Number Talks 12 x 13

I was cleaning up some files this evening and ran across these snapshots from a Number Talk in class a while back. 

Are all of them the most efficient?  For me, no.  However, if it made sense to that student at that particular moment, then it was most efficient for them.  I appreciate the various ways they consider “building” the product.

  I wanted to see their thinking on 2 digit multiplication to link back our unit on polynomial operations.

Yes, they all had a calculator available, but my question was, how do you know?  As I learned from Steve Leinwand, “Convince me.”