Additional Math Pages & Resources

Wednesday, May 16, 2012

Oldest Known Mayan Calendar Unearthed

A number of years ago, looters digging at the site of XultĂșn, once a sprawling Maya city-state in northern Guatemala, exposed part of a painted wall. In March 2010 a team from Boston University discovered a portion of the wall. Little did they know that the wall held never-before-seen paintings and an ancient Maya calendar.

Last week, in a paper published online in Science, William Saturno, an archaeologist at Boston University, and Anthony Aveni of Colgate University in Hamilton, NY, and their colleagues reported uncovering the oldest-known astronomical tables of the Maya. These tables are 500 years older than the astronomical tables previously discovered preserved in fragile bark-paper Maya books, many of which were burned in 1561 and later years by missionaries. Today, only a handful of these readable precolonial books survive.

The astronomical tables discovered in XultĂșn were incised and painted on the walls of a small room in a 1,200-year-old building. The room may have been a working space for scribes and was built with a stone roof. Human figures, including an elaborately dressed Maya king, also decorate the walls. You can tour the room at National Geographic Daily News.

One wall of this residential room contains a calendar based on phases of the moon, covering about 13 years. Anthony Aveni, an expert on Mayan astronomy, said the calendar would allow scribes to predict the appearance of a full moon years in advance. Record-keeping was a key to Mayan astrology and rituals, and might be used to advise the king on when to go to war or how good the year's crops would be, he said.

For years, some people had speculated that the Maya people thought the world would end in 2012 since the oldest Maya calendar discovered had ended at 2012. Others pointed out that our calendars also show a limited period of time, not because we think the world won't last beyond then but just for the efficiency of producing the calendar. With the discovery of this new calendar, those speculations are largely put to rest. The markings on this wall suggest dates thousands of years in the future.

"Why would they go into those numbers if the world is going to come to an end this year?" observed Aveni. "You could say a number that big at least suggests that time marches on."

"I think we are all astonished by this find," says Stephen Houston, an archaeologist at Brown University (not part of the team). "What you are looking at here is a fundamental human drive to make sense of the disparate patterns of nature, and somehow harmonize them into an elegant mathematical structure."

In Excel Math, we teach students math concepts they will use in everyday life. Students learn how to read a calendar, the days of week, the months of year, and how to calculate dates in the future. They also learn how to find a date in the past. In second grade, students learn how to calculate a date within a week. Take a look at this Excel Math student worksheet from Grade 2:
Excel Math Grade 2 Lesson 84 Student Worksheet
To help your students find the date within a week, going backward, have them write the first letter of the day you give them. (S=Sunday) Then write the days in reverse order, right to left, ending with the day they are trying to find:
T  F  S  S
 Next, put the given date under the given day and count backward. If it is exactly one week, subtract 7 from the given date since there are 7 days in one week.
Day you are trying to find = T  F  S  S = Given day is Sunday. 
Date you are looking for = 11 12 13 14 = Given date is 14.
For example:
If today is Sunday, May 14. Last Thursday was May _____

Day you are trying to find = T  F  S  S = Given day is Sunday.
Date you are looking for = 11 12 13 14 = Given date is 14.
So last Thursday was May 11.

Try another one:
If today is Friday, July 19. Last Saturday was July _____

Day you are trying to find = S   S   M  T  W Th  F = Given day is Saturday.
Date you are looking for =  13 14 15 16 17 18 19 = Given date is 13.
So last Saturday was July 13.

Let your students try circled #2 from the worksheet above in pairs or as a class, just to make sure everyone understands how to solve the problems.

Then let them solve the two problems in #1 on their own and use the CheckAnswer to make sure their work is correct. If the CheckAnswer is wrong, they can go back and try the problems again to fix their calculations.

This unique self-assessment enables students to confirm their work. The CheckAnswer process helps students develop confidence and good work strategies. Students solve a set of 3-5 problems (A-C), add the answers, and see if the sum matches the CheckAnswer (D)If it matches, they move on. If not, they go back and re-check their calculations:

Read more about the Excel Math Student Lesson Sheets at Watch a video of Excel Math in action at

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