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Tayfun Coskun/Anadolu Agency via Getty Images

Brain-Bending Buildings

These buildings take architecture to the extreme! From the skinniest skyscraper to a tilted tower, these structures show just how far design can go.

By Jeanette Ferrara
From the October/November 2022 Issue

Learning Objective: Students will write and solve numerical expressions related to extreme buildings.

Lexile: 870L; 660L

Tayfun Coskun/Anadolu Agency via Getty Images

Steinway Tower is only 60 feet wide!

Skinniest Skyscraper

One of the tallest buildings in New York City’s skyline is only as wide as the length of a bowling lane. Steinway Tower is the slimmest skyscraper in the world. This 1,428-foot-tall building is only 60 feet wide at its base. It opened in 2019. The residential building holds 60 apartments across 84 floors.

One of the tallest buildings in New York City is only as wide as the length of a bowling lane. Steinway Tower is the thinnest skyscraper in the world. It’s 1,428 feet tall. But it’s only 60 feet wide at its base! It opened in 2019. The residential building holds 60 apartments across 84 floors.

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Solar panels go around Apple Park’s roof.

Supersized Solar Power

This 2.8 million-square-foot building in Cupertino, California is the largest solar-powered building in the world. Called Apple Park, it’s the headquarters of tech giant Apple Inc. More than 80 percent of the building’s energy comes from the solar panels on its roof. Apple Park cost $4 billion to build. The panels of curved glass around the building are also the largest in the world.

This is the largest solar-powered building in the world! It’s located in Cupertino, California. The building spans 2.8 million square feet. It’s called Apple Park. It’s the headquarters of the technology company Apple Inc. More than 80 percent of the building’s energy comes from the solar panels on its roof. Apple Park cost $4 billion to build. The panels of curved glass around the building are also the largest in the world.

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Left to right: Capital Gate leans at a stunning 18 degrees! Leaning Tower of Pisa 

Titanic Tilt

There’s a new leader of leaning towers, and it’s not in Pisa! Capital Gate is a 35-story glass building in Abu Dhabi, the capital of the United Arab Emirates. It opened in 2010. The top 17 floors of the building lean dramatically off center. The building is supported by almost 530,000 cubic feet of concrete. It’s reinforced by 10,000 tons of steel to keep it from toppling over. Inside are
15 floors of office space, four restaurants, and a hotel.

There’s a new leader of leaning towers. And it’s not in Pisa! Capital Gate is in Abu Dhabi. Abu Dhabi is the capital of the United Arab Emirates. The glass building is 35 stories tall. It opened in 2010. The top 17 floors of the building lean dramatically off center. The building is supported by almost 530,000 cubic feet of concrete. It’s reinforced by 10,000 tons of steel. The steel keeps it from toppling over. Inside are 15 floors of office space, four restaurants, and a hotel.

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Would you stay in the Big Basket hotel?

Biggest Basket

Back in 1997, the Longaberger Basket Company opened its headquarters in Newark, Ohio. But it didn’t build a typical office building. Instead it designed a 7-story building, called the Big Basket, shaped like a giant version of the company’s signature products! The basket company went out of business in 2016. Now the Big Basket is home to a 180,000-square-foot luxury hotel.

Back in 1997, the Longaberger Basket Company opened its headquarters in Newark, Ohio. But it didn’t build a typical office building. Instead, it designed a building shaped like a giant version of the company’s signature products! The building is 7 stories tall. It’s called the Big Basket. The basket company went out of business in 2016. Now the Big Basket is home to a 180,000-square-foot hotel. 

A. Steinway Tower is 60 feet wide. In comparison, another narrow New York City skyscraper, 432 Park Avenue, is 93.5 feet wide. The Empire State Building is 424 feet wide. How much wider is the Empire State Building than Steinway Tower and 432 Park Avenue combined? Write an expression.

B. Evaluate the expression.

A. Steinway Tower is 60 feet wide. In comparison, another narrow New York City skyscraper, 432 Park Avenue, is 93.5 feet wide. The Empire State Building is 424 feet wide. How much wider is the Empire State Building than Steinway Tower and 432 Park Avenue combined? Write an expression.

B. Evaluate the expression.

A. There are 9,000 trees in and around Apple Park. Of those, 3,000 are evergreen oaks. There are 600 fruit trees. Write an expression for the number of trees that are neither evergreen oaks nor fruit trees.

B. Evaluate the expression.

A. There are 9,000 trees in and around Apple Park. Of those, 3,000 are evergreen oaks. There are 600 fruit trees. Write an expression for the number of trees that are neither evergreen oaks nor fruit trees.

B. Evaluate the expression.

A. Capital Gate leans about 20° (degrees) to the west—about 5 times the tilt of the eaning Tower of Pisa in Italy. Write an expression for how many more degrees Capital Gate leans than the Leaning Tower of Pisa. 

B. Evaluate the expression.

A. Capital Gate leans about 20° (degrees) to the west—about 5 times the tilt of the eaning Tower of Pisa in Italy. Write an expression for how many more degrees Capital Gate leans than the Leaning Tower of Pisa. 

B. Evaluate the expression.

A. The Big Basket is 208 feet long and 142 feet wide. Let’s say the hotel wanted to add a fence around the building that was 20 feet away. Write an expression for how many feet of perimeter fencing would be needed. HINT: The formula for perimeter is (2 × length) + (2 × width).  

B. Evaluate the expression.

A. The Big Basket is 208 feet long and 142 feet wide. Let’s say the hotel wanted to add a fence around the building that was 20 feet away. Write an expression for how many feet of perimeter fencing would be needed. HINT: The formula for perimeter is (2 × length) + (2 × width).  

B. Evaluate the expression.

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Games (1)
Activities (6)
Answer Key (1)
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video (2)
Games (1)
Activities (6)
Answer Key (1)
Step-by-Step Lesson Plan

1. SPARK ENGAGEMENT.

Play the video "History of Skyscrapers." Then, before or after reading the article, spark a discussion based on the following questions.

  • Describe the most interesting building you have ever seen or visited.
  • How is math involved in designing and building safe tall buildings?
  • If you could design your own skyscraper, what would it look like and why?

2. INTRODUCE THE MATH CONCEPT AND VOCABULARY.

  • What's a situation where the order in which you complete the steps makes a difference in the result?
  • Just as you would not start a recipe in the middle of the directions, there is a specific order in which we solve operations in math expressions so that we can ge the correct answer.
  • Display the expression: 3 x (4 + 2). With a partner discuss the steps you would take to solve this expression.
  • We could use the order of operations to help us determine our steps to solve an expression. Solve anything grouped in parentheses first.
  • Today, we will write expressions while keeping in mind the order of operations.
  • Play the math video, "Intro to Expressions."

3. WORK THROUGH THE "WHAT TO DO" BOX.

  • Which part of the math expression was solved first? (The multiplication inside the parentheses.)
  • Why was an addition symbol placed between the two sets of parentheses in the equations? (You are finding the total number of cinder blocks, so the two sets of blocks need to be added together.)
  • Would the answer have been the same without parentheses? Explain. (No; explanations will vary.)

4. REINFORCE WITH MATH PRACTICE.

Have students complete questions 1 through 4 on pages 10-13.

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