Authentic, Value-Added Algebra

About a month ago, my algebra class was working on the Math Forum’s Free Scenario called Val’s Values.  

There was a lot to question here (which they did) and a lot to wonder (which they did as well).  Something that was unsettling, however, was that they did not know the age of Val or Amir which they felt was pertinent to answering a major question:  Who has spent more on jackets in his/her lifetime?

We made some age estimates and answered our own question as best we could, but it felt less authentic than it could have been.  So, we submitted a comment on Valerie’s blog and today our attention to precision was answered with a response.

I gave my class another go at figuring out who spent more on jackets.  Here are a couple of their responses:

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What impressed me overall with their approach to this problem was not necessarily the mathematics itself.  The magic was in their careful identification of important variables and analysis of what mattered and what didn’t.  Additionally, they were able to look past the “right” answer and truly own THEIR answer from THEIR assumptions.  I had very few students ask Is this right?  Instead, they were communicating their methods with one another and challenging the reasonableness of their results.  The spark:  the flexibility of the scenario and the real response from a Math Forum Team Member willing to help add some authenticity to a classroom task.  Thank you, Valerie Klein.  We appreciate it.