Maths History
Counting with knots and strings
Explore quipu-style record keeping and string maths as a pattern and place-value adventure.
Quick answer
Counting with knots and strings is an ancient way of keeping track of numbers using knots tied on strings. It's a way to record information without writing, and it helps us understand how people in the past used patterns and place-value to solve problems.Learning outcome
By the end of this page, you will understand how to use knots and strings to show numbers and solve simple problems, just like ancient people did. Success signs:- You can make a string with knots to show a number
- You can read a string with knots to find the number
- You can solve a simple problem using knots and strings
- You can explain how knots help us understand place-value
Why this matters
Counting with knots and strings was used by many cultures long before we had numbers or writing. It helped people keep track of things like animals, crops, or money. This way of counting shows how we can use patterns, repetition, and place-value to understand and solve problems. It's a fun way to learn about how maths was used in the past and how it still helps us today.How it works
Using knots and strings is a way to show numbers by making groups. You can tie one knot for each item you want to count. If you have many items, you can group them together. For example, if you have 10 items, you can tie one knot, then make a group of 10 knots, and so on. The position of knots can show different values, like ones, tens, hundreds, and more. This is called place-value. You can also use different types of knots to show different things.Examples you can see
Let’s imagine you are a trader in an ancient village. You have 37 sheep. You can use a string with knots to show this.- First, tie 7 single knots to show 7 sheep
- Then, tie 3 groups of 10 knots to show 30 sheep
- So, you have 3 groups of 10 and 7 single knots
| Number | How to show it with knots |
|---|---|
| 1 | 1 single knot |
| 5 | 5 single knots |
| 10 | 1 group of 10 knots |
| 15 | 1 group of 10 knots + 5 single knots |
| 23 | 2 groups of 10 knots + 3 single knots |
Try it as a mini adventure
Let’s go on a counting adventure! Imagine you are a trader in an ancient village. You have a string with knots and need to find out how many items you have.- 1st time: You see 1 group of 10 knots and 4 single knots. How many items is this?
- 2nd time: You see 2 groups of 10 knots and 7 single knots. How many items is this?
- 3rd time: You see 4 groups of 10 knots and 2 single knots. How many items is this?
- 4th time: You see 5 groups of 10 knots and 9 single knots. How many items is this?
- 5th time: You see 0 groups of 10 knots and 3 single knots. How many items is this?
Common mistakes
- Mistake: Thinking that 1 group of 10 knots and 3 single knots equals 13.
Why it happens: Mixing up the place-value.
Fix: Remember that the group of 10 knots is worth 10, and 3 single knots are worth 3. So, 10 + 3 = 13. But that’s correct! The mistake is thinking the group of 10 knots is worth 1.
Correct answer: 1 group of 10 = 10, 3 single knots = 3. Total = 13. - Mistake: Counting knots wrong when there are many.
Why it happens: Not grouping knots properly.
Fix: Make sure to count groups of 10 first, then count the single knots.
Correct answer: Count 10 knots as one group, then count the rest. - Mistake: Thinking that 0 groups of 10 and 5 single knots = 50.
Why it happens: Not understanding that 0 groups of 10 = 0.
Fix: Remember that 0 groups of 10 = 0, so only the single knots count.
Correct answer: 0 groups of 10 = 0, 5 single knots = 5. Total = 5.
Parent and carer guide
You can help your child by making a string with knots at home. Use a piece of string and tie knots in different groups. Ask your child to read the number you made and to make numbers using knots. You can also play a game where you tell your child a number and they make it with knots. This helps them understand how place-value works. Encourage them to talk about what each group of knots means. If they make a mistake, gently correct them and ask them to count again. Don’t worry if they don’t get it right the first time – it’s all part of learning!Practice questions
- How many knots are needed to show 24?
- How many knots are needed to show 100?
- How many knots are needed to show 59?
- How many knots are needed to show 0?
- How many knots are needed to show 1000?
- 2 groups of 10 knots and 4 single knots = 24 knots
- 10 groups of 10 knots = 100 knots
- 5 groups of 10 knots and 9 single knots = 59 knots
- 0 knots
- 100 groups of 10 knots = 1000 knots
FAQ
What is a quipu?
A quipu is a system of knots and strings used by the Inca people in South America to keep records. It was used to count and store information.
Why did people use knots and strings to count?
People used knots and strings because they did not have writing or numbers. It was a way to keep track of things like crops, animals, or taxes.
How does counting with knots help us understand place-value?
Counting with knots shows how groups of 10 can be used to make bigger numbers. This helps us understand that each position in a number has a value.
Can I use knots to count anything?
Yes! You can use knots to count anything you want to keep track of, like toys, books, or even steps you take.
Are there any modern uses of knots for counting?
Yes, some people still use knots for counting in certain situations, like in traditional crafts or for educational purposes.