I picked up some food at Wendy's during the spring in 2009. The bag my food was in (picture above) had the following phrase: "We figured out that there are 256 ways to personalize a Wendy's hamburger. Luckily someone was paying attention in math class."
I began to wonder how did the marketing team come up with that number? I began to realize that the topic I was soon teaching my 9th graders, permutations and combinations, was more than sufficent math to calculate the number of ways to personalize a Wendy's hamburger. I developed a project based around the bag. In class, we discussed the number of toppings available at Wendy's (9 total) and then decided to use combinations to figure out the number of arrangements possible since order does not matter. Students could easily answer those questions.
The hardest part for students was how to set up the calculations. You find the number of combinations of 9 objects (toppings) taken 0 at a time (the number of hamburger personalizations with nothing on it), the the number of combinations of 9 objects (toppings) taken 1 at a time (the number of hamburger personalizations with 1 topping), and continue the process till the 9 are taken at a time (the number of hamburger personalizations with all toppings). Students typically pick up the pattern once started. I let my students use their scientific calculators to solve.
9C0 = 1
9C1 = 9
9C2 = 36
9C3 = 84
9C4 = 126
9C5 = 126
9C6 = 84
9C7 = 36
9C8 = 9
9C9 = 1
Total: 512 ways to personalize a Wendy's hamburger
The bag is wrong!
I then have students write a letter to Wendy's, requesting the bag to be changed. (They will not, appartently enough bags have been printed for the next 5 years!) I have a rubric to grade the letters and set the peramertors of the letter. This is what I count as the project grade. Each student brings 2 copies of the letter so that I can grade one and send another to Wendy's. Your students get a coupon for a special treat!
The activity is a great way to show how permutations/combinations is used in everyday life and in various fields. I have always gotten a positive response to the project and how many times are you given a free frosty at school?
EXTRA CREDIT/EXTENSION: Why does the bag say there are 256 ways to personalize a hamburger? Show the math to support your answer.
Handouts used in class:
Educator who loves math and working with students.