Day 6: Balancing Equivalence

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.

IMG_2458I wonder what the next expression left on the board will bring.



2 thoughts on “Day 6: Balancing Equivalence

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