Taking Down Applebee’s
So, I caught this image on twitter as a WCYDWT a few weeks ago…
How fortuitous that I was teaching combinatorics that week. And with Applebee’s, I can teach two life lessons in one: how to compute combinations, and the experience of a white suburban kid who was forced to go to Applebee’s ALL THE TIME during high school because in a little town in Ohio there really aren’t many cool places to hang out. My Brooklyn students think that I’m making up stories of going to high school across the street from a pig farm or having to run through a corn field to get errant shots during soccer practice or that school got canceled because of snow a lot because it took a long time for the horse & buggy to plow the streets.
So, I did some research. Here are the facts:
9 different menu items:
Boneless Buffalo Wings, Dynamite (!) Shrimp, Spinach and Artichoke Dip, Cheeseburger Sliders, Steak Quesadilla Towers, Buffalo Chicken Wings, Mozzarella Sticks, and two new additions: Wonton Tacos and Spicy Queso Blanco.
You are allowed to choose 3 for one low price (in Brooklyn, $15.49!!!)
There are allegedly over 200 different combinations.
So, I put this image on the board at the start of class. I started talking about how much I hated Applebee’s and that I was starting a boycott. Students are intrigued to join the cause, and want to know why. I explain the situation. Then I make the claim: Applebee’s has either false advertising or really bad mathematicians working for them.
Students are a little more intrigued than they were when I wowed them with solving trigonometric identities, so they humor me. Through some discussion, we come up with the following:
You can choose 3 different appetizers: 9C3, or 84 possibilities.
You can choose 2 of the same appetizer and 1 of another (example: 2 wanton tacos and 1 dyn-o-MITE shrimp): 9C2, or 36 possibilities.
Any of the previous 36 possibilities, but with the other choice doubled: (example: 1 wanton taco and 2 dyn-o-MITE shrimp): another 9C2, or 36 possibilities.
If you were really crazy, you could triple up on the same appetizer (i mean, 3 orders of cheeseburger sliders? should that count as an option?): 9 possibilities.
Grand total of choices is 165. Even my most difficult students were able to surmise that this is less than the 200 combination claim. They seemed sufficiently angry at being duped by the Man, so I claimed that the only option was to boycott Applebee’s.
My students instead demanded that we call corporate and complain. So I handed my phone to one of my more vocal students, hoping that some of the vitriol that had been directed at me at times could be channeled for mathematical good. Surprisingly, a call to 1.888.59APPLE was answered fairly quickly, and my student immediately started explaining our mathematical discovery. The guy on the other line claimed that there are 5 sauce choices, which count as different options. Immediately the class went into a calculating frenzy. 13C3 +2*(13C2) +13C1 = 455! Apparently Applebee’s had planned for this conversation with math students, because they verified that 455 choices were possible. The student on phone then asked: Why would they claim 200 if there are actually 455 choices? Maybe we should talk about your advertising rather than your mathematics! Another student: What if we ordered one thing with tomatoes and another without tomatoes? Is that a different choice? There are different meat choices for the wanton tacos too, does that count? With each question, the guy on the phone backtracked more and more, now claiming that different meats and different toppings were different choices, so now there were seemingly thousands of different possible combinations, until finally he hung up on us.
A couple weeks later, a couple of my students came in and told me that they had been by an Applebee’s over the weekend and had decided to raise some hell. They asked their waiter to show them all 200 different combinations, and when he claimed that he would not do that, they called him a liar and left.
I don’t know if I have ever been so proud as a teacher. Now if there were only some company misusing the quadratic formula…
“…they called him a liar and left.” What a wonderful story. I think my favorite part was calling Applebee’s customer service in the middle of class and demanding answers. Nice work.
Ok. That’s just great. Beginning to end. One of those stories, wow, I wish I had done it.
But I would like a second route to that 165.
Also, I don’t like that 455. 165*5 = 825. Wouldn’t that make more sense?
Finally, trick extension. Let’s stick with the 165 for a moment. If you knew the calories in each of the 9, (giving kids the numbers here would be a good thing) could you calculate the calories you would consume if you ate each of the 165, one a day, until you were through?
