# Algebra for the Real World

Last week, Math teacher Corey Hopp projected a fast-food menu on the smart board in Room 413. His students were delighted by the choices: Hamburgers, cheeseburgers, French fries, milkshakes, and something known as a “Double-Double,” which featured twice the amount of meat and cheese.

No, these Class 7 students weren’t deciding what to have for lunch. They were learning algebra.

“This is quite possibly my favorite math lesson,” said Mr. Hopp as his classroom buzzed with excitement.

The menu, which advertised hamburgers for \$1.50, cheeseburgers for \$1.75 and Double-Doubles for \$2.65, was from In-N-Out Burger, the popular West Coast eatery. Mr. Hopp explained that In-N-Out also had a secret menu, which allows patrons to order as many extra beef patties and cheese slices as they desire.

The most common “secret orders” are three burgers and three pieces of cheese, called a “3 x 3,” or four burgers and four pieces of cheese, the “4 x 4.” On the opposite end of the spectrum, it is also conceivable to order a “100 x 100.” To prove this point, Mr. Hopp showed a photograph of an impossibly long concoction, eliciting shrieks and laughter from his students.

“What do you notice about this burger?” Mr. Hopp asked. “Turn to the person next to you and discuss.”

After a few minutes of productive chatter, one student volunteered: “Every time you add a patty you have to add a piece of cheese.”

This concept, known as “balancing equations,” is fundamental to algebra, as these young mathematicians soon discovered. The students also observed that, while the meat and cheese numbers increase with each incrementally larger burger, the bun, lettuce and tomato quantities remain unchanged.

Next, during “independent think time,” the students were asked to tackle the following challenge:

If “C” is the cost of the burger, what does C equal for each below?

3 x 3; C = _______

20 x 20; C = _______

100 x 100; C = _______

N (any number) x N (any number); C = _______

Working through these problems in their math journals, they displayed focus and determination. When questions arose, Mr. Hopp guided them in the right direction. The students helped each other as well. One creatively demonstrated her understanding using items in the classroom to represent the burgers and the cheese.  “That’s a beautiful explanation,” Mr. Hopp remarked.

For the remainder of the class period, the students were asked to collaborate on a visual project that illustrated their grasp of this particular lesson. Rearranging themselves into groups of two or three – some pulling their desks into circles, others sitting together on the classroom carpet – they brainstormed various ways to calculate the prices of different size burgers.

When they settled on a plan of action, Mr. Hopp handed each group a sheet of poster board, and the energetic students got busy writing out their linear equations in bright marker. For example, for a “3 x 3,” one team wrote: 1.75 (3) - (3) (.85) + .85 = \$3.55. Another computed “20 x 20” this way: 1.75 + [(19) 0.9] = \$18.85.

Whether or not they indulge in any variation of the famous In-N-Out Burger, these Class 7 students are well prepared to assess countless real-world situations – including hamburgers, cheeseburgers and the Double-Double – through the amazing lens of algebra.

Browse photos from the class below: