Continuing on building number sense with my students, I decided to check what there initial reaction was to this expression:
12 + 6
Not a one of my students let me down on my expectation of an answer of 18. I asked them, “What would you say to me if I told you that answer was wrong?” I had immediate feedback, and it wasn’t pretty. After checking their work (and yes, I could see many flashes of panic in their faces), asking “Are you sure?”, and getting a unanimous “YES Mr. A!” I walked to the board. I asked how they got 18 and why. They said, “You gave us a problem, we found the answer.” “So you assumed I was asking you to find an answer?” “Yes Mr. A.”
So I wrote the dreaded “=” sign behind that expression. I asked what that meant. “It means to find the answer, 18.” <sigh>, I have a little bit of work to do. I wrote this:
12 + 6 = 8 + 10
Students looked at it a little bit, and I was slightly disappointed that they didn’t see the connection to the addition problem we did yesterday. After two minutes or so, I could see the light bulbs go on, and they started telling me other equivalences to write down. I told them they had 3 minutes to get as many as possible on their papers and they got to work.
I had some good questions during this time. “Can I add more than two? Like 5 + 5 + 8?” “Do I always have to add, can I subtract, multiply?” They starting thinking flexibly, and variations started to pile up.
Here is some student work for 17 + 2.