How to Use a Roman Abacus

Counting boards have been used for thousands of years across the globe as a way of "calculating sums too large to be worked out easily in the head". Stones or counters would be placed, moved or removed from a board, table or cloth. The different locations representing different values.

The Romans called these counters "calculi", which literally means "little stones". The Romans are credited with being the first people to innovate the idea of fixing the calculi to a frame making it quicker to use, more transportable and providing less possibility of accidents.

In this video Stephen from Classroom Adventures shows you what a Roman abacus looked like, how it works and how to use one.

Let's have a go!

Firstly draw an abacus/counting board on an A4 piece of paper. You can either have a go at drawing the one below (based on the Roman abacus but with modern numbers) or download at PDF copy of this image in the Downloadable Resources section of the DIY Roman Day page (scroll down) and print. There you will also find a version with Roman numerals.

If you are sourcing this for younger children then you may want to draw/print a simpler version like this one (you can also find a PDF version of this in the Downloadable Resources section in the DIY Roman Day page):

In the examples provided above each cell is filled with black and grey circles. The black circles indicate where to locate your counters like so:

For the complete abacus you will need 45 counters, if you are using the simpler version then you will need 20 counters.

The video at the top of the article explains how the abacus works. Here is a handy recap as to how to count to 10 on the abacus (the process is exactly the same whether you are counting from 1 to 10 or 1 million to 10 million):

For all of the white columns counting is done into the middle, or green line. When you are subtracting you are moving away from the green line.

The really interesting thing about the Roman abacus is that it is a "multi base" counting system. In the column to the right of the units you will find a column marked "1/12". This is for counting your unciae (meaning 1 twelfth). The Romans had several counting systems which used base 12, so this column would have been very useful. Counting in the unciae column works exactly the same as with the white columns except the single counter at the top now represents 6, rather than 5, and the whole column counts up to 11 rather than 9.

To the right of the unciae column, the last column is broken into 3 sections. The Romans were so clever they included a section for working out fractions. The top section is for halves, the middle is for quarters and the bottom for thirds. The fractions are all set to zero (or nihil in Latin) when they are at the lowest point in their box. The image bellow shows how to count your basic fractions with the abacus:

We wont worry about fractions for now, but we just wanted to let you know that they were there in case you wanted to play with them on your own accord!

Okay, that's enough talk, let's play!

Challenges

1. Try counting to 10 (1 counter at a time).

2. Try counting from 10,000 to 100,000 (it seems big but give it a go and you may be surprised how easy it is).

3. Practice writing different numbers on the abacus by moving the correct stones (if you want some suggestions try 17, 58, 762, 3,167, also try asking your friends).

4. Try working out some simple sums (start easy so that you are sure that you have mastered the method of using the abacus) i.e. 3+12=?, 11+8?, 9-7?, 22-8=?.

5. Once you feel that you have got the method down try some slightly harder sums i.e. 14+37?, 156+72=?, 73-46=?, 358-123=?.

6. When you have some "big sum" maths challenges come back to the abacus and see if you can use it to work out the answer.

7. Why not pretend to be a Roman merchant? See what you can find around the house to add to your shop. Find some playing counters for coins (if you don't have any/enough buttons/decorative glass beads/gravel will work). and decide how much you want to charge for each item (write out the prices on little slips of paper). Invite your family to your shop to buy your wares. When they buy several items you can use the abacus to calculate what they owe you!

Happy counting!