Learn what an abacus is and how to do abacus addition and subtraction. You’ll find information on using the different kinds of Abacus, and suggested resources.
What is an abacus?
An abacus is a Maths tool that uses lines of beads to represent numbers. By moving the beads, you can work out and show different amounts. It’s a visual and tactile method, were seeing and/or feeling the beads will tell you the answer. This means that abacuses are particularly useful for blind and partially sighted people and are great for teaching people with different learning styles.
An abacus is sometimes known as a counting frame and can be thought of as the earliest calculator form. People have been using abacuses for thousands of years, and many different kinds have developed over this time.
What are the different kinds of Abacus?
There are far too many types of Abacus to talk about here, but three are most common for teaching addition and subtraction. They can be thought of as broad categories with lots of variation.
School abacus
This is the popular name for the type of Abacus you might have first thought of when you came to this page. A school abacus has ten colorful beads on each of its horizontal rows.
It most closely represents the Russian style of the Abacus because the beads go across rather than up and down. As well as being great for teaching counting and simple Maths, they’re also fun toys!
Modern Abacus
We’ll use this name to talk about the kind of Abacus where the beads go vertically (up and down) and have a separation bar across all the columns. These kinds of abacuses come from Chinese and Japanese designs. The beads above the separation bar are worth five, while the beads below the bar are worth one.
There are different numbers of beads, depending on which kind you use. They’ll have one or two beads above the bar (the fives) and four or five beads below the bar (the ones). For this guide, we’ll talk about how to use a modern (or Soroban) abacus with one bead at the top and four beads at the bottom.
No matter how many, the system is the same: the beads touching the separation bar are the ones you count.
Place value abacus
A place-value abacus also has vertical rods for the beads, but this type differs from all the others because they’re not kept inside a frame. This is an open abacus, where you can remove beads completely instead of sliding them to a new position.
These abacuses are specifically designed for partitioning numbers. The beads you place on the rightmost pole are your ones, those to the left are your tens, hundreds are to the left of them, and, if you had more poles, it would keep going like that. Usually, a place-value abacus would have two or three.
Place value is important for every kind of Abacus, with each row, wire, or pole representing a different set of units in your calculation. But, if your focus is specifically on exploring place value, this might be the best for you.
What are abacus addition and subtraction?
As well as being great for simply counting, abacuses are fantastic calculation tools. Abacus addition and subtraction is where you use an abacus to work out adding and subtracting problems.
It would help if you started by setting your numbers. That means making the Abacus show the starting number. Then you want to count the beads for the number you’re adding or taking away. You’ll either move some of your starting beads back (for subtraction) or bring more beads to join them (for addition). Exactly how you need to move them will depend on the kind of Abacus, but it’s always about moving them in or out of the section you’re counting.
The Abacus will already show you your answer when you’ve done that! You need to count the beads you can see or feel in your counting area.
Maybe you haven’t quite finished adding or subtracting. That’s no problem. Your answer becomes your new set number, so you can keep going with more calculations. If you have a long list of numbers to add and remove, then an abacus is the perfect way to keep track.
If you feel ready to tackle some abacus addition and subtraction now, that’s great! Feel free to skip to our resources section for some lovely abacus activities. To find out more, read on as we go through how to add and subtract on an abacus in more detail.
School abacus addition and subtraction
On a school abacus, your counting area is one side of the frame, with all the beads you don’t want to count kept neatly to the other side. Use whichever side works best for you and your children, but be consistent; you don’t want to get confused about which side you’re counting.
So, move all your beads to your non-counting side to set the Abacus to zero. Then, choose whether you want your ones to be the top or bottom. You can either start at the top and increase the place value as you go down or start at the bottom with your tens, hundreds, thousands, and so on above you.
Now it’s time to set your numbers. Move the correct value of beads over to your counting side. For example, to set six, count out six beads on your ones (or units) row as you slide them to your counting side.
Say you wanted to add two; you’d move two more beads on the row. You’d then have eight beads on the counting side of that row. That’s your answer! 6 + 2 = 8.
Whenever you have a full row, you need to swap them out by moving them back to the non-counting side and using a bead from the next row to show ten. Try counting up to twelve on your Abacus. Once you get to ten, move these all back and put a ten bead on the counting side, then keep counting eleven and twelve as you move two more beads across on the one’s row. This will help you when adding digits that equal more than nine.
