Bedsheet Breakout!
Several years ago, 2 inmates broke out of a high-rise prison in Chicago by tying bedsheets together. Student were asked the questions "how many bedsheets would you need, and how much space would it take to store all those bedsheets?" In the process of solving these questions, students investigated concepts of length, area, and volume, and how those concepts (and their respective spatial dimensions) relate to each other. In the process, they gained practice modeling situations mathematically and geometrically and applying geometric concepts to solve problems with certain restraints (that is, how can you make a certain number of bedsheets stretch for 15 stories and take up the least amount of space?). After working on this for a while, students wanted a way to test their calculations without actually getting bedsheets and finding a 15-story building, so we got some dish towels instead. Students used similarity to find a scale factor between the bedsheets and the dishtowels, dilated their measurements and cut the towels so that they were similar shapes, and braided up their own ropes. They had discussion on whether or not they should cut the approximate weight that the ropes were supposed to hold by a the same scale factor, or if the weight shouldn't be affected by the dilation of the elements of the rope. Finally, we all went outside to see if their ropes held weight the way that they had predicted.