Memorizing times tables is one thing. Strengthening conceptual math skills is another. One way to strengthen your child’s conceptual math skills is to explore Mayan numbers together. Exploring the Mayan numeric system will heighten your child’s understanding of symbol, place value and base, and inspire greater recognition of how our own (Arabic) number system works. One extraordinary advantage to this activity is that once you catch on, there’s no end to the variety of games you can play.
If your child is old enough to read or write numbers, she’s old enough to have fun with this activity.
Despite what it may look like, the Mayan numeric system is pretty simple.
The Mayans use three symbols: a dot, a bar and a zero.
– The dot (originally a pebble) represents one.
– The bar (originally a stick) represents five.
– The zero (originally a shell) represents zero.
You can use things from around the house as you explore the system with your child. I used a Cheerio, a crayon and a partially flattened roll of masking tape (which I turned blue and shrunk down using a photo editor) to make the images that appear in this article.
Mayan numbers 0-9 are pretty straight forward. What’s interesting is that from the beginning you can see that the symbols contain mathematical operations. The number two is represented as 1+1. The number three is represented as 1+1+1. The number four is represented as 1+1+1+1. The number six is represented as 5+1. The number seven is represented as 5+2, etc. You can see how simply working with numbers 0-9 can strengthen the math skills of children learning to count.
The numbers 10-19 are also pretty straight forward. Essentially you have 5+5=10, 5+5+1=11, 5+5+2=12, etc. If the symbols for 0-9 make sense, the numbers 10-19 should offer no surprises.
Starting with the number 20 the Mayan system can seem a little tricky. That’s because we’re accustomed to place value in a base 10 system. Take the number 23, for example. There are two place values: tens and ones. The 2 is in the tens place. It tells us to multiply 2×10. The 3 is in the ones place. It tells us to multiply 3×1. In other words: (2×10)+(3×1)=23.
The Mayan system uses base 20. The number 23 has two place values: twenties and ones. It tells us to multiply 1×20 and 3×1. In other words: (1×20)+(3×1)=23. If that seems unusual, it’s because it draws attention to the idea of place values–something we may have forgotten about. Secondly, one of the place values is not familiar to us: the 20. It is widely believed that 20 came into play because we have 20 digits to count with–ten fingers and ten toes. Here are the numbers 20-29:
The use of two place holders continues all the way to the number 400. The number 400 starts a new place holder. Why? Because the system uses base 20. When you reach twenty 20s it’s time to move on to the next place holder (400s).
Our Arabic system uses the same principle with base 10. When you reach ten 10s it’s time to move on to the next place holder (100s).
In the Mayan numeral system the number 400 is represented with a dot (one 400) on top of a 0 (no 20s) on top of a 0 (no 1s). That’s 400+0+0=400.
The number 845 is represented as two dots (two 400s) on top of two dots (two 20s) on top of a bar (five 1s). That’s (400×2)+(20×2)+(5×1)=845.
What happens if you put two dots on top of 845? You now have four place values: the 8000s, the 400s, the 20s and the 1s. Where did the 8000s place value come from? Remember, it’s a base 20 system. When you reach twenty 400s you move into the next place value (the 8000s). So if you put two dots on top of 845, you get: (8000×2)+(400×2)+(20×2)+(5×1)=16,845.
Here are the place values viewed exponentially:
200 = 1
201 = 20
202 = 400
203 = 8000
204 = 160,000
205 = 3,200,000
You can see why the system is referred to as base 20–because the place values are established by using a base of 20 for the exponent (which increases by 1 for each new place value).
A good starter activity to do with kids is to practice making numbers with household objects–beans, popsicle sticks, etc.–or make the symbols using crayons or watercolor, then cut them out to get started.
Once you’ve caught on, here are some more Mayan number games to play: More Math Games with Dice.