the right answer

mr. person left this suggestion for the answer to Part B:

I used inverse operations. I added 5 to both sides of the equation because addition and subtraction are inverse operations (y/7 - 5 + 5 = 4 + 5, so y/7 = 9). Then I multiplied both sides by 7 because multiplication and division are inverse operations (y/7 x 7 = 9 x 7, so y = 63).

For me, this is perfect.

It's actually what I was reaching for....and just couldn't get hold of. I kept getting jumbled up trying to remember "additive identity" (or whatever it is)....I knew there was something simpler (is it simpler? I don't know!)....

Anyway, "I used inverse operations" was the description I was trying to find.

It's a significant step up in level of abstraction from "I added, then I subtracted," but it still sounds like something a 7th grader could say (in a perfect world) & doesn't require the student to know that math facts are theorems.

The other great thing about this answer is that it's the central point I've been trying to make with C. lately, viz.: solving an algebra equation means "undoing" what's been done to the number. (I recall Steve not being keen on this definition, and I certainly can't argue the case. I'm attempting to teach it to Christopher because it worked so well for me when I read Carolyn's post. Ed says he was taught that algebra was "undoing" when he was in high school, too.)

"Inversing" is "undoing."

I am going to have Christopher substitute "I used inverse operations [etc.]" for our previous standby, "I looked for a pattern, and then I used a strategy of guess and check to see if I was right."

So tonight I'm going to be breaking the news to C.: "I looked for a pattern & I guessed and checked" has become inoperative.

Thank you!