7.1: Quantway Core 3.7-TCU - Student Lesson

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SPECIFIC OBJECTIVES

By the end of this collaboration , you should understand that

proportional relationships are based on a constant ratio.
rules for solving equations can be applied in unfamiliar situations.

By the end of this collaboration, you should be able to

set up a proportion based on a contextual situation.
solve a proportion using algebraic methods.

BACKGROUND

In response to the construction of Mt. Rushmore, Lakota Chief Henry Standing Bear wanted to create a memorial honoring North American Indians. He wrote to a sculptor named Korczak Ziolkowski and asked him to create a memorial of a great hero, Crazy Horse.

Crazy Horse or Tasunke Witco was born as a member of the Oglala Lakota on Rapid Creek about 40 miles northeast of Thunderhead Mt. (now Crazy Horse Mountain) in c. 1840. He was a Oglala Lakota warrior famous for defeating Custer and the Seventh Cavalry at the Battle of Big Horn.

It was a time when cultures clashed, and land became an issue of deadly contention. Traditional Native ways were threatened and oppressed. Crazy Horse responded by putting the needs of his people above his own, which would forever embed him and his legacy in American History. He is a beloved symbol for the Lakota people because “he never conceded to the white man.” He was killed at Fort Robinson, Nebraska, by a soldier around midnight on September 5, 1877.¹

On May 3, 1947 Korczak began work on the Crazy Horse Memorial. He worked for over 35 years and his work is continued by his children and grandchildren to this day. This memorial carved from Thunderhead Mt. is much larger than Mt. Rushmore. If the President’s heads were stacked one on top of the other, they would only reach a little more than half way. The scale of the Crazy Horse Memorial when complete will be grand, becoming the largest sculpture in the history of the world.²

Photograph of the unfinished Crazy Horse memorial. ³

There are many Lakota who praise the memorial, grateful that it offers an unmissable reminder of the frequently ignored Native history of the hills, and a counterpoint to the four white faces on Mt. Rushmore. But others argue that a mountain-sized sculpture is an ill-chosen tribute. When Crazy Horse was alive, he was known for his humility, which is considered a key virtue in Lakota culture.

PROBLEM SITUATION 1: CRAZY HORSE MEMORIAL

As of Fall 2020, the Crazy Horse Memorial is far from complete. To begin construction on the Crazy Horse Memorial, two sculptures were created as scale models. Scale models are smaller versions, but proportionally equal, to the final model.

Photograph of sculpture of Crazy Horse memorial. ⁴ ⁵

(1) These models are at a scale of 1:34 and 1:300. Which scale model do you think is larger? 1:34 or 1:300? Explain your thinking.

(2) Crazy Horse Memorial is 641 feet long and stands 563 feet high.⁶

(a) Complete the table by finding the length for each scale model shown above. Round your answers to one decimal place.

Scale Model	Length
1:34
1:300

(b) Complete the table by finding the height for each scale model shown above. Round your answers to one decimal place.

Scale Model	Height
1:34
1:300

(3) On the Crazy Horse Memorial, Crazy Horse’s outstretched arm is 263 feet. Here again, is the photo of the original model with the artist:

Photograph of sculpture of Crazy Horse memorial with the artist.

(a) What is a more appropriate measurement for Crazy Horse’s arm on the model?

(i) Inches

(ii) Feet

(b) Using the scale factor of 1:300, what is the length of Crazy Horse’s outstretched arm on the model? Round to two decimal places.

(c) On the Crazy Horse Memorial, Crazy Horse’s face is 87 feet, 6 inches. Using the scale factor of 1:300, what is the height of Crazy Horse’s face on the model? Write your answer rounded to one decimal place.

(d) On the original model, Crazy Horse’s pointing finger is 1.18 inches long. How many feet and inches long is that finger on the Memorial?

PROBLEM SITUATION 2: DEVIL’S TOWER

A scale factor can be used to enlarge or reduce any shape.

One large rectangle with corners ABCD; height AD is 14 feet. A smaller rectangle has corners EFGH; length EF is 8 feet.

(4) The scale factor of ABCD to EFGH is 3:1. Determine the missing lengths of EFGH.

(a) The length of \(\overline{AB}\) (the distance from A to B) is ___________ feet.

(b) The length of \(\overline{EH}\) (the distance from E to H) is ____________ feet. Round your answer to two decimal places.

(5) Devil’s Tower is 867 feet tall, but the length across the base is unknown. There is a scale model of Devil’s Tower that is 5 inches tall, and it has a base length of 9.7 inches. Round to the nearest foot.

Image of Devil's Tower.