Jonathan
Applebee’s on the phone verified the 455, so I assumed it was correct, but now I’m reconsidering… and they had been wrong once before…
The sauce is for the buffalo wings only, so that is why we only used 13 (assuming that the wings have to have some sauce to begin). You can’t make a choice when ordering spicy queso blanco to get either hot sauce or with honey BBQ sauce. If a drink were included, and they offered 5 different drinks, that would be an instance to use the fundamental counting principle, but I don’t think it works this time. So, we went with the Applebee’s assumption that ordering wings with hot sauce and ordering wings with medium sauce was qualitatively the exact same as ordering wings with hot sauce and wonton tacos… they were seen as completely different choices.
However, now I notice that they have both boneless wings and regular wings, and I guess I should assume that Applebee’s would consider the 5 different ways of ordering chicken wings and the 5 different ways of ordering boneless wings all different. Does that make 17 distinct ordering possibilities?
I guess another good takeaway from this lesson was that probability and combinatorics can be really tricky, and people can screw it up pretty easily.
That was my WCYDWT link! Glad you got so much mileage out of it! Well done!
This was my reasoning, as to how they might have arrived at the “over 200″ claim. In the original capture (http://dl.dropbox.com/u/5733401/applebees.jpg), you’ll see that of the 9 options listed, 2 are “NEW!” So there were originally 7 options when the promotion started. Now, 7C3 is merely 35… but 7P3 is 210.
We all know that confusing C & P is a very common error, and I have no doubt that the ad people are capable of committing it–intentionally or not. So they merely counted “sliders, shrimp, tacos” as a different choice than “tacos, sliders, shrimp”.
That’s my theory, and I’m sticking to it. It would mean that the people you spoke to on the phone were totally winging it, which… well, is not exactly a stretch.
I think confusing permutations and combinations only happens in high school, where a tiny subset of counting is taught.
I think an adult would either know what they were doing, or not have a clue.
I knew before I got to the phone call that “dipping sauces” was going to be part of the bail out position Applebee’s would take. Seemed pretty obvious to me, anyway.
As a way to stimulate a conversation about the mathematics, this is great. As a way to get kids to question advertising, ditto.
However, channeling the rage of inner-city kids (or poor kids, or suburban kids, or disaffected rich kids wherever they may be) strikes me as a trick one wants to save for something that actually matters.
Quite frankly, getting kids in the schools I work with in Detroit to distrust is rather trivial. They essentially trust very little. Getting them to express their outrage? Don’t have to do anything: that’s a given. Getting them to actually think about some social issue (preferably with mathematical connections) that MATTERS in any real way to them (and by that I don’t mean that they can get pissed off about, blow some steam off at some innocent waiter(ess) who in fact is NOT a liar but just doing his/her job, one that doesn’t require running mathematical calculations to determine if corporate advertising claims are mathematically sound or not)? Not so easy.
I’m a little disturbed by the collective high-fiving here given that the issue is trivial at best. How is anyone’s life diminished or improved by the number of combinations at an Applebee’s restaurant, pray tell?
Before anyone decides to strike back, let me suggest that there are incidences of corporate lying and mathematical baloney that deserve serious investigation. If you want to use this example as a launching pad, fine, but I would not like to see the students of the teachers I coach running off to a local restaurant to harass wait staff. I don’t think any of the teachers wish to see that sort of thing, either, no matter how clever it might seem at first blush. Calling the company to politely ask good questions is reasonable, but there’s a line between wanting a real answer and just trying to make people embarrassed over relative trivia.
If there’s no real payoff here (what did the kids accomplish by their little demonstration with the poor waiter?), is this responsible teaching? If you’re going to tap into the huge reservoir of anger these kids have, you need to think through both the stakes and the consequences. Which means that you’d either better pick more meaningful initial examples or have some in reserve as follow-ups if you must use an Applebee’s ad as the starting point.
