Fool me twice, shame on me

I made the mistake of looking at a visual pattern number talk and thinking that I knew the ways that students would see it.  Yesterday we did a number talk with the following visual pattern:

    

I made the mistake of thinking that they would all simply see it as the pattern just adds an additional column of three red blocks.  Boy was I wrong.  The Lab Class students came up with all kinds of different and creative ways that they saw the pattern growing.  

One student saw it like a movie theater with the front (blue blocks) being the handicapped section and the rest as rows of seats that were growing.  Another student saw it as a growing family.  There was also the "Frozen" method that say it as ice crystals coming up from the ground like the movie Frozen.  We had another Tetris method (like in the WIM activity).  There was the building method where the blue section would be completed and turn red. Then another blue section would be built and completed and so on.  And one student actually saw it in a diagonal pattern (pictured below). 

Then on the next day, I gave them a problem from a new website that was shared with my called Which One Doesn't Belong.  The site give numbers, shapes, and graphs & equations in groups of fours.  Students are to choose which one doesn't belong and tell why.  I used the following problem:

This time I was sure that I knew what the class would come up with.  I chose this one because I wanted to do a quick number talk.  Ha!  Once again the students were incredibly creative with their thinking.  

I saw that there was only one even number and only one number that was a single digit.  I figured those were the two answers that all students would come up with.  I personally felt that 43 would was the "right" answer because it's the only one that not a square.  If figured a couple students would come up with that as well.  

The first answer that was shared was that was that 9 didn't belong because it was a single digit.  Ok.  But then students amazed me.  They said that 43 didn't belong because its tens didn't follow the pattern (0, 1, 2...).  Nice!  Then 43 was given but because it wasn't part of the family of 25-16=9 or 16+9=25.  Great!  There was also the answer that 9 didn't below because the sum of its digits isn't 7.  Excellent!

I will never underestimate what students can come up with in a number talk (or anywhere for that matter) again.