Magic City Math Trail

Birmingham, Alabama

Birmingham, Alabama, the Magic City, was an early planned community developed by the Elyton Land Company in the early 1870s.  The downtown area was set up in a grid pattern with streets running north-south while avenues ran east-west.  Both are numbered instead of named, which makes downtown addresses very easy to find!

Birmingham became known as “The Magic City” because of its early rapid growth.  Nestled in a valley near the southern end of the Appalachian Mountains, the city lies in a region containing limestone, iron ore, and coal, all necessary ingredients for steel-making.  This industry became the foundation of the early economy and the inspiration for the statue of Vulcan, which sits atop Red Mountain overlooking the city.

The current economy is based on education, medicine, banking, and telecommunications. The University of Alabama in Birmingham, and its medical center, is the city’s largest employer.

The math teams of Berry Middle School and Simmons Middle School, both located in the city of Hoover, an over-the-mountain suburb of Birmingham, went on a joint math trail in the business center of Birmingham.  Starting a block from Linn Park, City Hall and the Jefferson County Courthouse, the trail wound around the skyscrapers and historic buildings of the city center.

Problems

AmSouth – Sonat Building

What is the height of the flagpole on the plaza in front of the building?

We couldn’t climb it or reach the top so we used proportions. The shadow of the flagpole was 22 feet and 4 inches. Michelle is exactly 5 feet tall. Her shadow was 2 feet 8 inches. Therefore we know that (in inches) the proportion is:
height        60       ?
--------  =  ----- = -----
shadow      32      276

The answer works out to be almost 42 feet.

 

 

The plaza in front of the building has a raised area in one corner.  What percent of the plaza does the raised area contain?  The entire plaza has measurements of 82’ and 103’.  That makes the area 8446 square feet.  The raised area has dimensions of 21.25’ and 27’.  Its area is 573.75 square feet.   The percent the raised area takes is 6.79%.


McDonald’s Millionaires

Rachel, Piyanka, and Christina are going to McDonald’s for dinner. They each got a medium order of French fries so they could play the Who Wants To Be A Millionaire game. They wanted to find the probability of each of them winning a cash prize.

Each had a ¼ chance of correctly answering the question on the box of french fries, and each had a 1/6 chance of scratching off a cash prize.

For each:  ¼ x 1/6 = 1/24
Combined for all three:  1/24 x 1/24 x 1/24 = 1/13824

 

SouthTrust Tower

The SouthTrust Tower is located on 20th Street and 4th Avenue.  When looking above the third floor, you can distinctly tell that there are twenty-four sides to the building.  What is the correct name for the shape of the polygon with 24 sides?

 

Bird’s-eye view of the
SouthTrust Tower

 

 

 

A polygon with 24 sides (according to Ask Dr. Math at mathforum.org) is called an icosikaitetragon.

 

City News

On the corner of 20th Street and 5th Avenue North stood 18 vending machines for newspapers and magazines.  Some hold free publications such as “Apartment Guide” while others hold local and national newspapers.  Of the 18 machines, 12 had free publications on the day of our trail.  What is the probability that, if you chose a machine at random, it would have a free publication?

          12 free                   2
          ----              =       ---
          18 total                  3

The Birmingham News costs $.35. The machine will take nickels, dimes and quarters.  In how many different ways can a person put in $.35 to buy a newspaper?

 Make a table of possible ways.

Quarters

Dimes

Nickels

1

1

0

1

0

2

0

3

1

0

2

3

0

1

5

0

0

7
 

There are six possible combinations of coins that will make $.35.

 

Cashing In at Heritage Bank

If Lauren wanted to deposit $1500 in a CD with an interest rate of 4.75% (compounded annually), how much interest would she earn after two years?

Step 1: Set up a proportion to find the first year’s interest.
                    ?           4.75
                   ------ = -------
                   1500      100    

Lauren earned $71.25 her first year.

 

 

 

Step 2: Add the first year’s interest to the original amount.

                   1500 + 71.25 = 1571.25

Step 3:  Set up another proportion, but this time use the total amount of money.

                      ?            4.75
                   ---------- = -------
                    1571.25    100      Lauren earned $74.63 her second year.

Step 4: Add the two interest amounts together.

71.25 + 74.63 = 145.88     Lauren earned $145.88 in interest over two years.

 

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