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CCSS: 8.G.B.7, 8.G.B.8, MP4, MP5, MP7
TEKS: 8.7C, 8.7D
The Lost Lucky Ball
YOUR MISSION: Use the Pythagorean theorem and the distance formula to search through the city of Tenochtitlán (tay-noch-teet-LAHN) for the rubber ball used in the ritual game played across Mesoamerica. Round answers to the nearest tenth on the online answer sheet.
The Pythagorean theorem is used to find a missing side length of a right triangle:
a2 + b2 = c2
The distance formula is a variation on the Pythagorean theorem and is used to find the distance between two points on a coordinate plane:
The court has two stone hoops. Each is 15 feet high on the wall. A player is 6 feet away from a hoop. What’s the diagonal distance from his feet to the hoop?
You’re 9 feet away from the hoop. What is the diagonal distance from you to the hoop?
You and a teammate are at opposite corners of the court. The court is 100 feet long and 50 feet wide. How far would the ball travel if you were to hit it along the diagonal distance to your teammate?
A player is 12 feet directly in front of you. Another is 7 feet to your left. He hits the ball to the player in front of you. How far did the ball travel?
A - ball court
Site where ball games are held
B - templo mayor
Pyramid at the center of the city’s sacred precinct. On the top are twin temples dedicated to Huitzilopochtli (weet-see-loh-POHCH-tlee), the sun and war god, and Tlaloc (TLAH-lohk), the god of rain.
C - calmecac (kal-MEH-kak)
Elite school that trains future priests of Quetzalcoatl (kweht-suhl-kuh-WAH-tuhl).
D - eagle gate
One of four gates that lead into the sacred precinct, where the city’s shrines and temples—as well as schools, ball courts, and more—are located
E - great plaza market
City’s main marketplace
1 unit = 100 Feet
You leave from (-2, 1) near the ball court and head to (5, 0) at the Templo Mayor to pay your respects to the gods. How many units did you travel?
You leave the temple at (5, 0) and head to the Calmecac to meet up with a friend outside the school at (-3, -3). How many units did you travel?
You leave the Calmecac at (-4, -5) and head toward the Eagle Gate at (0, -8). How many units did you travel?
A large cylindrical container holds more olives than you can count! It’s 3.6 feet tall with a radius of 2.25 feet. What’s its volume?
From the Eagle Gate at (0, -8), you head to the market to browse the stalls and then meet your family at (-1, -11) before going home for the night. How many units did you travel?
The Templo Mayor’s two temples sit atop a 180-foot-tall pyramid, with two staircases to the top. The horizontal distance from the edge of the pyramid to the temples is 131 feet. How long is each staircase?
The Templo Mayor was built on top of smaller pyramids. An earlier pyramid was 90 feet tall, with staircases that were 118 feet long. What was the horizontal distance from the top to the edge of the old pyramid’s base?
Students at the Calmecac have a smaller practice court, where the hoop is 9 feet off the ground. A student is 4.5 feet away from the hoop. What‘s the diagonal distance between the student and the hoop?
A student 10 feet in front of you throws the ball to you, and you throw it to another student 5 feet to your right. Then that student throws it back to the first one. How far did the ball travel in total?
Some vendors show off their goods using tall racks. One rack is 11 feet tall, full of woven baskets. The vendor has a 12-foot ladder that he sets 4 feet away from the rack. Is this ladder tall enough for him to reach the top while standing on it?
Now that you have your lucky ball, it’s time to head back to the court! The vendor’s stall is at (-3, -11). The court is at (-2, 0). But you must go through the Eagle Gate at (0, -8). How many units in total do you travel?
Use any of the coordinates on the map (on your answer sheet) to write your own Pythagorean theorem question.
1345 - 1521
AREA OF THE EMPIRE:
80,000 square miles
POPULATION OF TENOCHTITLÁN:
140,000 to 200,000 people
260 days divided into 20 weeks of 13 days
POPULATION OF THE EMPIRE: