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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

Focus Area: Algebraic Thinking,

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.

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.

The History of Skyscrapers

Watch a video about the world's first skyscrapers.

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.

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.

Intro to Expressions

Watch a math helper video about how to write expressions and equations.

Math Talk

Why is it important to include units when you’re working with expressions?

Expressions

A crane lifting up a pallet of cinderblocks

What to Do

An expression is a math phrase that can include numbers, variables, and operators. Sometimes there are multiple operations in one expression. Parentheses help you organize your problem-solving steps. Perform operations within the parentheses first.

Example

A construction site has 8 pallets of cinder blocks with 70 blocks each. It also has 5 larger pallets with 90 cinder blocks each. Write and solve an expression for the total number of cinder blocks at the site.

• We need to find the total number of cinder blocks, but there are pallets of two different amounts. Let’s multiply the number of blocks by the number of pallets for each size separately.

8 pallets × 70 cinder blocks per pallet
5 pallets × 90 cinder blocks per pallet

• Next, put each expression in parentheses and add them together.

(8 pallets × 70 blocks/pallet) + (5 pallets × 90 blocks/pallet)

• Now evaluate, or solve, the expression.

(8 × 70) + (5 × 90) = 560 + 450 = 1,010 cinder blocks

There are 1,010 total cinder blocks at the site.

Expressions

What to Do

Example

• We need to find the total number of cinder blocks, but there are pallets of two different amounts. Let’s multiply the number of blocks by the number of pallets for each size separately.

8 pallets × 70 cinder blocks per pallet
5 pallets × 90 cinder blocks per pallet

• Next, put each expression in parentheses and add them together.

(8 pallets × 70 blocks/pallet) + (5 pallets × 90 blocks/pallet)

• Now evaluate, or solve, the expression.

(8 × 70) + (5 × 90) = 560 + 450 = 1,010 cinder blocks

There are 1,010 total cinder blocks at the site.

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. 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.

Multimedia

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Intro to Expressions

Watch a math helper video about how to write expressions and equations.

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.

Class Discussion:

Architects have to identify and overomce many challenges to build extreme buildings. Have a class discussion about challenges students may face in math class, such as having trouble solving a problem. Then brainstorm ways in which students could overcome these challenges as a class.