In summary, students often come up with a variety of creative strategies for solving multiplication problems.  The open array model serves as one useful tool for viewing this variety of strategies and connecting the model to the mathematical symbols.  It can also be used for generating other solution methods that students might not have considered.  In the previous videos, all students chose to chunk one factor while leaving the other intact.  It is possible, however, to chunk both factors.    Consider the following examples that show an open array representation for 112 x 23:

This method allows students to break apart numbers in any way that makes sense to them.  Thus, even though it may appear to others to be an inefficient way, the whole experience of doing things in an inefficient way helps them to see a more efficient way.  Thus, when looking at the two examples shown above, a teacher might ask a student which solution makes more sense.  Students might consider the original chunking, or which sets of partial products would be easier to combine.