The abacus story

Quick answer

The abacus is an ancient calculating tool that helps people count and do maths using beads. It’s still used today in some countries and helps children learn mental maths.

Learning outcome

By the end of this page, you will understand how the abacus works and how it helps with counting and addition.

• You can explain what an abacus is and where it comes from.
• You can use an abacus to show numbers up to 99.
• You can add two small numbers using beads.
• You can see how abacus maths helps with mental maths.

Why this matters

Learning about the abacus helps you understand how people did maths before calculators. It also shows how beads and groups can help you count and add. Many children still use abacus tools today to learn mental maths, which makes numbers easier to understand. You might even use the abacus to help with your homework or in a fun game!

How it works

The abacus is a frame with beads that you move to show numbers. Each abacus has rows of beads. In a traditional abacus, there are usually 13 beads in each row. The beads are divided into two parts:

• Top beads: These are usually one bead per row and are worth 5.
• Bottom beads: These are usually four beads per row and are worth 1 each.

To show a number:

1. Move beads towards the middle bar to represent the number.
2. Each row shows a different place value – like tens and units.
3. For example, to show 12, you would move one bead from the top row (worth 5) and two beads from the bottom row (worth 2) in the tens row, and one bead from the bottom row in the units row.

Examples you can see

Let’s imagine you are using a simple abacus to show the number 23.

• On the tens row, move 2 beads from the bottom row (2 × 1 = 2).
• On the units row, move 3 beads from the bottom row (3 × 1 = 3).

Another example: to show 47

• On the tens row, move 4 beads from the bottom row (4 × 1 = 4).
• On the units row, move 2 beads from the top row (2 × 5 = 10) and 2 beads from the bottom row (2 × 1 = 2). Total = 10 + 2 = 12.

Wait! Let’s correct that. To show 47:

• On the tens row, move 4 beads from the bottom row (4 × 1 = 4).
• On the units row, move 1 bead from the top row (1 × 5 = 5) and 2 beads from the bottom row (2 × 1 = 2). Total = 5 + 2 = 7.

So 47 = 4 tens and 7 units.

Try it as a mini adventure

Imagine you are a trader in ancient times, and you need to count your goods using a special abacus. You have 35 apples and your friend gives you 24 more. You must use your abacus to show how many apples you now have. Let’s go step by step!

1. Start by showing 35 apples on your abacus.
2. Then add 24 apples by moving beads.
3. Count the total beads to find the answer.

Let’s do it together:

• First, show 35: 3 beads in the tens row, 5 beads in the units row.
• Then, add 24: 2 more beads in the tens row, 4 more beads in the units row.
• Count your beads: 5 tens and 9 units = 59 apples.

You did it! You used the abacus to add 35 + 24 = 59. Great job!

Common mistakes

• Mistake: Thinking that each bead is worth 10.
  Why it happens: The beads are grouped, and it’s easy to confuse the place values.
  Fix: Remember that top beads are worth 5 and bottom beads are worth 1.
• Mistake: Mixing up tens and units when moving beads.
  Why it happens: Young children often confuse the order of numbers.
  Fix: Always start with the units row and then move to the tens row.
• Mistake: Adding 5 + 5 and getting 10 instead of 10 beads.
  Why it happens: Children might think the top bead is worth 10.
  Fix: Use the abacus to show 5 + 5 = 10 by moving beads correctly.

Parent and carer guide

Help your child learn about the abacus by:

1. Using a real or paper abacus to show numbers together.
2. Practising counting in tens and units using beads.
3. Playing a simple game where you say a number and your child shows it on the abacus.
4. Encouraging them to explain how they moved the beads.
5. Not worrying if they make a mistake – it’s part of learning!

Remember, the abacus is a fun way to explore numbers. It’s not about speed, but about understanding how numbers work.

Practice questions

1. How do you show the number 18 on an abacus?
2. What is 23 + 15 using an abacus?
3. How many beads do you move to show 47?
4. What is 39 + 21?
5. How many beads are in the top row of a standard abacus?

Answers:

1. Move 1 bead in the tens row (top), 3 beads in the units row (bottom).
2. 38
3. 12 beads (4 in tens row, 7 in units row)
4. 60
5. 13 beads

FAQ

What is an abacus?

An abacus is a counting tool made of beads on a frame. It helps people do maths by moving beads to show numbers.

Where did the abacus come from?

The abacus was invented in ancient times, probably in Babylon or China. It was used to count money and goods.

Is the abacus still used today?

Yes! Some people still use it in schools and markets, especially in Asia. It helps children learn mental maths.

How does using an abacus help with mental maths?

Using the abacus helps you understand how numbers are made up of tens and units. This makes it easier to add and subtract in your head.

Can I make my own abacus?

Yes! You can make a simple abacus with a cardboard frame and small beads or counters. Try it with your child!