Related rates and rec letter

We started related rates today in calculus. I always start by reviewing some basic geometric formulas. I asked the kids if anyone remembered the formula for volume of a sphere with radius r. *Crickets.* So I gave it to them. The next formula was surface area of a sphere. I asked the kids what the derivative of volume was (wrt r). “4*pi*r^2,” they stated. 

“And that’s the formula for surface area!” I told them. We also noticed how circumference of a circle is the derivative of area. 

“WHAT?!!” I heard from the back of the room. As I looked to see what was going on, I saw a boy with his head in his hands, eyes about to pop out of his face. “ALL THESE FORMULAS WE’VE KNOWN FOR SO LONG AND THEY’RE ALL RELATED?! My mind is BLOWN right now! Maaaaaaaath, guys! Math!”

I love it when my students are walking, talking public service announcements for my subject. 

Also: related rates went so well today! What?! There were no tears, no books being thrown in frustration! What a success!

*****

One of my students asked me to write a rec letter for her. I sent her some questions to answer, one of which was “What do you love most about your school?” Her response was just beautiful:

My experience at Union has been so wonderful thus far, but what stands out to me the most is the people. The people here are so friendly, including the teachers. Everyone seems to accept others with open arms. This stands out to me over anything else because it is a daily experience.

I love that last sentence. The norm at this school–this school of 3300 students–is acceptance. 

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