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:
18 Comments
Suz
9/8/2011 04:58:30 am
I'll mark my calendar to see if they don't change that bag 5 years from now! Awesome assignment.
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Lisa Brogan
1/27/2012 04:43:07 am
I love this project! Do the bags stll say that?
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Natalie Turbiville
2/2/2012 11:43:39 pm
Yes! The bags will still in production for the next few years. It's neat when my students come back and let me know that they got the bag when they ordered food from Wendy's!
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Corey Colosky
4/5/2013 11:53:00 pm
Are you sure there are 9 toppings? Cause if there are 8 toppings, then it comes out right. What are your 9 toppings?
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April Gonzalez
2/16/2016 02:29:45 pm
Mayo
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tom Wild
4/9/2013 03:47:19 pm
I have been trying to come up with 9 toppings. I only come up with 8. Lettuce, onion, pickle, Ketchup, mustard, mayo, cheese, and tomato.
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April Gonzalez
2/16/2016 02:27:52 pm
Bacon
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Natalie Turbiville
4/10/2013 12:09:44 am
Great question!
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Tom Wild
4/10/2013 01:38:19 pm
Thanks yes that helps. I went to Wendys in Burbank in California and they did not have those bags.
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8/5/2013 10:57:47 am
First, let me say how much I love your blog and how I have used so many of your ideas to help boost my first year.
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Victoria
11/14/2013 03:35:54 am
Regionally, you can add chili and slaw to your burger. This is called a "Carolina Classic." Therefore the 256 ways is way under if you consider those two toppings as well!
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John
1/19/2014 06:30:10 am
Hi. It should be mentioned that the sum of choosing from 0 to n items out of an n item set will always equal 2^n, which is why you came up with 512 when you did this with 9 toppings. The simplest way to see this is to look at each item in turn and either put it on the burger or leave it off. This argument can easily be made with a tree diagram, and would be an excellent extension to this project.
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Marissa
4/21/2014 07:06:04 am
I love this project! However, Wendy's really isn't wrong. They were correct when there were 8 toppings...the only thing that makes it wrong is that another topping was added
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vera
4/22/2014 01:49:55 am
great extension John!
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hi
2/3/2015 04:58:14 am
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Catherine
4/6/2017 03:31:00 pm
Hi i have a question
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Adam Green
4/3/2018 07:03:01 am
9C2 is the equation used for combinations, the way I learned it was 9 options and choose 2. When put in a calculator using the C you do get 36 when you have 9 options and you choose only 2 of those options and you have 36 possible combinations when using those parameters.
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Natalie Turbiville
Educator who loves math and working with students. Archives
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