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:

20^{0} = 1

20^{1} = 20

20^{2} = 400

20^{3} = 8000

20^{4} = 160,000

20^{5} = 3,200,000

etc.

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.

Good luck!

## 29 responses so far ↓

1

Jeff Hamer// Mar 19, 2010 at 7:17 pmI’m a single dad with a 5 and a 7 year old. I just want to say-really nice job with this material. You made it very accessible. I can see how it could improve conceptual math skills. I’m going to introduce the activity to my two sons this weekend.

Thanks-

Jeff

2

Catherine// Mar 19, 2010 at 8:20 pmFascinating, it is a shame sometimes that maths is taught without any reference to its history. I think playing with Mayan numbers would help with understanding the concept of place value (and noticing that it is a convention we’ve decided on, not the way it has to be).

3

Spaghetti Box Kids// Mar 19, 2010 at 10:08 pmCatherine: Good point about the history– studying Mayan numbers can definitely serve as an entry to cultural exploration. In the least, questions can motivate trips to the library to get things started.

Jeff: Thanks for the comment–I appreciate it. Hope your sons enjoy learning about Mayan numbers.

4

rosebelle// Mar 21, 2010 at 12:37 amThis is great Anthony. My daughter is having a hard time memorizing her multiplication table. She just learned about place values and had a pretty hard time. I’ve never heard of the Mayan system and glad you post about it. I’ll try it out with my daughter and hopes it can help strengthen her math skills.

5

Spaghetti Box Kids// Mar 21, 2010 at 3:36 pmRosebelle – Good stuff. I’m glad to hear it. Just remember that making (or finding) the symbols can be half the fun. It’s a very kid-friendly way to start the activity. Have fun. -AV

6

Michelle// Apr 21, 2010 at 9:36 pmWow, what a great activity. Math concepts rolled up with history. Very cool.

7

Spaghetti Box Kids// Apr 22, 2010 at 4:40 amThanks for the feedback. It was a fun article to write.

8

Ladygoodwood// Jun 6, 2010 at 7:53 pmI was in mexico earlier this year and went and visited Chitchen Itza. Some of the native Mayan children were engaging the tourists in these sort of number games and selling little wooden sets they had made. I bought a few – $1 each – the money goes direct to the Mayan community. Am amazed to find you writing about the mayan numerical system here. How amazing is that?

9

Spaghetti Box Kids// Jun 7, 2010 at 4:36 pmThat’s very encouraging to hear. Mayans were separated from their own written heritage up until only a few decades ago. It’s good to hear that the numeric glyphs are so readily available to tourists. The more mainstream they become, the more likely we will see widespread cultural and mathematical applications.

10

jamie// Oct 3, 2011 at 7:17 pmvery useful and interesting for my homework

11

Spaghetti Box Kids// Oct 4, 2011 at 8:02 pmThat’s excellent. I’m glad it helped. It’s kind of fun once you get the hang of it, isn’t it?

12

sydneyy// Oct 9, 2011 at 9:34 pmOMG! This makes it so much easier to learn about!

13

Spaghetti Box Kids// Oct 10, 2011 at 1:19 amSydneyy, that’s good to hear. I’m glad you enjoyed the article. -AV

14

Trudie// Oct 25, 2011 at 8:46 pmI love this website..so creative and switched onto kids thinking. Will be using these ideas in my Reception class in the UK. thanks.

15

Spaghetti Box Kids// Oct 26, 2011 at 12:10 amTrudie- I love hearing from teachers. I have nothing but admiration for your profession. Thanks for the endorsement and good luck with your Reception class (what a great age).

Hope to hear back from you.

-AV

16

Patrick// Feb 12, 2012 at 10:43 pmHi,

I came across your article about Mayan numbers while I was looking for other games that use dice. Originally I came across this project for Mayan Dice…. Thought that you might be interested in this.

Here’s the project URL:

http://www.kickstarter.com/projects/745436261/mayan-empire-inspired-dice

Thanks, Patrick

17

Spaghetti Box Kids// Feb 13, 2012 at 1:52 pmThose dice look fantastic. Thanks for sharing the link.

Cheers–

AV

18

Kanoni// Feb 15, 2012 at 10:06 pmIm studying mayan numbers in my class and this article was very helpful towards my homework. :)

Thanks,

Kanoni

19

Spaghetti Box Kids// Feb 15, 2012 at 11:48 pmKanoni-

That’s great to hear. They’re kind of catchy once you get going–aren’t they? Thanks for dropping by and sharing–

Cheers,

AV

20

star// Apr 13, 2012 at 1:49 pmThis was a big help on my homework. Thanks for making it easy to understand. -star

21

Spaghetti Box Kids// Apr 26, 2012 at 12:11 pmStar- That’s good to know. As always, I appreciate the feedback.

-AV

22

Stella// May 9, 2012 at 5:09 amTHis really helped with my homework. I completely get it now! THaaaaaannnnks!!!

23

Lulu// Mar 10, 2013 at 10:52 pmhey SUCH A GOOD SITE!! I was doing a assingnment and this helped me so much thx. Lulu

24

Mayan Numeration | brooklynsabin// Oct 3, 2013 at 9:19 am[…] http://spaghettiboxkids.com/blog/mayan-numbers-for-kids/ […]

25

Catherine// Apr 27, 2014 at 10:55 amAmazing article I am working on my on a final presentation in college about the Mayan numerical system, and how is use in the classrooms today, this article is exactly what I was looking for. Conceptual learning is a great approach to teach young children and keep them focus on new things.

26

Claire// Apr 22, 2015 at 9:46 amThanks spaghettiboxkids! this helped with my assignment!!!

27

????????????? (Jeff)// Oct 22, 2018 at 3:18 pmthis is cool i think it is cool.

28

Someone// Oct 22, 2018 at 3:19 pmI enjoyed reading this article it is very informing it gives me a better understanding of the Mayan counting system. I hope you can produce more content such as this.

29

Lisa// Nov 12, 2018 at 3:03 pmI am a middle school math teacher. I was asked to sit in for a Social Studies teacher whose flight was late one day (so he hadn’t left plans). I did a quick Mayan Math lesson, to combine Social Studies with Math. A semester later, those kids still come to my classroom to do more Mayan Math. I had found a game that had a maze where you had to do Mayan math problems to open doors, but I can’t find it any more. In any event, great activity.

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