When people counted in twenties

Quick answer

People in many cultures counted using twenties because they used their hands and feet to count, which gave them twenty fingers and toes. This system is called a base-20 or vigesimal system.

Learning outcome

By the end of this page, you will understand how some cultures counted in twenties and why they did it, and you will be able to show how to count to 20 using your hands and feet.

• You can count to 20 by using your hands and feet.
• You can explain why some cultures used base-20 counting.
• You can see how numbers are written in base-20 in some cultures.

Why this matters

Understanding how people counted in the past helps us see how maths developed. It shows us that maths isn't just about numbers today, but it's also about creativity and the way people solved problems. This knowledge helps you think about numbers in new ways and understand how different cultures use maths in their daily lives.

How it works

Counting in twenties is simple when you think about it. Imagine you have 20 fingers and toes. If you count each finger and toe, you get 20. So, if you want to count higher than 20, you can use this system to make bigger numbers. It's like having a special way to count using all your body parts.

Here’s how it works:

1. Count all your fingers and toes: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.
2. Use this system to count even higher numbers by grouping them in twenties.
3. Some cultures used this method for counting money, time, and even land.

Examples you can see

Let’s imagine you're in a story where you and your friend are counting apples in a basket. You have 20 apples, and you want to know how many more you need to have 40 apples.

Using base-20 counting:

• 20 apples = 1 group of 20
• 40 apples = 2 groups of 20

This is like saying you have 2 sets of 20 apples, so you have 2 times 20, which is 40.

Another example: if you are at a party and there are 60 people, you can think of this as 3 groups of 20 people. This makes it easier to understand big numbers!

Some cultures, like the ancient Mayans and the Celtic peoples, used base-20 counting. The Mayans even had a special symbol for zero in their number system!

Try it as a mini adventure

Let’s go on a counting adventure! Imagine you are a young explorer in an ancient land. You have found a treasure map that says, “Count to 100 by twenties to find the treasure.”

Your first step:

1. Count all your fingers and toes to make 20.
2. Count 20 more to get to 40.
3. Count 20 more to get to 60.
4. Count 20 more to get to 80.
5. Count 20 more to get to 100.

Each time you count 20, you’ve found a new part of the treasure map. How many times did you count 20 to get to 100? That’s right, 5 times!

Common mistakes

• Mistake: Thinking that 20 is a group of 10, not 20.
  Why it happens: Confusion between base-10 and base-20.
  Fix: Use your hands and feet to show 20 items.
• Mistake: Counting 20 fingers instead of 10 fingers and 10 toes.
  Why it happens: Not paying attention to what is being counted.
  Fix: Count your fingers and toes separately, then add them.
• Mistake: Mixing up base-20 with base-10.
  Why it happens: Familiarity with the numbers 1 to 10.
  Fix: Practice counting in groups of 20 using objects or your body.

Parent and carer guide

As a parent or carer, you can help your child by:

1. Using your hands and feet to show how 20 items make one group.
2. Playing counting games where you count in twenties together.
3. Looking at old number words or stories about different cultures.
4. Encouraging your child to draw or act out how they would count in twenties.
5. Using real-life examples like counting toys or pieces of fruit in groups of 20.

Remember, it's okay if your child gets confused at first. The key is to keep practicing and making it fun. Don’t worry if they make mistakes – they’re part of the learning process!

Practice questions

1. How many fingers and toes do you have altogether?
2. If you have 2 groups of 20 apples, how many apples do you have?
3. How many times do you need to count 20 to get to 80?
4. Can you show how to count to 60 using groups of 20?
5. What are two cultures that used base-20 counting?

Answers:

1. You have 20 fingers and toes.
2. You have 40 apples.
3. You need to count 20 four times to get to 80.
4. You count 20, 40, 60 – so 3 groups of 20.
5. Mayans and Celts used base-20 counting.

FAQ

Why did people count in twenties?

People counted in twenties because they used their hands and feet to count, which gave them 20 items to count. This system was used by ancient cultures like the Mayans and Celts.

Is base-20 counting still used today?

Not often in everyday life, but some cultures still use it for special purposes. It's also used in some games and for historical learning.

How can I practice counting in twenties?

You can practice by counting your fingers and toes, using objects like blocks or coins, or even counting in a game with friends.

What is the difference between base-10 and base-20?

Base-10 uses groups of 10, while base-20 uses groups of 20. In base-10, 20 is two tens. In base-20, 20 is one group of twenty.

Can I use base-20 counting to count big numbers?

Yes! You can count 20, 40, 60, 80, 100, and so on by grouping numbers in twenties. This makes it easier to understand large numbers.