# Maya Maths

Amazing Fact:

The Maya were only one of two cultures in the world and the only culture in the whole of the American continent to create the number zero!

Dr Diane explaining the Maya Maths System

This resource can be used for the History Key Stage 2 (KS2) Curriculum in the UK or Grades 2-6 in the US.

NB: specialists of the Maya civilisation say âMaya numeralsâ, “Maya number system”, “Maya mathematics” and not âMayan numeralsâ etc. The adjective “Mayan” is used only in reference to Mayan languages  (see: 10 red-flags for spotting unreliable online resources).

## How to Read Maya Numbers

The Maya were advanced mathematicians, using the number zero and place-values. They were able to calculate extremely large numbers, unlike for example, the Romans.

Their number system enabled them to make really accurate astronomical predictions and they traced movements of the sun, moon, stars and even planets like Mars!

In their numeral system, the ancient Maya only used three symbols to represent all numbers. A dot has a numerical value of 1, a line (or bar) a numerical value of 5 and a shell has the value of 0

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Do you think the shell is an appropriate symbol for zero? If you had to invent a symbol for zero, different from the one you use now, what would it be?

These symbols (dot, bar and shell) are thought to represent items that the Maya people might have first used to count with, such as pebbles, sticks and shells.

In other words, zero is represented by a shell; 1 to 4 are represented by dots. The Maya wrote their numbers from top to bottom rather than from left to right. Multiples of five are represented by lines, with extra dots being added to complete the numbers as shown below:

So where we learn to count on our fingers, Maya children counted on their fingers and toes.

The numbers above nineteen are indicated on the basis of their vertical position. The Maya used a vigesimal (Base-20) system, so each position is a power of twenty.

## The Maya x20 mathematical system

Our own number system uses powers of tens (“ones place”, “tens place”, “hundreds place”); it’s a decimal or Base-10 system. The ancient Maya used a vigesimal (Base-20) notation in which each position is a power of twenty.

In a Base-10 system, there are 10 digits (1, 2, 3, 4, 5, 6, 7, 8, 9 and 0). When writing numbers, once we get to â9â we then have to move across to the next column. We write a âoneâ followed by a âzeroâ to show that we have moved across. Zero is a âplace-holderâ.

From there, we’re going to use the 9 numerals to represent the number we want up to 99. Then, when we go beyond ’99’, we move across to the next column and write ‘100’.

So, for example, in our decimal system, 39 is ‘3 x 10’ and ‘9 x 1’

The Maya used a similar system using their 19 numerals and then moving to the next section and putting a zero (represented by the shell) as a placeholder.

Another difference is that the Maya used rows instead of columns, starting from the bottom and working upwards. So the place values were multiples of 20s: 1s, 20s (20 x 1), 400s, (20 x 20), 8,000s (20 x 400) and so on.

Using the previous example, ’39’ would be written as follows in the Maya system:

## How to convert Maya numbers to our numbers

In the decimal system ‘815’ is:

And now in the Maya vigesimal system:

And now, let’s try a bigger number:

The Maya vigesimal system is every bit as useful and efficient as our own decimal-place system. Besides being base 20 instead of base 10, it differs from ours in using combinations of just three symbols (shell, bar, dot), whereas we have to use 10 different symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).

## How to convert our numbers to Maya numbers

To figure out the Maya equivalent of a number from our decimal system, you need to divide the number into powers of twenty (8000, 400, 20). Let’s take 4285, for example:  4285 = (10×20Â˛) + (14×20Âš) + 5

How did we get there: we know that 4285 is smaller than 8000 (20Âł) so we’re going to divide it by 400 (20Â˛) which gives us ’10’. The remainder is 285 which we’re going to divide by 20 (20Âš). That gives us ’14’ plus ‘5’ units left over.

Here is another way to calculate a Maya number:

## How to calculate with Maya numbers: Adding and Subtracting

Adding and subtracting numbers using the Maya number system is quite simple.

### How to add Maya numbers

Addition is performed by combining the numeric symbols at each level.

### How to subtract Maya numbers

Similarly with subtraction, simply remove the numeric symbols.

## Children’s Activities

Why don’t you try to make a Maya maths game or a display?

#### Maths Quiz

What number is being shown in each of the images? (You will find the answers at the bottom of the page).

Maths Powerpoint:

These resources were written by teachers on a CPD trip with Dr Diane to the Maya area. You can download these below.

You can access the complete scheme of work for a small fee, in the form of a donation to the charity Chok Education, which supports the education of Maya children.

### And there is more…

Maya Maths Activity (1 hr class time required)

Dr Diane explains in detail how the Maya number system works, for numbers under 20 and also for numbers up to and over 800. She will give exercises for the children to complete with answers. Children will then look at Maya addition and subtraction with examples and quizzes. Finally, children will look at an ancient Maya codex (paper book) and try their hand at working out the numbers on this.

Live Question & Answer Session with Dr Diane (30 mins)

Do you have questions about Maya maths? Dr Diane is available in real-time using the platform of your choice to answer any questions children, teachers and others interested may have.

## Other Resources on Maya Maths

• Smithsonian National Museum of the American Indian– Pupils can take the Maya Maths Challenge where they are asked to calculate numbers in the Maya number system. The game has varying levels of difficulty.
• Math Maths video demonstration by the Jaguar Stone website that shows you how to add and subtract both simple and complex numbers:
• Maya Codices â by Gabrielle Vail and Christine HernĂĄndez. This site features a searchable translation and analysis of the four remaining Maya codices, including the Dresden Codex (screenfold books), painted by the Maya scribes before the Spanish conquest in the early 16th century. They contain calendrical and astronomical information and so give examples of Maya numbers.
• Digit Number Sheet – Maths calculation sheet.
• FAMSI has a great number and calendar guide.
• If you would like a more in-depth knowledge on the subject of the Maya maths system then have a look at my article in the public resources section.

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b, 2005

### 2 responses to “Maya Maths”

1. Hello. I’ve always wondered how the ancient Maya kept track of debt. Obviously, the poor farmers, who owed their particular king a cut or most of whatever they produced, had to express it in terms of negative numbers, yet to my knowledge there is no record in the inscriptions or elsewhere about them. Personally, I think they could be expressed by going down in their progression rather than up, which are positive integers. That still leaves the problem of fractions. It seems to me that these gifted people had to have a way to express something like half an ear of corn, or half a plate of food left, or whatever. Also, are there schools teaching other languages such as Chorti? Thank you for your attention.

• Diane Davies says:

Yes, i am afraid the subject of inscriptions concerned elite rather than the average person’s life. Maya codices which may have contained this sort of information, at least from the tax collectors perspective have not survived. We also haven’t found any evidence of the use of fractions as yet. Regarding Mayan languages, many of them can be studied at various institutions in Central America and the US, such as the Mayan Language Institute, but unfortunately not the UK.