Kay 35 + 7

So Kay (6) became intrigued about the calendar.  She started reading dates as we completed our monthly ritual of changing the dates.  She told me that being able to count by 7's would be a good skill for keeping track of the date.  She then went over to the calendar, paused a minute and started reading off, "7, 14, 21, 28..."  She paused as she calculated the next number.  "35".  She stopped.  To egg her on I told her, "If you add another seven, you get my favorite number."  (Hitchhikers' Guide anyone?)  She asked what it was to which I replied, "I'm not just going to tell you".
She came up with the correct answer of 42, but instead of confirming, I asked her how she got that.  Matter-of-factly she stated, "I used my Make 10 facts".  I assumed she did what I did, which is break the 7 into 5 + 2 and add the 35 and 5 to make 40.  Just to be sure, I asked her what fact she used.  She told me "7 + 3 is 10".  I was totally confused.
She wanted to show me on a calculator, but since one was not handy, she ran over to where we keep our base 10 blocks.  "I can show you".  It was hard to contain my excitement!  What ensued, was a pretty amazing explanation, I think.



It was about more than just the addition.  Kay showed me a completely new way to think about decomposition.  I never would have thought to take from the larger number to make my 10.  Here I am, a math teacher in my 11th year, with a Bachelor in Math and a Masters in Math Ed, learning about addition from a 6 year old.  I was truly and genuinely interested in her method, especially since she's my kid, but she was oh so eager to share it with me.  It took her a lot of processing time, and she made a few mistakes.  Once the ball was rolling, my job was to listen.  As always though, whenever she shares her method, I try to share a different one, just for comparisons sake.

So how can we replicate this in the classroom?  How can we make sure that students have a place to voice their thoughts?  How can we give students enough time to make sense and explore their sense making?  How can we be genuinely curious about the voice of each of our students on a daily basis?