesson, ask: 'How could you record three numbers — say 47, 132, and 8 — without paper, pen, or phone?' Take a few answers. Some students will think of fingers, sticks, or memorising. Then say: 'In an empire of 12 million people, you would need millions of these recordings every year. A whole civilisation worked out how to do it — with knotted string. Today we are going to look at how.'
  2. INTRODUCE THE OBJECT (10 min)
    Describe the quipu: a bundle of dyed cotton cords hanging from one main cord, with knots tied along each one. Used by Andean cultures for over 1,400 years, and especially by the Inca empire from about 1400 to 1532 CE. Trained officials called quipucamayocs could read and write them. Pause and ask: 'Why might cords be a good way to record information?' Listen to answers. They will lead naturally into the ideas of durability, portability, and three-dimensional storage.
  3. UNDO THE WRONG STORIES (15 min)
    On the board, write three statements: (1) The Inca had no writing. (2) The Inca empire was a small kingdom. (3) Quipus stored only numbers. Take each in turn. Replace each with what we now know — the quipu was a sophisticated information system; the Inca empire had 12 million people and stretched over 4,000 km; quipus may have stored words, names, and stories as well as numbers. End by asking: 'Why might these wrong stories have lasted so long?' Bring in the Spanish destruction gently — 'because the Spanish burned them, and then the people who wrote the books were Spanish'.
  4. THE NUMBER QUIPU ACTIVITY (10 min)
    Each pair of students gets a piece of string about 30 cm long. They tie knots to record three numbers — their age, the number of people in their family, and one more number they choose. The knots must be in three groups, with high knots for hundreds, middle knots for tens, and low knots for ones. They swap with another pair and try to read the numbers. Discuss: how easy was it? What would you need to add to make this a real quipu? Colour, more cords, perhaps a hierarchy of cords from one main cord.
  5. CLOSING (5 min)
    Ask: 'Most quipus were destroyed. What might we have learned about the Inca that we will never know?' Take a few honest answers. End by saying: 'The quipu is one of the most clever record-keeping systems humans have ever made. Most of it is gone. Some of it is being read again, slowly, by people who care. Whenever someone tells you a civilisation had no writing, ask what they mean by writing — and remember that the cords kept their secrets for a long time.'
Classroom materials
The Class Quipu
Instructions: Stretch a long piece of string or cord across the front of the classroom — this is the main cord. Each student adds a hanging cord (a piece of string about 30 cm long, tied to the main cord). On their cord, they tie knots to record three things: their age (knots high), the number of people in their household (knots middle), and the number of years they have been at this school (knots low). Discuss: how does the class quipu compare with a class register? What can it show that a list cannot? What can a list show that it cannot?
Example: In Mr Quispe's class, 30 students made cords and tied them to the main cord. By the end, the room had a quipu nearly two metres long. The teacher said: 'Look at this. With one glance, you can see something about every person in the class. The Inca did this for 12 million people. They had warehouses full of cords. The information system was as careful as anything anywhere in the world at the time.'
What Was Lost
Instructions: In small groups, students imagine they are descendants of an Inca quipucamayoc whose family's quipus were burned by Spanish soldiers. They write a short paragraph saying what they would tell a researcher today about what was on the destroyed quipus. The paragraph should be specific — names, places, events, ideas, numbers. Each group reads aloud. Discuss: how much can be remembered, and how much is lost forever?
Example: In one class, the strongest paragraph said: 'My great-great-grandmother kept the records of our village. The numbers are gone — every harvest for 200 years, gone. But the songs that used the numbers are still here. So we know roughly when there was hunger and when there was plenty. We just cannot prove it any more.' The teacher said: 'This is exactly what real Andean families and scholars are doing now. Slowly, carefully, putting the knowledge back together.'
Many Ways to Record
Instructions: On the board, list as many ways to record information as the class can think of in five minutes. Examples: writing on paper, writing on screens, photographs, videos, voice recordings, music notation, sign language, drawings, maps, knots, beads, sticks, woven patterns, scars, stories told over and over, songs, dances. Discuss: which of these have we used in school today? Which would the Inca have understood? Which would Inca have looked at and said, 'Yes, that is recording'? The quipu fits with most of them, in different ways.
Example: In Ms Mamani's class, students filled most of the board with different recording methods. The teacher said: 'In every culture, in every time, humans have figured out ways to keep what matters. Some of these ways look strange to us. Others are familiar. None of them is the only correct one. The quipu is one of the most beautiful examples we have, and it is a reminder that there has never been only one way to write the world down.'
Where to go next
  • Try a lesson on the Rosetta Stone for another famous case of an unfamiliar writing system that took centuries to decode. The two stories run parallel — one was eventually read, the other is still being read.
  • Try a lesson on the cuneiform tablet to see another ancient record-keeping system, this time on clay rather than cord.
  • Try a lesson on the Maya codices, only a handful of which survived the Spanish burnings — a closely related story with a different ending.
  • Connect this lesson to maths class with a longer project on number systems around the world. Different cultures have built numbers differently — base 10, base 20, base 60, and more. The quipu is one of many examples.
  • Connect this lesson to language class with a discussion of what 'writing' means. Different definitions give different answers. The quipu is a good test case for any of them.
  • Connect this lesson to citizenship by asking students to think about what is being recorded about them today, and by whom. Are records always neutral? Who decides what to keep?
Key takeaways
  • A quipu is a record-keeping device made of dyed cotton or wool cords with knots tied along them. The cords and knots carry information.
  • Quipus were used in the Andes for over 1,400 years, and reached their greatest development under the Inca empire from about 1400 to 1532 CE.
  • The Inca state used quipus to run an empire of 12 million people, stretching over 4,000 km along the Andes mountains.
  • Most quipus were deliberately burned by Spanish colonisers in the 1500s, who saw them as religious idols. About 1,500 survive.
  • Numerical content can be read on many quipus today. More complex content is partly understood, with new findings every few years. Some Andean villages still make and use simple quipus.
  • The quipu is one of the clearest pieces of evidence that 'writing' as we know it — letters on paper — is one choice among many. There is more than one way to record the world.
Sources
  • Signs of the Inka Khipu: Binary Coding in the Andean Knotted-String Records — Gary Urton (2003) [academic]
  • The Khipu Field Guide — Khipu Database Project, Harvard University (2024) [institution]
  • Untying the Khipu Code — BBC Future (2018) [news]
  • Code of the Quipu — Marcia Ascher and Robert Ascher (1997) [academic]
  • Quipus from the Inca Empire (object pages) — Larco Museum, Lima (2024) [museum]