Unlikely Students in Unknown Places

I recently got back from Santa Fe.  I was attending a conference there for a few days last week and afterward, I drove to El Paso to visit my brother’s family (he’s currently stationed in the middle east so I didn’t get to see him – unless you count face time) for a day before flying home.

Let me preface this story by saying that we all probably have a story similar this, but how we handle it can be a possible game changer.

Somewhere on my long drive, I stopped at a fast food restaurant to grab a quick bite.  So, I went inside and got in line.  The following outlines the beginning of our interaction as I stepped to the counter:

Cashier:  May I take your order?

Me:  Yes, please.  I’d like a number 2.

Cashier:  Large or medium.

Me:  Medium, please.

Cashier:  (after pushing more buttons than is conceivably necessary to enter my choice of “medium”): Your total will be $6.05.

I dug through my wallet (receipts from the trip and everything) and found that all I had was a $10 bill, so I handed it to her.  She entered $10.00 correctly and the correct change of $3.95 showed up on the little screen.  At just about that point, I remembered that I had a bunch of change in my pocket and said quite enthusiastically, “Oh, wait, I think I have a nickel.”  Who wants to carry around $0.95 in change in their pocket.

The cashier didn’t miss a beat, and said, “So, your change will be $4.00 even.”  I kind of smiled as I continued to look through my change, proud that she had a mental strategy to adjust to the situation and that she seemed quite confident and comfortable using it in this situation.

Unfortunately, I didn’t have a nickel, but I still didn’t want change falling out of my pocket into the depths of the rental car, never to be seen by me again.  So, I told her, “Oh, I’m sorry, I don’t have a nickel, but I do have a dime.”

As I handed her the dime, I saw her face morph from a confident smirk to a confused, almost terrified look of despair .  I had just taken her from a mathematical point of “Yeah, I can do this math stuff.  I may not use the computer for the rest of my shift” to “Holy $#!+, what the #=|| just happened!”

I went into math teacher mode and waited patiently for her to begin breathing again.  And then I waited for her begin thinking.  She adjusted my change with my introduction of the idea of a nickel, why not a dime? After what seemed like 5 minutes (probably more to her), it was painfully obvious to all around that her anxiety in this situation was taking over her ability to tackle this problem. So, I tried to think of a “least helpful question” to ask.  Now I put myself on the spot.  If she only knew that we were both now feeling some of this pressure.

So, I finally asked her my question and she gave me the correct change within a few seconds.  She smiled as she gave me my change and my new “unknown” student and I parted ways.  I know I felt good about helping someone develop a strategy outside of the classroom.  I hope she had a similar feeling about learning to make sense (no pun here) of making change.

Being a math teacher is a 24-7 job sometimes and we can find our students anywhere – even in a fast food restaurant in New Mexico!

What you would have asked the cashier in this situation.  I’d love to hear what your “least helpful” question would have been. No pressure, take as long as you like.  No one is waiting in line behind you!

Feed the hungry!

Oh, here’s my question:  “If you could change the dime into some other coins, what would you change it for?”


  1. Mike, I absolutely love this. I want to think about this some more, and I want to know what you said! This might be “too helpful” or convoluted, but here’s how I first thought of it: I would try to help her establish a pattern, something like, “The original change you were going to give me was $3.95. If I added a nickel, you knew the change would increase 5 cents to $4.00. So if I add another nickel (that would make 10 cents, or 1 dime) what would the change have to be?” Like for every additional 5 cents you give her, she has to give you back an additional 5 cents in change.
    This is also a good illustration of how anxiety can block our thinking process, both as a student and as a teacher.

    1. Thanks, Joe. Great question. I think if this was something that happened in a classroom with a similar contextual problem, I would probably go there without hesitation. The anxiety of this “lesson” in an unlikely place created a bit of tension for all. My thought of “How do I help this girl make sense of this problem based on what she just said?” coupled with my other thought of “How do I not piss off the line of people behind me waiting to order?” definitely rushed us both. Hopefully I did feel some relief, when she made the correct change with a bit of a smile. I think I would like to try this in the classroom/school store and see what happens. this was definitely a teachable moment in the real world! Thanks again!

  2. I was thinking the same thing as Joe. “If I would get $4.00 back with a nickel and I give you 5 cents more than that, how much would I get back?” I know that’s not least helpful though. My dad does this to cashiers all the time, he is not a math teacher so just likes to see them squirm before telling them the answer.

    1. Thanks Christy. I’ve been thinking about this a lot. We, as teachers, can see the dime as two nickels as we work the problem mentally. Many adults probably don’t realize that this flexibility is even possible because they were never given the opportunity to do this as they were learning mathematics. I would probably bet that the cashier I encountered was trying to mentally subtract $6.05 – $4.10 using a procedure that she could do on paper, yet was very inefficient when working mentally.

      Good for your dad. See if he’ll try to ask a question & not give an answer.

  3. Mike,

    This post just affirms my solid love for you as a real human being. Always patient, always thoughtful, always empathetic. I’m always learning from you, whether you know it or not! As the student who froze, I would have loved having you as my math teacher. Wait. You are my math teacher! Hooray!


    1. We tend to learn from those we respect, that’s why I continue to learn so much from you. I guess that makes us two of the learning-est people we know. . . and that’s a big Hooray! for both of us!

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