Patterning and Algebra

I know this has been on the minds of many of my parents.  "What in the world is my child learning in math?  I haven't seen homework from them in weeks!"
Don't worry, we still work on math in school but math has changed from when you and I went to school.  Instead of "drill and kill" or "around the world", which really only meant memorizing your basic facts, we are now understanding and explaining how math works and is inter-related.  In the past two weeks we have been part of a brand new focus group that is working on increasing the student's understanding of multiplying through algebra and patterning.  It is truly amazing to see what they are doing and they will soon be coming home with some demonstrations for you.  In the meantime, here are some patterns that they are finding rules to.  Have them tell you what the composite rule is and how they know it is correct.