1. Maya Math Presentation
By Fabiola Cedillo
For Grades 5-6
Note: This presentation is meant to be guided with discussions and follow-up activities as noted in inserted comments at the margins.

2. How did people count before they invented numbers?

3. The Maya, for example, were a group of people that without numbers
studied the sun’s rotation
mapped stars
mastered math
developed a communication system using pictures, called hieroglyphs.

4. The Maya World Who and when?
Ancient group of people that lived 1500 years ago (between A.D. 200 and A.D. 900). Let’s draw a timeline!
Mayans were farmers for houses and were surrounded by religious cities that had temples for houses for the nobles and priests.
Mayans were great traders and were famous for making up the counting system, the basic numbers,0-20.

5. Where did they live?
Southern Mexican states of Chiapas and Yucatan, and neighboring Central American countries Guatemala and Belize. Let’s find it on the map!

6. Let’s compare them to other cultures…
Like the Greeks because of their accomplishments in science
Like the Romans because of the extensive road systems they built
Like the Egyptians because of their pyramids
Like the Phoenicians because of their ocean-going travels on trading missions

7. Grouping solves a problem:
Write a big number using dots:
•••••••••••••••••••••••••••••••••••••••••••••••••
To make it easier we can group the dots by fives:
•••••/•••••/•••••/•••••/•••••/•••••/••••/•••••/•••••/•••••
Or we can group them by tens:
••••••••••/••••••••••/••••••••••/••••••••••/•••••••••

8. The Mayan number system:

9. Bars, dots and a shell! ••••• → Three symbols:
Five dots are traded for one bar:
••••• →
Five bars are traded for one dot in the second place and a shell in the first place
→ The zero shows that the place has been filled up and you must move to the next highest place.
Three symbols:
= 0
= 1
= 5

10. So if you have and you add one more dot, what you see is a bar in the next highest place. That’s because the 5 dots trade for a bar. And then, because no more than 4 bars can be clustered, the 5 bars trade for one dot in the second place and a shell in the first place.
one group of twenty
• → →
no ones

11. Counting in the First and Second Places
The bottom space is called the units place
The second place is called the twenties place

12. So…. 1 dot in the units place = 1
1 dot in the twenties place and a “shell” in the units place = 20

13. Let’s try a few…
26 =
22 =
67 =
145 =
53 =
84 =
95 =
100 =
32 =

14. The Third Place:
The third place in a Maya number is the “four hundreds place.”
four hundreds x 400 = 400
twenties x 20 = 0
units x 1= 0
So 800 equals:
2 x 400 = 800
0 x 20 = 0
0 x 1 = 0

15. Let’s try a few… = 260 = 803 = 421 13 x 20 = 260 1 x 0 = 0
= 260
2 x 400 = 800
3 x 1 = 3
= 803
1 x 400 = 400
1 x 20 = 20
1 x 1 = 1
= 421

16. How much can the third place hold?
If we follow the Maya rule of never having more than three bars and four dots in any one place, what is the biggest number we can write using only three places?
Maya Our
Number Number

17. Comparing Maya Numbers and Our Numbers
Maya Number Our Number
3rd place→
1st place
2nd place→ nd place
3rd place
1st place→
The value of each place in our number system is a multiple of ten
The value of each place in the Maya number system is a multiple of twenty

18. What happens if… …we change the order of digits in our numbers?
How is 327 different from 723?
…we change the order of glyphs in Mayan numbers?
How is
different from ?

19. Let’s think out loud… How many four hundreds? 1
Our number: Maya number:
How many four hundreds? 1
How much left over? 182
How many twenties in that? 9
How much left over? 2
How many units in that? 2

20. Let’s try a few…
200 = =
762 =

21. Using numbers to keep track of time: calendars!
The Maya also used their skill in numbers and math to work out calendars. They calculated how long it took the Earth to go around the Sun and the Moon to go around the Earth. They knew exactly how long a year was and their calculations were as precise as those by scientists and computers today.

22. 2 Mayan calendars! Tzolkin Calendar Ritual calendar
Days were given one of 20 names and a number from one to 13. It took 260 days (20 x 13) for the first day to come round again.
Haab Calendar
20 days in a month, which was called a uinal. Eighteen uinals made a year of a tun. This added up to 360 days. Then, they added five extra days that they considered to be unlucky.

23. Our terms for measuring time:
A millennium has 10 centuries
A century has 10 decades
A decade has 10 years
A year has 12 months
A month has 30, 31, 28, or 29 days
A day has 1 day

24. Mayan terms for time in the Haab Calendar
Maya word for day is kin
A baktun has 20 katuns
A katun has 20 tuns
A uinal has 20 kins
A tun has 18 uinals
A kin has 1 kin

25. Let’s compare our calendar to the Mayan calendar…
Terms in our calendar are 10 times bigger than the next smallest term
Terms in the Mayan are 20 times bigger than the next smallest terms
A few exceptions to the place value system in both calendars: 12 months, not 10, are in our year; 18 uinals, not 20, are needed to make a tun.

26. How many days is each Maya term worth?
A baktun has 20 katuns and means days
(20 x 20 x 18 x 20 x 1)
A katun has 20 tuns and means days
(20 x 18 x 20 x 1)
A tun has 18 uinals and means days
(18 x 20 x 1)
A kin has 1 kin and means 1 day
(1 x 1)

27. Now, let’s compare again…
How does a tun compare to our year?
How does a uinal compare to our week?
How does a katun compare to our decade?
How does a baktun compare to our century?

28. Well done! We have learned:
How numbers came about in ancient cultures like the Maya
How place value is at the heart of how we write numbers, and central to the rules for addition, subtraction, multiplication, and division
We have learned to use an arithmetical system that represents numbers in a more visual and concrete way than the one we currently use
We have taken an archeologist approach by going through the process of figuring out the meaning of glyphs
In order to explore we have speculated, which is guessing about what something might symbolize and keeping in mind about the possibilities