PACKAGING THE CHOCOLONGO BAR

SCENARIO:
"Since the public is becoming increasingly concerned about the impact that food packaging is having on the environment, the president of the Chocolate Company, The Sweet Bite, has called a crisis management meeting of her strategy team. Sales of the company's signature chocolate bar, the Chocolongo, have plummeted since a recent article named the company as the largest producer of packaging waste in the chocolate bar industry. This is very distressing news for the company. Before the appearance of the article, the Chocolongo Bar had always met with rave reviews because of its unique long, thin shape."

"The president wants to continue providing her loyal customers with the same volume of chocolate while reducing the amount of packaging used. Therefore, her strategy team must determine a different format for the bar. To preserve some similarity between the original Chocolongo Bar and the new one, the team leader requires that the new bar have only a single wrapping. No additional sleeve is to be used. The team must provide proof that the selected format will result in the least amount of packaging. A member of the strategy team has asked our class for assistance with this challenge."

THE TASK
"Your team has 36 interlocking cubes, which represent the total volume of a Chocolongo Bar. Your task is to work with the 36 interlocking cubes to find all other possible formats for the new and improved bar. For shipping and storage purposes, the final product must be in the form of a rectangular prism."

“You will be working in teams of four. As a first step, you will each work independently to contribute to this group blog in the comment section just below, noting every possible format for the new Chocolongo Bar and identifying the total surface area. During sharing, you will compare your possibilities with those of your team members and determine which format best meets requirements."