# 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.

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

## 2 thoughts on “Day 6: Balancing Equivalence”

1. Ah the dreaded equal sign. I’ve used the following Open Middle with 1st and 2nd graders and it really helped drive home the meaning of “equals”. Students left saying that equals refers to “the same as”. http://www.openmiddle.com/equality/

2. Thanks Graham, I think I uploaded that question to Open Middle, I really liked it and use it with my middle school students.