In order to solve the problem, students must assume that the steps are of uniform height, which looks reasonable given the picture. The first of these approaches falls under the 6th grade ratio and proportion standards while the second aligns better with the 7th grade.
The main goal of the third approach, using Egyptian fractions, is to provide an example of calculating fluently. The methods of the first two solutions are vital for a deep understanding of proportional reasoning. The numbers make this an advanced 6th grade task. It could be used as a transition from 6th to 7th grade expectations for work with ratios and proportional relationships, or it could be used as an assessment task in 7th grade either formative or summative, depending on the time and way it is used.
If used in an instructional setting, the teacher could ask the students to estimate before they compute. Since there are 91 steps and we want to know about the 50th step, we know that the height should be a little more than half of the total 24 meters in height.
This, the first number we use to assemble our formula for the decoding process. The second number is Kukulkan has four staircases, one on each side of the monument, on each staircase are 91 steps.
For the four. We now have our second number - In the overhead view, we see that the pyramid has four sides, and four staircases. These are , 42 and Two rational numbers and an irrational, but these are not shown on the pyramid. These appear only on maps. Hence, those other three numbers of , 42, and All Rights Reserved. When the Toltec people moved to Chichen Itza, they merged their own zenith cosmology with the Mayan system, and the result was the Pyramid of Kukulcan.
This has been designed so that every year, on Spring Equinox, the afternoon sun causes a shadow play so that it appears that a huge serpent is descending from the sky, down the pyramid. However, John Major Jenkins shows that the pyramid is much more than an equinox indicator. Photo from souvenir book. The Pyramid of Kukulcan at Chichen Itza.
This image shows the Seven Triangles of Light and Shadow as they appear on the west face of the northern staircase of El Castillo between and PM during the Spring equinox on March 21st. Jenkins says that Kukulcan, or Quetzalcoatl , the plumed serpent , was the symbol of a sun-Pleiades-zenith conjunction.
Exactly 60 days after the Spring Equinox, on May 20, the zenith passage of the sun takes place over Chichen Itza. The moving snake on the Pyramid is an annual reminder of a conjunction of the zenith sun with the Pleiades over Chichen Itza, but this is an event which will only occur during a year time window, from to Right at the centre of this time window is the year , when the Great Cycle ends.
On May 20 , the zenith passage combines with a solar eclipse, on the Tzolkin day 10 Chichan, which means serpent. Key dates that are all approximately 91 days apart from each other. July 16 Start of Mayan new year. Add 52 days to this date the same as the number of years in Maya "cycle" and you arrive at Sept 6th. Sept 22 Fall equinox Day and night equal length when seven triangles are visible.
This is 92 days from previous summer solstice of June Dec 21 Winter solstice, longest night of the year. March 21 Spring Equinox. Day and night equal length Seven triangles between - 5 PM.
April 6 Nine triangles between 5 and PM All possible triangles visible at this time. June 21 Summer solstice. Longest day of the year. A poetic combination of form, style, function, religion, philosophy, mathematics and geometry. A true symbiosis of all of their intelligence and art in one location, to be studied and admired by all that visit. By far the most impressive aspect of the Pyramid of Kukulkan is it's relationship with the sun and how it reflects the equinoxes and solstices of our solar year with stunning accuracy.
Before one can fully understand the workings of the Shadow of the Equinox, a few basics on astronomy need to be reviewed. An equinox occurs twice each year when our sun, in its orbit around the earth in a fashion unique to these times of the year, passes directly over the Earth's equator and the length of the daylight and evening hours is equal. Hence the word equinox is derived from the Latin for "equal" aequus, and nox meaning "night". The spring equinox occurs on March Six months later, on Sept 22, we have the Fall Equinox.
The summer solstice occurs on June 21st. On this day earth sees the longest duration of daylight. Six months later is the winter solstice on December 22, when we see the shortest daylight and the longest night of the year. On these days the sun almost seems to pause in its orbit before resuming its course, and it is why the word solstice is based on the Latin sol, for "sun", and sistere or "to cause to stand". This cycle then repeats itself as the Earth continues to rotate around the sun.
