I have been avoiding posting because I feel like I have to share THE BEST open ended problem. I am positive that about 2 hours after writing this post, I’ll think of one that I like better, and I’ll be mad at myself. But I said that I would do this, so I’m doing this!
One of my favorites for an entry level algebra or geometry unit on proportions / similarity is this:
“The human body is extremely proportional. Your task is to determine the length of the Statue of Liberty’s torch arm as compared to her nose. Her nose is 4 feet 6 inches. Use your nose and arm measurements to calculate what the measurement of the statue’s arm should be.
Once you have calculated this measurement, find the real length of the Statue of Liberty’s right arm. If your calculation is very different from the actual length, then check your work. Explain possible reasons why your solution is not the exact same as the actual arm length.”
That’s all I tell them. If they ask for help, I ask how many noses they have in their arm. They look mad, then confused, then they get to work. It’s simple, but not really what I would define as open ended since there really is one correct answer. But I do love it!
Another favorite is a task from the Mathematics Assessment Project: Patchwork . It’s a non-linear pattern, but it is presented in a way that students can visualize how the pattern is growing and usually after much struggle they develop a formula that works. Then the fun part is I get to employ the procedure described in the 5 Practices book and allow an opportunity for students to determine that their formulas are equivalent.
Later we develop a formula for the number of diagonals in a polygon and students relate it back to their work with the Patchwork problem.
Thanks Sam, for your rant. I needed that extra rant to get myself to post something!