This task is from Tools 4 NC Teachers. Students build rectangular prisms, find the volumes, and then explore the commutative property. This is remixable. 

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Carter’s Candy Company is selling a new type of chocolate.  They have decided to sell the candy in packages of 24.  Each candy will need 1 cubic inch of space.  You are leading a team in charge of developing a box for the candy.  The boxes can be placed in a single layer or multiple layers. 

Use unit cubes to build all of the possible boxes for the package of candy.  How many possibilities are there?  Record the dimensions and volume of each box.  What do you notice about all of the volumes?

After determining all of the possible boxes, you must make a recommendation to the president of the company about which box should be used.  Write a paragraph explaining which box would be best.  Make sure to explain your reasons for choosing this box.

Two of your team members get in an argument about the boxes.  Cathy says that a 2 x 3 x 4 box is the same as a 4 x 2 x 3 box.  Curtis says that these dimensions would lead to two different boxes.  Who do you agree with?  Why?