Teaching Math Across Cultures: Connections to the Maya
Maya Math WebQuest
Which Way Is Up:
Take a look at the Maya text below. This text shows part of the Dresden Codex, one of the few existing examples of Maya writing. Can you find some clues to help you figure out which way to read this writing?
Did you notice the position of the figure of the person? This helps you tell which way is right side up. When archaeologists study a manuscript, they begin by using clues like that. Now you can look for patterns in the Maya writing. If you look at the pages from a distance, you’ll see that the symbols on each page are in groups. If you still don’t see a pattern, try squinting.
One thing to notice is that there are groups of symbols inside rectangles. In some rectangles, these symbols—called glyphs—are made up of elaborate designs with roundish borders. Other groups of symbols are made up of simple bars and dots. There are both numbers and words in this text. Which do you think is which?
If you figured that the glyphs are the words and the groups of bars and dots are the numbers, you were right.
Reading the Numbers:
Now take some time to focus on the numbers. How can you figure out what the bars and dots mean? Suppose that one of these symbols counts the 1s. Which do you think it is—the bars or the dots?
The dots are simple and are similar to the small, round pebbles that people all over the world have used to keep count of things. Let’s start by counting them as single marks—1s.
Now look for the largest number of dots that appear together in one row.
Notice that there are never more than four dots side by side. If the dots are 1s, and there are never more than four dots together, how would you represent five items?
What about the bars? There are never more than three bars in a group. Could each one be a 5? A 10? Here’s a way to explore that question: Assume the bars are 10s. Now try writing the numbers from 1 to 20. (The dots are 1s, and you can use only four dots together.)
You probably discovered that if a dot is 1 and a bar is 10, there’s no way to write the numbers from 5 to 9 or 15 to 19. But if the bars are 5, you can write all the numbers from 1 to 20.
What Base Are We In?
Now that you can read individual numbers on the codex pages, look for the largest single grouping of bars and dots you can find. (A group is a single row of dots and the bars under it. Some of the numbers may be only dots or only bars.)
In some places, the number symbols run together, making them hard to read. If you look at the clearest number groups, you’ll find that the largest one contains three bars and four dots. If the bars are 5s and the dots are 1s, what is the value of this largest number represented by this group of bars and dots? Does this give you a hint about the base being used here?
The number 19—three bars plus four dots—is the largest single number in the Mayan counting system. So how could the Maya write bigger numbers?
Think about how our number system works. We use ten different symbols, 0 through 9, and combine them to write larger numbers. We can tell what each symbol means from where it appears. For example, “4” means four 1s, but “400” means four 100s, zero 10s, and zero 1s.
The same idea applies to the Mayan counting system. Each group of bars and dots is an individual digit that is part of a larger number. The position of the digit tells us what its value is.
If 19 is the largest number the Maya could write in any one position, it makes sense that their system might be base twenty. To represent 20, the Maya would write one dot in the second position, just as we would write a 1 in the second position to represent 10 in our base-ten system. The next position in the Mayan system would be the 400 (20 x 20) place value position.
