First, I just love the question. Second: theorize! What happened to this student? What are some good signs in the student’s work?

Thanks to Bree for the submission.

Also: I categorized this under “Standards for Mathematical Practice.” Does anyone have another CCSS standard that fits this problem and work?

## One reply on ““Prove the following conjecture: The sum of any 3 positive consecutive odd integers will be divisible by 3.””

The student seems to understand that they want an expression that has a factor of 3.

I wonder what they had for the x+3 prior to erasing? My guess is that they needed something divisible by 3, so they stuck a 3 in there, and figured that if they multiplied the 4 by the 3, then everything would be good.

In other words, they knew what kind of pattern had to happen, but they didn’t know how to get there, and were willing to fudge the early steps a bit in order to get the final bit to match the pattern.