You make some valid points, and I agree that we should use some more substantive examples than Applebee’s. If the username “sarcasymptote” wasn’t evidence enough, I’ve got a pretty acerbic, sarcastic nature that covers up a lot of the seriousness of my class. I did follow up a couple days later with the following example:
A company is being accused of racism. Here are the facts: the company has 200 employees. It claims that when it chose a committee of 15 people, the people were drawn randomly. However, none of the 56 minority employees were selected for the committee. Could it be argued that racism was involved in the selection of the committee? Verify your opinion with math.
However, my students did not get as excited about this example. They didn’t demand that I call anyone during the middle of class. While it is our job as educators to help get students excited about things that really do matter, sometimes the examples just have to be a bit more tangible. All of my students are aware of Applebee’s, and it seemed like a fun thing to do.
I think the problem with the second example is that it sounds canned and is likely not connected to anything real. That is to say, it’s typical textbook math TRYING to sound important.
I apologize if that sounds harsh. I don’t mean to belittle the creativity you used, as I think you’re doing basically what needs to be done. I see my criticism here as “from the Left,” not the Right: that means I like the idea and the motivation and just want better examples.
Of course, if I’m so smart, why don’t I offer some of my own?
I have a feeling there are a host of amazing lessons on probability and statistics waiting to leap out at us from the immigration law fiasco currently raging in a state somewhere near California and New Mexico (hint: rhymes with “Narizona”).
Don’t know if many of the families of your kids play the lottery (but I’d bet a random sampling would discover that the percentage is frighteningly high). A little expected value on the state lotteries is often provocative.
If you want to get really cute, tying the EV of a $1 invested weekly in a high-payoff, Powerball style lottery to the growth rate in various investments might be interesting.
Indeed, looking at misleading advertising in the credit card industry. . .
I know that short and snappy is a great way to get their attention. I don’t know if there’s some lovely bit of video that would jump start any of the above. But I doubt that my off-the-top-of-the-head ideas above exhaust the possibilities.
I look forward to what else you do along these lines.
I wouldn’t worry too much… the level of engagement with the math really tells you what you need to know.
Getting good examples that engage and tap into issues of justice is not just an exercise in imagining good stuff. You also need to be aware of your curriculum, and identify places where the problems fit. And some problems won’t.
I got lucky recently, while I was unhappily teaching regression, to find a problem that struck a nerve with my kiddies: Regression Problem and How the lesson played out.
But those sorts of opportunities don’t show up all the time. And you can’t force them. And you can’t easily, readily, or usefully leave your curriculum behind to chase what might be a neat problem for another course (unless you really don’t mind leaving your curriculum behind). Expected Value is usually not taught when combinations and permutations are first introduced, and with good reason.
The one criticism that sounds right: tell the kids not to hassle the waitress. But you can do that in a powerfully positive way – if you want, you can point out that they now know more math than many other people, and that they should use their knowledge to help and inform, not hurt or embarrass. (“Use your power wisely” – ask them which movie or book contains that lesson, if not those exact words). They’ll like hearing that they have to be careful of how smart they’ve become…
Jonathan
I, too, appreciate your comments. They represent a thoughtful perspective I hadn’t initially considered upon reading Sarcasymptote’s entry.
I do, however, take issue with calling this issue “trivial at best.” Students under the age of 18 vote with their spending habits. Advertising is an attempt to manipulate those spending habits. Any problem which incorporates increasing media literacy particularly with media that targets our students has to be considered something more than trivial, don’t you think?
Then there is the message of the ad itself. 200 choices! All math aside, that is a ridiculous number of options. Do we need that many? What do we get from those choices? Do other countries and cultures have that many choices?
Or maybe this problem could spark a discussion about food politics, farm-to-table issues, and the fact that Applebees positions themselves as a neighborhood restaurant, yet when students protest a message they see in that restaurant to an employee of that restaurant, that employee is powerless to do anything about it. If it was actually a neighborhood restaurant, one with five calendars on the wall, each put out by a different local community organization, then I’d be willing to guess that the waitress would have the power to get someone to change the message on the hand-lettered marquis.
