How Much is This Cheeseburger?

We have reached spring break. This past Friday, we had our school’s spring carnival. This meant that teachers lost a day with 6th and 7th periods. My Algebra II classes are 4th and 7th period; so I didn’t have class with 7th period on Friday. Since we had just tested the day before in 4th period, I decided Friday was a perfect day to experiment.

The first day of class in my classroom changes each year. I always start the year placing my students in a mathematical situation. While it may not be directly from the curriculum, I feel that my students can get the best idea what my class is about by doing math…as weird as that sounds. Placing them in the thick of a math problem and see how they respond gives me a lot of information about my students. Likewise, being in the thick of a math problem can tell my students a lot about what I expect of them.

My 4th period class likes to be a challenge. They don’t like math/ think math is hard/ just want me to tell them what to do so they can move on with their lives/ are tired of the school year and are looking forward to summer (and probably summer 2015 for a bunch of them). This mindset is perfect for my experiment.

So here’s the experiment:

In and Out Burger Lesson_1

What a simple question. How much was that cheeseburger. There tended to be two common responses: “ewww” and “I want one.” Then the guesses started flying. Some were reasonable, some definitely weren’t. I didn’t care about the unreasonable guesses; at least they were engaged in the question and were taking some ownership in the problem. Finally some questions were asked. The most important questions got me to tell them that on this burger there was one bun, one hundred patties, and one hundred slices of cheese. Now the question is accessible. “Give us some prices Mr. Cloud.”

So I did:

In and Out Burger Lesson_2

That’s all they get. That’s all the menu at the restaurant has. There weren’t any complaints. Nobody said this is stupid. They went right to work trying to figure it out. There were wonderfully insightful conversations/questions. “A cheeseburger has one bun, one patty and one piece of cheese. You can’t just multiply by 100. You’ll have 100 buns.” It was a magical 15 minutes. I didn’t have to lead or quiz or scold or encourage. They were doing it; they were doing math. They were discussing and justifying. Groups started collaborating with other groups. They were getting the same answer. Groups that didn’t get it asked for explanations from other groups. All of this from a group of students who couldn’t care less (at times) how the fundamental theorem of algebra relates to the real and imaginary roots of a quintic polynomial. This lesson worked and will work as a way to create a setting for next year’s classes. Now just to figure out how to do this every day. This 15 minutes is how I picture my classroom all 50 minutes all 180 days.

Oh here’s the answer by the way:

In and Out Burger Lesson_3

Somewhere in the neighborhood of 95% of my students got to the answer. They used systems of equations and didn’t even know it!

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