I came very close to going into shock at the beginning of the school year. Let me elaborate…I promise it has a good ending.
I had the opportunity to work with 6th grade students and I used one of Robert Kaplinsky’s lessons that provides context for least common multiple, which just so happened to come from one of my favorite movies, “Father of the Bride.” (I know, I know…took me long enough to blog about this, right?) To provide some background to the story, this was my first time working with this teacher at this school year. I did not know the students and the teacher had not introduced LCM to her students. I showed her the lesson and she asked if I could do the lesson with her students. Here’s my experience…
How Many Hot Dogs and Buns Should He Buy?
I ran this lesson in three class periods and I would like to think that it finally got better by the third class…#storyofmylife… This was my first time using one of Robert’s lessons and I tried to orchestrate the activity similar to how I’ve seen him do it and based on the suggestions he listed in the lesson.
First attempt:
I began the lesson by providing some background to the movie. I explained that George Banks (Steve Martin) is at the grocery store buying food for dinner. At this point in the movie, George is stressed out about how much his daughter’s wedding is going to cost. If you’ve seen this movie, we come to learn that George Banks is…um…to say it politely…he is very…um…frugal or careful with his money.
After giving the students some information about the movie, I played the clip and asked the students, “What questions do you have?” Hands went up and I was pumped. Here were some of the questions I got:
 “Why is he wearing a suit?”
 “Why is he so angry?”
 “Who is that?”
Hmm…not the questions I thought kids would ask, so I tried another question: “What do you think we are trying to figure out?” The response…crickets. Damn.
Third question — “Why is George so upset?” “Because there is a different number of hot dogs and hot dog buns in each package.” Sweet! I’m not as bad of a teacher as I thought…
“Interesting. What would happen if he buys only one package of hot dogs and one package of hot dog buns?” “He would have 4 extra hot dog buns?” Yes. My batting average is now .500!
“How would that make someone feel?” “Angry.” “Mad.” “Upset.” I’m Leonardo diCaprio right now…King of the World!
“Okay. Let’s try to help George not be so upset. Let’s investigate this question…‘How many packages of hot dogs and packages of hot dog buns should he buy?’”
I used Robert’s Problem Solving Framework and asked the students to write the question on their worksheet and make a guess. Then, I asked the students to list everything they absolutely knew about the problem and what we need to know to solve the problem. To raise their level of concern, I stole a strategy from Robert and told the students, “I won’t provide you information about the problem unless you ask for it.” Here’s what the class came up with:
What do you already know from the problem?  What do you need to know to solve the problem? 


After we confirmed the information that we already knew, I went through each of the questions that they had and told them, “I don’t know” for each of their questions. “But, remember, he is very frugal and he doesn’t want to spend a lot of money.” After that, I let them loose and many of the students’ work looked like this:
Student sample #1:
Student sample #2:
Student sample #3:
(This student’s comment made me LOL, but also cry at the same time when I saw the work in the top left corner…)
Overall, I felt great. The students were having great conversations, many were able to get the correct answer, and we did an extension question, where I asked students to figure out how the answer would change if there were 10 hot dogs in one package and 6 hot dog buns in one package. I went into the next class period feeling like I had a better game plan.
Second attempt:
I decided to make the following changes:
 Continue to provide background information about the movie
 Don’t ask students, “What questions do you have?” or “What do you think we are trying to figure out?”
 After showing the video clip, start the conversation with “Why is George so upset?”, followed by, “What would happen if he buys only one package of hot dogs and one package of hot dog buns?”
 Ask students to complete sections about what information they knew and what information they need to solve the problem
 Let students solve the question
The class started MUCH better and I was pretty proud of myself for making the changes above. The class list of information they knew and information they needed to solve the problem was similar to the first lesson attempt and I kept my response the same — “I don’t know.”
I walked around the classroom and one student asked me, “Mr. Luevanos, can there be more than one answer?” What in the world? I stopped myself from saying no and asked, “Tell me more about that.” The student began to explains that it depends on how many people are coming to dinner. I noticed he wasn’t alone and saw this among some students:
Student sample #4:
Student sample #5:
Student sample #6:
Are you thinking what I’m thinking?! O…M…G!
In this very moment, I couldn’t help but think of the great tune from “Van Halen II”…
You better call up the ambulance, I’m deep in shock.
Overloaded, baby, I can hardly walk.
Somebody get me a doctor!
These kids are finding not just one, but several common multiples for 8 and 12! Once I saw the students’ work and asked clarifying questions, I realized in that moment just how powerful this lesson is! I didn’t even consider that there are multiple answers to this question, but I saw this as a powerful teachable moment.
It took every ounce of my being to hold in my excitement and, somehow, I managed to stay calm. I had these three students share their strategies with the rest of the class and asked the following questions:
What do the numbers 8 and 12 represent?
Why are you adding 8 here? Why are you adding 12 here?
What does the number 24 represent?
How many packages of hot dogs and packages of hot dog buns will he need for 24 hot dogs?
Where do you see the number of packages of hot dogs and number of packages of hot dog buns in (student’s name)’s work?
Then, I dropped the bomb…and probably one of my most memorable moments in teaching. I asked:
“Knowing that there is more than one correct answer and what you know about George Banks, which answer seems the most reasonable?”
Many students said 3 packages of hot dogs and 2 packages of hot dog buns, while some were unsure.
“Why?” I asked.