The efficacy of this problem has to do with empowerment. These students had access to an Applebee’s. They were able to get to one on their own. That problem penetrated their cone of reality, and they incorporated it into their lives. They went on an unprompted field trip on their own time. Sure, that empowerment manifested itself as a group of teens being rude to their waiter, an experience, I would guess, that was less about the math and more about teenage rebellion, but they might remember the time when some slickly presented authority lied to them and they protested.
Again, I appreciate your response, especially since it seemed to be a response to the generally positive reception that the blog has been receiving in the comments. I agreed with those comments and was inspired by your response to stop and think. Upon reflection though, I think there was more to this lesson than your response indicated.
@Michael I get the point you are trying to make, but I’m stymied every day by how hard it is to come up with content-relevant situations that kids have direct experience with. I think that’s the power of this problem – if they all haven’t been to Applebee’s, they’ve at least all been to one of these chain restaurants. Since the venue is familiar, there’s a common vocabulary, they can all jump in without intimidation. Nobody’s seriously suggesting, I don’t think, this lesson is serving an exalted social justice purpose, but it’s still much better than what’s going on in most classrooms. Where even if you try to explore an example like whether or not there’s evidence of racism in choosing a committee, it strikes a chord of being contrived. (This is making me wonder if stories exist about, perhaps, the Supreme Court using prob/stats to evaluate evidence of racist hiring practices, or something.) I certainly would like to the hear better, more effective examples of using a math lesson to raise awareness or effect change that you are using in Detroit.
Here was my attempt that I ultimately wasn’t happy with: This year I organized my exponential functions unit around credit cards – predatory lending practices, compounding interest, you get the idea. At the end, we watched almost all of the episode of Frontline called The Card Game. There is a poignant segment about payday lending near the end. The kids did their best to understand what I was trying to get across, but I think the idea ultimately fell flat, because they just don’t have experience yet with a credit card. Most of them have never seen a payday lender, nor know anyone who uses one (I think they might be illegal in NY? I’ve never seen one here.) Statistically, some of their families are probably in trouble with debt and credit, but I think it’s pretty common to hide finances from your kids. I’ll probably do something else next year instead.
Kate – so glad I read this comment. I was going to investigate the cc companies with my MS students this year (my sister worked for a very crooked cc company and has great stories to share for flavor). My intent was going to be to warn them NOT to get a cc in college and rack up years of debt. However, I am now concerned that they just won’t “get it”, or even care. Hmmm…. at the very least I am rethinking this one. Julie
Kate (and Julie) — Even if the lesson fell flat, I wouldn’t underestimate the long term good you may have done. The kids may not have gotten all of the details, but I’m sure that in the long run they’ll remember the underlying idea, which I’m sure you emphasized: “Be very careful with debt.” Just that is important. Many, many adults don’t understand that. If even a few of your kids got the basic idea, that they should pay off their credit cards right away, that they shouldn’t buy things they can’t afford, then they’re better off.
So, I have a different thought about the answer, but it seems too simple…
If the two wing options each have 5 different sauces, then there are really 5 + 5 + 7 options to choose three from. From there, it’s simply:
Any three choices, order doesn’t matter: 17C3
]
Any two choices, order matters in which one you double: 17P2
Any one choice: 17P1 or 17C1 [doesn't matter
Which gives me 969.
Is this valid? If so, then Applebees would be justified in advertizing “almost 1000 combinations”.
Even in your original setup, I think Applebee’s barely clears 200 options. If I order two of A and one of B then (A,B) and (B,A) are distinct options, so the total is 165 + 36 = 201.
Whoops, I didn’t notice that you counted the 36 twice. Nevermind.
Thanks for this. I love the idea of getting Applebee’s take on it, and then recalculating. I did a similar thing a few years ago when a local burger chain ran a campaign saying there were hundreds of ways to choose a combo of three items. My kids did the calculation, but I never thought to call corporate from the classroom. As more and more teachers read this and try it, I wonder if Applebee’s corporate office will continue to be as accommodating to phone calls.
I love this – activism backed up by math! Your kids should have gone out to protest on the streets.