Learning Maya mathematics is easy if you use the grid system to count and do your arithmetic.
The “Grid System” is basically what it sounds like. You use a system of grids to do your addition and subtraction.
The grid system works extremely well in the Maya stacked vigesimal system. This is also a wonderful exercise tool that can be used to teach Maya numbers, adding and subtraction, and help to better to better understand the Maya counting system in general.
You start by making a simple grid. You can make a grid the ground using sidewalk chalk or by using masking tape on a table. Gather up some stones and small sticks. Or you can use items that you may have around, such as beans and Popsicle sticks, for example. Begin by making two grid squares, side by side. Start the count by placing one bean in each grid square.
Examples of how the Grid System works in simple Addition:
A single bean or ‘dot’ in each square is how the value of “1” is measured and conveniently, also written in Maya. The value of one is a single dot.
For simple addition, we have a single bean or dot in each square representing 1 + 1.
We add our 1 + 1 by sliding the beans from the left grid (grid A) into the grid on the right (grid B), making our total count equal to 2 (1 + 1 + 2).
We’ll try another example by adding 3 + 3. We take three beans, representing the Maya symbol for the count of 3 in each of the two grid squares.
Here, we have 3 in grid A and 3 in grid B to add.
We take all the beans in grid A and slide them all into grid B to be summed up.
Remember, in Mayan, five dots equals a bar. So we gather 5 beans and we exchange them for a bar, or stick.
After removing the 5 beans and exchanging them for a stick (bar), we have the represented sum of 6. This is also properly represented in Maya writing, as six is written with one dot over one bar.
In this example, we will add 6 and 7, represented by 1 bar and 1 dot in grid A and 1 bar and 2 dots in grid B.
We again, push all the sticks and beans from grid A into grid B. We then add the number of bars (sticks) and dots (beans) to get a total count of 13 (two 5’s (bars) + three 1’s (dots) = 13).
Here, we shall add 4 and 13.
We move all the dots and bars from grid A into grid B.
Remember, gather every group of 5 dots and exchange them for 1 bar.
We add the exchanged bar and have our sum of 17.
Let us continue by trying to add 11 and 17 together.
Move all the dots and bars into grid B.
We now remove 4 bars to make 1 dot for the next tier, because four 5’s equals 20 and the count moves up a value in tier per 20 values on the previous tier.
We remove the 4 bars from tier one and exchange it for a single dot in tier two representing the value of 20. We add a single dot in the 20 tier plus 3 dots and a bar in the ones tier and our sum is 28 in total (20 + 5 + 3 = 28).
Here we begin our addition using two tiers (the 1’s tier and the 20’s tier). On tier two, in both grids, we have a dot in place of the 20. On tier one, we have our sums 18 and 13, making the total as 38 + 33.
Again, we move all the beans and bars from grid A into grid B, staying in the tier levels of each grid.
Starting on the bottom tier, we remove each group of 4 bars and exchange them for a bean to place in the second tier group.
Next, on tier two, we again remove any groups of 4 bars and exchange them for a dot for the next level tier up, tier 3 (202).
And now we have, as it would also look if written in proper Maya, the sum of 489.
(400 + 1) + ( 20 + 4) + (4 + 5) = 489.
Let us try another on three tiers.
We shall add 2373 + 799, without counting past 5 to get our total.
As before, we move all the dots and bars from grid A and slide them all into grid B, staying in whichever tier level they were in.
We begin by starting on the bottom tier and add groups of 4 bars and exchange them for a dot to the next tier level up.
We also exchange all the groups of 5 dots for bars, if you hadn’t already done so.
We continue by going up the next level tier and add a bar for every 5 dots.
We also add a dot to the next level tier for every 4 bars that we have.
And now we have the sum of 3152.
The grid system works with subtraction as well as it works with addition. The except is when we subtract in Maya, we borrow from 20, instead of 10 like in the decimal system.
In this example, we shall subtract 17 from 31 (31 – 17).
Subtract first the lowest value, in this case the ones. Remove one dot in grid B for one dot in grid A. To Subtract, you remove a value from one grid and match and remove the same value in the other grid.
At this point, we’ve run out of dots from grid A. To resolve this, we remove 1 bar in exchange for 5 dots in grid A.
Here, we’re exchanged 1 bar in grid A for 5 dots.
We then continue removing dots in grid A for every dot we have left in grid B.
And continue subtracting by removing every bar from grid A for every bar in grid B.
Now that we’ve removed every bar in grid A for every bar in grid B, we find that we are short bars in grid A because we still have 2 bars in grid B to subtract. In this case, we borrow from tier two and subtract 1 dot (value = 201) and add 4 bars to tier one in it’s place.
By borrowing from tier two, we now have bars in grid A to remove for the remaining 2 bars we have left in grid B.
Continue subtracting bars in grid A for every bar grid B has.
Now that we’ve removed every dot and bar from grid A that we had in grid B, we finish with our total of 14.
31 – 17 = 14
This article is an excerpt from the book: Kane, Njord. “Chapter 12 – Ancient Maya Arithmetic.” The Maya : The Story of a People. 2nd ed. Yukon: Spangenhelm, 2016. ISBN: 978-1943066032 Used by permission from the author and publisher exclusively for use on readicon.com only.
- Kane, Njord. The Maya : The Story of a People. 2nd ed. Yukon: Spangenhelm, 2016. ISBN: 978-1943066032
- Kane, Njord. Maya Math Simplified. 2nd ed. Yukon: Spangenhelm, 2016. ISBN: 978-1943066087
- Georges Ifrah, “From One to Zero, a Universal History of Numbers”, Penguin Books, 1987.
- G Ifrah, A universal history of numbers : From prehistory to the invention of the computer (London, 1998).
- J B Lambert, B Ownbey-McLaughlin, and C D McLaughlin, Maya arithmetic, Amer. Sci. 68 (3) (1980), 249-255.
- Lounsbury, Floyd G. Maya Numeration, Computation, and Calendrical Astronomy. In Dictionary Of Scientific Biography. New York, New York. Charles Scribner’s Sons. Volume 15, Supplement 1. 1978. P. 759-818.
- McAnany, A. Patricia (1998). “Ancestors and the Classic Maya Built Environment.”
written by Njord Kane © 2016 Spangenhelm Publishing
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