Stages of Development for Multiplicative Thinking

I thought I would share a graphic I received last year showing the development of multiplicative thinking.  I shared it with the kids today too.  You can see it's a sort of ladder, that grows from repeated addition to the standard algorithm that we learned in school.  My job this year is to move kids up the ladder.  Some are already making their own way up.  

Please note that we WILL be teaching the standard algorithm.  If you want to share it at home...that's absolutely fine! 

So, here are some samples of work the kids did this morning.  Beautiful Brains!