I gave my 7th graders a quiz today on solving equations. It was fun (admittedly in a slightly evil way, but not really) to see their frustration with the final problem, which over the years has quickly become my favorite algebra problem. Of course I don’t put it on the quiz to be mean, but to teach important lesson about reasoning and life. Here is the question, always coming after a series of much more complicated ones that they usually have no trouble with:
x + 1 = x -1
An American Math Teacher in Sweden 
Jan 03, 2015 @ 02:23:29
it is undefined
Jan 03, 2015 @ 02:25:23
I mean its called a contradiction because it states that 0=1
Jan 03, 2015 @ 11:00:01
I was never so picky about exactly how they explained it, as long as they showed they had the general idea.
I tended to emphasize what it means when they are asked to “solve an equation” – my answer being “we are asking what number or numbers we can substitute for the variable to make the equal sign true”. That is the real question being asked and the important base idea.