Hot Dogs and Buns (Least Common Multiple)

So, starting with this slide…


…leads to this slide…


…and then to this one.


The question is: how many hot dogs of a particular type do I have to buy so there are no extra buns?

Alternatively, what is the least common multiple of the two numbers?

(Kudos to Chris for figuring out the second slide in the comments, who may or may not be a fan of the meltdown scene from Father of the Bride.)


11 Responses

  1. I am not familiar with that scene. But this is something I have thought about before. I wish I were teaching LCM right now so I could use this. Maybe next year.

  2. This is cool. I like it.

    Friendly critique: It would be engaging to let the kids come up with the question. Let them observe that they will have leftover buns, and nudge them into wondering how much they would have to buy to even it out. (Variations…”what’s the next question?” “where’s the math here?” “why do you think I’m showing you this in math class?”)

    Also, your third slide is a gift! In this lesson I would want the expectation to be that the kids organically see the need for organizing the information, and then put that up for neatness sake after they have it or almost have it. Or maybe project/hand out a blank table and let them fill it in, as part of the problem-solving process.

    Just ideas – thanks for sharing it!

  3. And then (sorry, thought of more stuff) how your dialog goes after slide three? What do you do after? Where do you drive it? What’s the follow up question? After your class has hot dogs and buns figured out, it would be great to ask a different question/puzzle that could also be solved with LCM.

  4. It could be cool to turn it into planning a party. Say party hats come in packs of 5, or cups come in backs of 12, napkins in packs of 25. Adding in other items makes them find LCM between multiple objects. And it is more fun.

  5. Actually, I do have the students organize the information themselves first; in a way I try to keep up the game of guess the next slide. (Note also that the table isn’t done yet! They need to figure out what extra columns should be added to solve the problem. They may or may not decide, for example, to have a factoring column.)

    My follow-up is a more abstract explanation and practice, including a Venn diagram thing I ripped off somewhere on the Internet. You’re just wanting my entire fractions unit, aren’t you? 🙂 Since I’m writing this for my fractions unit next year I might change things up a bit, but if there’s interest I can post all of it.

    One of the links Maria D. pointed to (in your recent post) has another LCM activity, but I’d likely do it on a follow-up day without explaining to the students first it is the same concept, letting them discover that for themselves. I’d feel hesitant to do the follow-up on the same day because it would give the connection away.

    Polyrhythmic beats

  6. Chris posted while I was typing, but that idea sounds brilliant. It would go nicely with one of my follow-ups involving a plat diviseur.

  7. Jason, I hope I didn’t come across like I thought that was the extent of your lesson. I just wanted to hear more about where it went from there. (And, it wasn’t obvious to me that more columns were intended in the table.) I think it’s a great hook.

    I like the party idea too, though to make it actually fun, you might have to have an actual party. And not, hey, we are going to plan a pretend party that we don’t get to go to. 🙂

  8. I likely should polish off the rest of the materials anyway. And I like getting the comment feedback, so getting it on the whole thing would be even better.

  9. To go with the actual party idea. It would be cool to find candy that is packaged differently. Like an 8 pack of fun size snickers, a 10stick pack of gum, a bag of 100 starbursts, etc. Then tell the students you want to make goodie bags in which everything has the same amount and you don’t have any left over. How much do we need, once they arrive at the solution, you could “conveniently” have this candy and let them check their answers by making the goodie bags. This will make it a little cheaper, more fun, and easier.

    Now I wish I was teaching this.

  10. So, how many packs of buns would we need to be able to buy any kind of hotdogs with no meat or bread left over?

    I like this, even though it wasn’t the intent. I had to think…


  11. Nice! I need to remember that one.

    With my target students I’d probably lead up to that one slowly (start with presuming we can buy buns individually but our hot dog sizes 5 and 6, then 5, 6, and 8, and finally all five; only then returning to all five but having buns in packs of 8).

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