Introduction to Tangent Lines

I've been loving this introduction to calculus that we're doing with our Pre-Calc classes currently.  I don't know about you, but when I was in Pre-Calc, I didn't do any calculus.  Not a single thing.  I had no clue what a limit was, and certainly not a derivative. My Pre-Calc class was pretty much just trig, trig, and more trig, with a bit of "advanced" algebra thrown into the mix.  (I'm not complaining though--it was a great class, honestly...and I'm told I should be thankful that I'm young enough to even have had a class termed "Pre-Calculus.")

Anyway.  All this to say--it's darn exciting introducing kids to concepts such as limits, derivatives, and integrals because they're so powerful and beautiful...and so unlike other stuff we teach (no?).

So, a few things I'd like to share from this week.  Nothing's super original, but I did put a lot of time and energy into making them work for my students.

First:  Visualizing secant lines turning into the tangent line via Desmos.  Again, I know there are plenty of applets out there, but I couldn't find any that my students in the back of the room would be able to see.  Also, I wanted to input my own functions.  Also, I wanted to create it because it's fun and allows me to use mathematics.  So, here you go.  Slide a, change the function, change the point of interest.  Best of all, put it in projector mode so everyone can see--even the kids in the back.

Second:  We had an extra day built-in for tangent lines, so during collaboration, I asked if we could create a packet that introduces the kids to how to draw those lines exactly.  And how does the algebra relate to the geometry?  My department head and I discussed the objectives, and then she miraculously turned our words into this beauty:

Tangent Line to a Curve

Third:  This Warm Up that I rather like (Day 3 of Tangents):

Fourth:  I used these sites so the kids could get some practice visualizing what the derivative function would look like without taking the time to actually find it algebraically.  I love exercises like this because they truly require deeper thinking.  You can't bs your way through them.

• Some multiple choice practice
• Derivative plotter