“Well, it depends on how many people are eating for dinner.”
“I think he’ll only want to buy enough food for 24 hot dogs because he doesn’t like to spend money.”
“Yeah! He’s cheap!”
“Oh yeahhhh!”
“Hmm. Interesting. You are all correct. We don’t have enough information to decide whether he needs to buy enough food for 24, 48, 96 or more hot dogs. But…based on the information that we know, and knowing that George is careful with his money, which of the scenarios do you think George prefers such that he doesn’t have any extra hot dogs or hot dog buns?”
The class agreed that he would prefer to only buy 3 packages of hot dogs and 2 packages of hot dog buns. Here are some samples of student work:
Student sample #6 (continued):
Student sample #7:
To wrap up the class, I told them, “Wow, this is so cool. And if I were George Banks, I would also prefer to not waste food and spend the least amount of money possible. What you just figured out is a topic you and your teacher will discuss in more detail tomorrow, which is known as the least common multiple.”
Yes, I pretended that the Expo marker was a microphone and did a “mic drop” right before the bell rang. I was over the moon! One of my favorite days in teaching to date!
This made me more pumped for the next period. Now that I knew how great this lesson was, I made a few adjustments for the third class.
Third attempt:
Here was my game plan for the third class:
 Continue to provide background information about the movie
 Start with the questions, with “Why is George so upset?”, followed by, “What would happen if he buys only one package of hot dogs and one package of hot dog buns?”
 Ask students, “Okay, well let’s investigate how many packages of hot dogs and how many packages of hot dog buns he could buy?”
 Ask students to complete sections about what information they knew and what information they need to solve the problem
 Let students solve the question
 Followup question, “Knowing what you know about George Banks, how many packages of hot dogs and how many packages of hot dog buns should he buy?”
 Close the lesson linking to least common multiple
The class went phenomenal and better than I could imagine. Just by changing the question from should to could in the beginning really made a difference. The question made students think of as many scenarios as possible. I had more of an appreciation for the saying, “Third time’s a charm.” Here are some student work samples:
Student sample #8:
Student sample #9:
(The work on the bottom relates to the same extension question we did in first period)
Student sample #10:
Student sample #11:
(I think this student takes the cake…)
My TakeAways:
 I would highly encourage teachers to use this lesson as an introduction to least common multiple (check out Robert’s recent post about determining why we choose math problems in our classroom…great read). Many students came up with their own strategies that the teacher was planning on referring to with her formal lesson the next day.
 I would adjust the question in the beginning to, “How many packages of hot dogs and how many packages of hot dog buns could he buy?” Then, ask, “How many packages of hot dogs and how many packages of hot dog buns should he buy?”
 I would make sure that the teacher spends time at the end of the activity to formalize that this is known as the least common multiple for the students only if students have had the opportunity to have the conversation about which scenario George Banks would prefer and why.
I hope you see the beauty in this lesson. I had a blast teaching it and it was a great lesson for the beginning of the school year. Again, I cannot emphasize this enough…you have to check out Robert’s website, try one of his lessons and subscribe to his blog. I promise you…you will benefit from his work and ideas. I sure have.
For those about to rock, we salute you! \m/ \m/
What an awesome lesson and post! You are so thoughtful and reflective in your instruction. Just reading about the students’ discoveries about LCM in this post made my math heart happy! Rock on Daniel!
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Thanks, Mrs. Carr! Now you need to start blogging about your adventures with students 🙂
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I really appreciate your authenticity here, especially the part in the beginning about students’ questions not matching what you had hoped for. I think it’s worth reflecting on, as you did, how different contexts make a specific question more or less obvious and how you can adjust what you say/do in response.
I love the part on reflecting on how a minor change from should to could really impacted how students thought about it. I’m going to change that in the problem and then link to your post from the problem.
Thanks for sharing all of this!
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It’s a great lesson and I appreciate you sharing it with everyone. One thing I love most about PBLs is even though I do my best to anticipate student responses or questions, I find myself making mathematical connections while the lesson is going on that I didn’t notice before. And I have the students to thank for that! It makes all the hours of prep worth it in the long run.
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Thank you for sharing wonderful lessons with reflective feedback. I’m looking forward to trying some of these lessons with my 5th grade students.
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Awesome, Tracy! I would love to hear how the lesson goes with your students.
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As an emerging secondary ed math teacher I love how genuine your post is here. The days I’m I get to observe a great math teacher in the classroom, I often wonder things like “What can they be thinking of in this very moment in the lesson?” I feel like I do have a good idea on how to approach teaching, but when it’s my turn to take over a classroom during one of my observation placements, I become a bit overwhelmed at all the different things I should be watching out for, key phrases I should use, and overall just thinking about the different directions I could go with when the original plan gives me crickets from students. There’s so much to think about that I’d freeze up, pause, or take back a few words I was saying.
With that said, I thoroughly enjoyed your styling in this blog that gave real insight to the kinds of obstacles you and many other teachers face. I feel better reading about how humane this profession is, and have no doubts that I’m bound to get better. Awesome read!
Ricardo
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Thank you for your comments, Ricardo. Teaching is overwhelming and it is easy to fixate on all the things we need “to get done” in a lesson. There are many things that can go wrong, but there are so many things that can (and will) go RIGHT! It’s all those things that make teaching such a wonderful profession. My advice to you is this — while there is always room for improvement, don’t forget to celebrate all the good things!
Enjoy the ride, my friend!
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