It is interesting to note that there are exactly 91 days between each of these events, and 92 days between the June 21 summer solstice and the September 21 equinox.
This adds up to a day solar year with the 91 days between each event matching the 91 steps to each side of the pyramid described here. Each of these solar events, the two solstices and the two equinoxes, can be measured and predicted using the patterns of light and shadow that fall on EL Castillo at various times of the year.
It is believed that the Mayans used the various shadows and designs formed by the Pyramid to signal the beginning of a harvest or of a planting, to predict the best dates to be married or to be buried, and for other various ceremonial reasons. The cycles of the sun also play out to another Mayan tradition of the number To us, it is a coincidence that this is the number of weeks in our standard year. But to the Maya it represented, in years, the time of one "cycle".
The Mayan Calendar began on on the first day of Pop month, or our July 16th. They kept a count of 52 days breaking down into 2 months with 20 days each, 2 weeks with 5 days each, and 2 additional days.
This count puts us in the 12th day of the 3rd month called Sip , or September 6th by our calendar. This was the day the Mayans held their most significant ceremonies at the base of the pyramid as September 6th as well as April 6th is when the complete nine triangles of shadow and light can be seen on the western side of the north staircase. Nine triangles being the most complete example of the phenomenon, with eight visible on the staircase and the ninth illuminating the head of Kukulkan.
Also visible just to the right of the illuminated serpent head is the entrance to the inner antechamber and the smaller structure over which the larger one was constructed. From the 12th day of Sip or September 6th count foreword three weeks Mayan weeks with 5 days in each and one additional day 16 days total and we arrive at the 9th day in the 4th month Zoodz or September On this date there are seven triangles on the same side of the main staircase which indicated to the Mayan astronomers that the Earth had completed its cycle around the sun.
Two of the triangles seen on September 6th completely shift off the pyramid and are projected onto the ground at the floor of the staircase. On the 6th day in the month of Tseek October 9th or 17 days after September 22nd there are 6 triangles visible.
There are several dates and variations of the shadows and triangles as the sun approached the positions for which the pyramid was built. They all had varying degrees of significance within the Mayan culture and I have only focused on the "main" ones.
Related Link: Hypothesis of how the the location for the pyramid was derived. Chichen Itza at Spring Equinox. Quetzalcoatl : "Feathered Snake. The story goes that he descended to Mictlan, the underworld, and gathered the bones of the human beings of the previous epochs.
Upon his return, he sprinkled his own blood upon these bones and thus fashioned the humans of the new era. After he banned himself from earth, and was burned while traveling on the ocean, the heart of Quetzalcoatl became the morning-star.
This glorious step pyramid demonstrates the accuracy and importance of Maya astronomy—and the heavy influence of the Toltecs, who invaded around and precipitated a merger of the two cultural traditions. The temple has steps—one for each day of the year. Devising a day calendar was just one feat of Maya science. Incredibly, twice a year on the spring and autumn equinoxes, a shadow falls on the pyramid in the shape of a serpent.
Spanish records report that young female victims were thrown into the largest of these, live, as sacrifices to the Maya rain god thought to live in its depths. Archaeologists have since found their bones, as well as the jewelry and other precious objects they wore in their final hours.
During ritual games here, players tried to hit a pound 5. Competition must have been fierce indeed—losers were put to death.
It was also a sophisticated urban center and hub of regional trade. But after centuries of prosperity and absorbing influxes of other cultures like the Toltecs, the city met a mysterious end. Recently this World Heritage site was accorded another honor. The ruins are open daily. Spring and autumn equinoxes offer the chance to see the incredible shadow serpent of El Castillo—but the often crowded site is absolutely packed at these times.
There is also a light show on the site at night. All rights reserved. How to Get There.
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