Applying Connections
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Consider this fictional scenario: Mr. Glover is a teacher from Sparks Middle School. His students have been working with hexominos. They have found all of the hexominos that will fold into a cube. Mr. Glover wants to connect this activity to a real-world application for his students, so he gave them the following problem:

 Here are the 11 hexominos that will fold to make a cube:

You are starting a company to make boxes that are three inches on each side. You have to make the boxes out of a special type of paper, which comes in rolls that are three feet wide and three feet long.

You want to cut out the boxes from the rolls of paper and then fold them and attach the adjacent faces with tape. You must use one, and only one, of the nets (hexominos) shown above, and you want to waste as little of the paper as possible. Which net will result in the least waste? (A net is a two-dimensional pattern that you can fold to make a three-dimensional shape.)

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