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!

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Thanks for posting! I particularly like how your task has an answer that is actually checkable in real life (they look up the true length of the arm) instead of just having some arbitrary number they have to confirm by looking in the back of the book or waiting for you to tell them they are right or wrong. I also like that you encourage them to think of reasons why their answers might be (slightly) different from the real answer. Lots of good thinking going on! Also, I’ll definitely check out the Mathematics Assessment Project!

Hey Crazy Math Teacher Lady! Great idea about proportion using the Statue of Liberty.

Because of the MTBOS I recently purchased the 5 Practices book and have also checked out the MARS site. This site looks like it has some great tasks.

This is a great task! I think you could even modify it for higher level students by leaving out the part about comparing their own noses! Can’t wait to see what else you have!

What a cool project! It looks like a great problem and I might just have to use it when we’re talking about proportions in my own classroom! Thanks for the ideas!

Its a nice, simple intro, But if your’e talking about proportions make sure you include this:

http://mrvaudrey.com/2012/05/03/the-only-lesson-theyll-remember/