Derrick Houck (Mid-Atlantic '10, Algebra 1)
In this example, I had a student match a function's graph to its equation, table of values, and narrative description (Yay for Ellen Clay!). I mixed four pieces of paper, one with each of these representations on it, with the representations of three other functions. So there were 16 tiles to sort into 4 groups of 4. I included two linear relationships, one quadratic, and one exponential to test students' ability to discern between these types of relationships but wound up covering lots more (like what a 2 in the exponent means--see video below). The template I used is attached (I drew the graphs by hand and made photocopies).
The activity could be easily modified to assess various other topics including representations of numbers (decimal, fraction, etc.) or transformations on functions.
When students produce their four sorted groups, they must justify why each member belongs in the group it does. This step is crucial to locate the specific misunderstandings a student has. In the video below, I had the student do this verbally but with a full class, writing would obviously be much more efficient.