One of my favorite problems (and the one I presented at TMC this year) is What it’s Worth? from Nrich. To say I “like” this problem would be like saying Sarah Hagan “likes” interactive notebooks. Clearly an understatement.
Anyway, here’s the prompt:
What I like most about this problem is that there are so many, OH so many, methods to solving it. It is a FANTASTIC way to get students to focus on the pathways to the solution rather than the solution itself. After the students figure out the value of the question mark, they go about discussing the numerous methods they used in order to arrive at their answer. Furthermore, the problem includes 6 “beginnings” of solutions and learners then need to make sense of those as well as determine how a solution was reached along that path.
Left: New format for discerning methods. Right: Old format for discerning methods.
To my surprise, along with Nrich’s site updates, this problem has improved as well. Rather than showing a written start to the problem, provided are 6 visual introductions.
This allowed for an incredible amount of discussion involving each method. And even those METHODS broke down into different methods. It was method madness (awesome madness). 
Number Loving Beagle 
http://goo.gl/iAU2na
This is gold, pure gold.
I love this format. It also looks like we can recreate the idea with not too much effort.
I often feel like the abstractness of variables freaks people/students out because of mental blocks on the boringness of x and y. Thank you soooooo much for posting this and this is just a testament to how many gems come out at TMC. Bummed I missed your session (and yet still glad for all the other gems I was able to glean).
Keep rockin’ the classroom.
What a nice thing of you to say, Jed! Thank you!
Neat idea. Great puzzle. Took me a few minutes. I wish more teachers would encourage students to use their brain to do math. The math portion isn’t really difficult in this one, it is all about setting up the problem. Thanks for sharing.
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