Friday, July 12, 2013

Trying to Improve this Question

This summer I have been working with a few other teachers to help shape the math curriculum for our county. Part of that process has involved compiling tasks for each unit that are meant to serve as representations of what students should be able to do within that unit of content.

I like that a lot of these tasks have a focus on student discovery, and all in all most of the tasks that we have put together have the potential to establish good learning opportunities. One, however, stood out as a candidate for fixing. 

In the spirit of Dan Meyer's Makeover Monday posts, I set out to improve the task below.  

The main reason this problem stuck out as a candidate for fixing is it makes poor use of the cabin idea. My first inkling was that this could do much better in engaging the connection between triangles and roofs. From that motivation, my goal became getting at the same congruence content with something that got away from the step by step set up. 

Below is what I came up with. I did some searching about roof structure and trusses, and I found a visual that made use of triangles complete with all of the terminology.

I'm happy with the facts about common trusses that the students will use to support their proof, but I'm struggling with the task portion. I think that it is a good problem that would require students to make a number of connections as they built their proof, and I like that it's to the point and the pictures can speak for themselves. My trouble comes in establishing a driving motive for why anyone would care that those two triangles are congruent.

The fact that the triangles are congruent does appear to be obvious, and the main challenge is in structuring the reasoning for why that is true. But why does it matter that they are congruent? Why would anyone care that they are congruent? And if no one cares, then how could this problem be saved?

As a bonus, I did find an interesting resource related to the pitch of a roof and how to calculate the angle measures for the truss cuts, but that didn't relate to congruence. It relates more to slope, and so I will save it for then.

In the meantime, what would you do to improve this task? How would you have improved the original problem?

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