How Many Hot Dogs And Buns Should He Buy?

 

 

• How many packages of hot dogs and hot dog buns should he purchase so that there are no extra hot dogs or hot dog buns?

 

These questions may be useful in helping students down the problem solving path:

• How many hot dogs come in a package?
• How many hot dog buns come in a package?
• What might happen if you buy one package of hot dogs and one package of hot dog buns?
• How might that make someone feel?
• What is a guess that is too low?
• What is a guess that is too high?
• What is your best guess?
• How can we represent this using pictures, numbers, symbols, and words?

 

This problem provides a context for a real life application of least common multiple (LCM).  Students will likely have limited experience with buying hot dogs and hot dog buns, so it would be worthwhile to develop the context prior to showing the video.  Questions like the four below will help establish why Steve Martin is so frustrated:

• How many hot dogs come in a package?
• How many hot dog buns come in a package?
• What might happen if you buy one package of hot dogs and one package of hot dog buns?
• How might that make someone feel?

In the movie clip there are 8 hot dogs and 12 hot dog buns in a package.  If he doesn’t want to have any extra hot dogs or hot dog buns, he will need to buy 3 packages of hot dogs and 2 packages of hot dog buns for a total of 24 hot dogs with buns.  Something to keep in mind is that students may give the answer of 24, which is the least common multiple of 8 and 12.  However the question is specifically asking about the number of packages, so anticipate needing to have a conversation about what units we are measuring with.

Below I have provided images with examples of hot dogs and hot dog buns in various packaged quantities to use as an extension.
 

• A package containing 7 hot dogs

• A package containing 8 hot dogs

• A package containing 8 hot dog buns

• A package containing 12 hot dog buns

• A package containing 16 hot dog buns

 
Daniel Luevanos shares a wonderful reflection of how it went when he used this lesson with his students.  He includes actual student work samples and even the lessons he learned from teaching it to each class and tweaking it along the way.
 

• CCSS 6.NS.4 – Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2)..

 

• Father of the Bride
• Stacey Olson of Capistrano USD originally provided me with the idea for this lesson