Overview and Background

Maya math was the most sophisticated number system ever developed in the Americas. It allowed scholars, astronomers, and architects to make complex calculations, but it was simple enough to be used by market traders and illiterate farmers.

Where we use ten different symbols to represent numbers (1, 2, 3, 4 , 5, 6, 7, 8, 9, 0), the Maya used only three: a dot for a one, a bar for five, and a symbol (usually a shell) for zero. (The Maya were the first civilization to discover and understand the concept of zero.) Below are the Maya numbers from 0–19:

We use a decimal system, based on the number ten, but the Maya used a vigesimal system, based on the number twenty. So where we learn to count on our fingers, Maya children counted on their fingers and toes. In fact, the number twenty was very important to the Maya, so much so that the words for “human being” and “twenty” share the same root in most Mayan languages.

The Maya wrote their numbers from top to bottom rather than from left to right, but apart from that, their system was not so different from ours.

Objectives

Identify the Maya number system as a place-value system
Identify the symbols used in the Maya number system
Read and identify the value of Maya numerals

Standards

FINE ARTS: Visual Arts

GRADES 5 - 8

NA-VA.5-8.4 Understanding the Visual Arts In Relation to History and Cultures
NA-VA.5-8.6 Making Connections Between Visual Arts and Other Disciplines

LANGUAGE ARTS: English

GRADES K - 12

NL-ENG.K-12.9 Multicultural Understanding
NL-ENG.K-12.10 Applying Non-English Perspectives
NL-ENG.K-12.12 Applying Language Skills

LANGUAGE ARTS: Foreign Language

GRADES K - 12

NL-FL.K-12.1Communication
NL-FL.K-12.2 Cultures
NL-FL.K-12.4 Comparisons

SOCIAL SCIENCES: World History

GRADES 5 - 12

NSS-WH.5-12.2 Early Civilizations and the Rise of Pastoral Peoples
NSS-WH.5-12.3 Classical Traditions, Major Religions, and Giant Empires

Lesson Plan and Activity

Introduce students to the structure of the Maya number system. The Maya number system is a vertical place-value system. It is a base-20 system (a vigesimal system) made up of three symbols: a dot represents 1, a line represents 5, and a shell represents 0. The symbols are repeated to represent larger numbers.

The place values were multiples of 20, so each place value was 20 times greater than the one that came before it. The place values were: 1s, 20s (20x1), 400s (20x20), 8,000s (20x400), and so on.

The numbers 1 through 4 were written using a row of dots. The number 5 was written using one horizontal line. Numbers 6 through 19 were written using a combination of lines and dots, or a combination of 5s and 1s. For example:

6 was written using one line with a dot above it (5+1)
10 was written as two stacked lines (5+5)
19 was written using three stacked lines with a row of four dots above them (5+5+5+1+1+1+1)

For numbers greater than 19, the symbols were arranged in place values based on 20s, with the greatest value on top.

The shell, representing zero, was used as a placeholder for numbers greater than 19. Many believe that the Maya were the first to use a symbol for zero and consider this to be one of their greatest achievements.

Review these examples with students to explain the process of writing Maya numbers:

30 was written using a dot in the 20s place and two lines in the 1s place: (1x20) + (5+5)
80 was written using four dots in the 20s place with a shell beneath it representing zero ones: ((1+1+1+1) x 20) + (0x1)
302 was written using three lines in the 20s place, above two dots in the 1s place: ((5+5+5) x 20) + (1+1)
400 was written using a dot in the 400s place above two stacked shells: (1x400) + (0x20) + (0x1)
2,040 was written using a line in the 400s place, 2 dots in the 20s place, and a shell in the 1s: (5x400) + (2x20) + (0x1)

Distribute the Maya Number Tiles to groups of 2-3 students and give them a number up to 7,999 and have them recreate the number in top to bottom fashion using the handed out tiles.
Have a representative from the group go to the front of the class and have the other groups figure out the represented number and compare to number that was assigned to the group.

Duration of Lesson

60 minutes

Preparation

Briefly discuss the geographical area occupied by the Maya; explain that the Maya were excellent mathematicians and that they used a counting system different than our Arabic System. Base 20 vs Base 10
To prepare for this lesson you will need the Maya Number System tiles

Rubric and Assessment

Can students recognize and write the Maya numbers 0-19?

References

Sara Otto-Dinez; Mysteries of the Maya

PBS.org: Ancient Civilizations/The Maya Chronicles

Mayan Math Basics