My calc kids haven’t learned any derivative short cut rules yet (we start tomorrow–woo!), so in terms of actually finding a derivative using the limit definition, I keep it pretty simple–mostly linear and quadratic functions. However, when they see a linear function, I ask them to think conceptually of what’s going on and what’s being asked of them. If they can spot that they’re working with a line and a line’s slope never changes, I encourage them to simply identify the slope as the derivative instead of working through the formal definition. “Work smarter, not harder,” right, Sarah? 😜
So on today’s quiz, a couple kids realized midway through the problem that all they had to was give the slope of the line. I wish I would have taken pictures of their papers. One student had the entire limit set up and then wrote, “lol wait…it’s linear…duh.” Another kid had obviously worked the whole problem out, erased it, and then written, “Can we pretend that never happened?”
Oh lordy. They can make me laugh even on a day where I just administer and grade quizzes. God bless them.
Also, they rocked a Monday quiz. 👏🏼👏🏼
One of my students I had in precalc a couple years ago came in today to ask if I would be one of her recommenders for National Merit. What an honor.
I told a girl I loved her last week. It was quick, as I was leaving.
Today she asked me if I loved her.
I don’t know if it means anything other than it reminded me that my kids do pay attention to what I say and do. It also made me wonder if when kids ask that question, seemingly jokingly (you know how it goes: “Mrs. Peterson? Do ya love me!” more of a statement than a question…), maybe they’re seeking more validation than I’ve realized.