Parabolic Fruitcake

Jacquelyn Kilgo was forever looking for problems - math problems, that is, for the students in her high school algebra class.  Which is why the ad in the magazine for the Collin Street Bakery's Classic Christmas Cake had caught her eye.

"I wanted to show the kids that math problems weren't just in textbooks," says Jacquelyn, who taught at Hubbard High School, just about twenty-five miles from Corsicana and Collin Street.  "I wanted them to think outside the box."  And so they did: out of the box, and into the bakery.

"The Classic Christmas Cake," the magazine ad announced.  The ad went on to list three sizes of fruitcakes and their (1995) prices:

Regular (1 7/8 lbs.)   $15.75
Medium (2 7/8 lbs.)   $22.95
Large    (4 7/8 lbs.)   $37.95

It was a perfect problem for Jacquelyn's students, who were using their Texas Instruments graphing calculators that had just come into vogue.  "The beauty of the TI calculators was that the machines did the math but the students did the problem-solving," says Jacquelyn's.

The two sets of numbers - the weights of the fruitcakes and the prices for each - provided ideal points to plot on a graph.  "Was this a quadratic, liner, or cubic function?  I wanted the students to see the answer on the graph," says Jacquelyn.

Having drawn a graph of the information, the students then had to answer some questions:

  • What was the equation for the graph?
  • What was the slope?
  • What was the real-world significance for the slope?
  • What was the y-intercept?
  • What was the real-world significance for the y-intercept?

And then:

  • How much would a 3 1/2 -pound fruitcake cost?

What the students (along with their teacher) soon realized was that it wasn't the straight-line equation they thought it'd be, but rather, a parabolic function.  (Translation for those who need a refresher course in algebra; it curved.)

About thirty students were in Jacquelyn's two math classes, and most of them got the problem right.  "I was hoping the advanced ones would solve the regression equation, and they did," she says.

Jacquelyn was a teacher for thirty-one years.  (She retired in 2001.)  She started off in elementary education but, dismayed by how her own children learned math in high school. went back to school to become a math teacher.  She was determined to make math challenging but enjoyable for her students.

A fruitcake equation did just that - especially when the kids received a complimentary DeLuxe® Fruitcake from Collin Street Bakery as thanks for their applied mathematics.

Jacquelyn had another reason fro choosing a fruitcake; it was Christmastime when she assigned the problem, and she figured the kids would be thinking about traditional holiday foods.

As she would.

As a child growing up in Hubbard, Jacquelyn grew up on Collin Street Bakery fruitcakes.  Her grandparents lived there too, and every Christmas it would be there at her grandparents' open house; her grandmother's homemade eggnog and the Collin Street Bakery fruitcake.

"From the time I was 3 years old I remember that," says Jacquelyn.  "I can just see that fruitcake tin in my grandmother's dining room."

Today she still remembers those Christmases" she inherited her Grandmother's dining room furniture, teh very furniture where the bowl of eggnog and the tin of fruitcake would be.  Every time she dusts the table, it serves as a touchstone of family and holiday memories.

One of Jacquelyn's greatest joys is bumping into her former math students and having them tell her she'll never guess, but they're now teaching high school math.

"When you're a teacher, a little bit of you gets passed on to the next generations," says," says Jacquelyn of the career she loved.

And perhaps, a little bit of fruitcake math as well.

Grade your paper

Did you take Mrs. Kilgo's math test?

More than twelve years after she gave her kids the "fruitcake test," Jacquelyn worked out the answers for herself ("fortunately, I still had my graphing calculator").  Here they are, and with this caution: remember that these were 1995 prices.  It's always good to check your math.

     The Classic Christmas Cake

     Regular (1 7/8 lbs.)   $15.75
     Medium (2 7/8 lbs.)   $22.95
     Large    (4 7/8 lbs.)   $37.95

What is the equation for the graph?
     Linear: y = 7.34x + 2.32
     Quadratic:  y = -0.3899x2 + 10.03x - 1.689

What is the slope?
     Linear: 7.34
     Quadratic: no slope

What is the real-world significance for the slope?
     Cost per pound

What is the y - intercept?

What is the real-world significance for the y - intercept?
      Fixed cost before weight is considered.

How much would a 3 1/2-pound fruitcake cost?
     Using a linear function:          $28.01
     Using a quadratic function:   $28.64