The Correct Way to Use the Area Model

Is there a WRONG way to use the area model?  I think so, but you may disagree with me.  I don’t know where this started, but I am very tired of seeing area models being modeled incorrectly.  It is so prevalent that I even saw one of the keynote speakers at an NCTM Regional Conference use the model incorrectly in her presentation.  So somewhere, some curriculum (maybe???) has shown teachers a way to use the area model that turns the area model into just a PROCEDURE instead of a MODEL of the problem.

Compare these two versions of the area model:

How teachers are doing it: every model is ‘sliced’ down the middle, making four equally sized areas.

How it should be done: ‘slice’ the sides proportionally, which is hard because I know even my example here isn’t perfect, but I try to get as close as I can without getting a ruler out.  However, the only time you should slice a side in half is if you are decomposing that side in half (14 becomes 7+7).

What’s the difference?????  Proportionality of your ‘slices.’  The power of the area model is that it gives us another opportunity to talk about how numbers relate to each other.  If I cut the 14 into a 10 and a 4, the part that gets sliced into the ‘4’ should be a little less than half the size of the 10.  Plus, we really do want the Representation of the Area Model to connect to the Concrete Area Model we can build with base 10 blocks.  Models should be a MODEL of what actually happens.  When you have a 10×10 area that is larger than a 10×4 area. (FYI, the images below were created using The Math Learning Center’s wonderful Number Pieces app.)

Am I just getting upset about something that I shouldn’t???  I really emphasize with teachers that their area models need to be proportional in order to help the kids make connections.  Otherwise, kids just think it is magic and the area model does not become a model…it’s just another procedure.  What are your thoughts?