How do you think you would set three hundred and forty-two? You need to move two beads on your one’s row, four beads on your tens row, and three on your hundreds row. To add one hundred and twenty-five, you’d move across one more hundred beads, two tens beads, and five one’s beads. Your Abacus would now show four beads on the hundreds, six on the tens, and seven on the ones. What does your answer mean? 342 + 125 = 467.
But how do we subtract on a school abacus? It’s the same, just the other way around! Move their beads away from the counting side and back to the start to take away numbers. So if you wanted to work out six minus two, you still set six, then move two of them back across. That leaves only four beads on your counting side, which is the answer.
Again, it’s the same with bigger numbers. Let’s take the four hundred and sixty-seven from earlier. To subtract sixty, move six beads from the tens row back across. You now have four hundred, no tens, and seven ones. But don’t forget the tens row! The answer isn’t 467 – 60 = 47. Remember to count any empty rows in between your other place values. Your Abacus is actually telling you that 467 – 60 = 407.
But what if a row goes below zero? We can work that out too. Remember back to when we swapped a full row of ten for a single bead on the row after it. Now we want to do the opposite: swap a single bead for ten beads on the row before it.
Imagine you need to take five away from twelve. First, set twelve, with one tens bead and two unit beads. Now you want to put five ones back to your non-counting side. After moving beads one and two, you’ll have run out of unit beads to move. So, slide a tens bead out of the counting area and all ten over to fill its place. Now you can move beads three, four, and five back out again to complete the problem. You’ll have seven beads in the one’s row and none in the tens row. We’ve worked out that 12 – 5 = 7.
This is why an abacus is great to use if your children struggle to understand how they carry over numbers in complicated sums. This gives them a multisensory way of learning why the concept works, so they can apply it to written working out (such as the column method) in the future.
How to use a modern abacus
Using a modern abacus follows the same main principles, so have a read of the section above to make sure you understand them. There are still different wires for place value and the same movement techniques. However, now we’re moving beads up and down rather than side to side, and the counting area is the separation bar.
Once again, choose which wire you’re using for units. We usually use the middle bar to leave space for larger place values on the left and decimals on the right. Now you can count by moving the bottom beads up one by one toward the separation bar. This lets you count zero, one, two, three, and four.
When you get to five, you need to move all these four down again and move the top bead down to touch the bar. Then, you can move the bottom beads up again to count the six to nine. To get to ten, you need to move all the beads back to their original positions and move a bottom bead up on your tens wire to the left of it.
The important difference with this system is that you aren’t making a simple trade between one way of representing five or ten and another. Every time you make these swaps, you’re going up or down from what the Abacus showed before. For the modern abacuses with more beads per wire, you will do ordinary swaps like on a school abacus.
Now you know how to use a modern abacus, you’re ready to try addition and subtraction by moving different numbers of beads closer or farther away from the separation bar. If you get stuck, remind yourself what we did with the school abacus.
Addition and subtraction on a place value abacus
Time to take a breather. The place value abacus is much easier to use, so if you nailed the examples above, you’d be perfect at this. Set, add, and subtract numbers by partitioning them, putting beads on the poles, or taking them off.
One exciting thing you can do with a place value abacus is keep hold of the beads you remove to find the difference. For subtractions, you can reset the Abacus to the second number and count how many beads you need to take off each pole to make that happen.
An abacus is a fantastic way to help your children understand partitioning and place value, and that’s why we have lots of great resources for place value abacuses.
The history of the Abacus
Abacus counting has a long and rich history. We must look at ancient times to understand the mathematical device’s origins. The ancient Greeks conceived of The Salamis Tablet, a slab of white marble over one meter in length. It was a counting board with lines and symbols used to strategize and calculate market costs.
The Romans later developed equivalents called the Roman Calculi and the Hand-Abacus. Sadly, many of them were destroyed because they were made of stone. However, those made of metal can tell that Romans used a design like an abacus with vertical lines and dots.
In the Middle Ages, coin boards with horizontal lines started to appear in Western Europe and East Asia. The Suan-pan, the Chinese Abacus, was first written around 1200CE. Unlike the Roman design, it was made of wood with metal reinforcements. The design of the Suan pan survived unchanged until 1850, when it changed to the format we know today.
Abacus counting continues to evolve, however, as it has since been turned into a portable computing device that, along with a traditional abaci, is used for education in Chinese schools and other Asian countries.