WODB- Differentiation Techniques

We just finished implicit differentiation last class and I wanted to get my students thinking about when to use which differentiation technique as we come to the close of this unit. I made this quick WODB to have students analyze differences among structures. This isn't as true to WODB form as I'd like, but it will still get them talking and thinking. 

Comment suggestions if you have any! 

A: Only one that uses implicit differentiation, only one where point is given (not just x coordinate)

B- Only one asking for general derivative, not derivative at a point

C- Only one that requires product rule, only one not in terms of y (in function notation with g(x)), only one with trig function

D- Only one that does not equal 1/2 (equals -1/2), only one from a table, only one that requires quotient rule

Limit Definition of the Derivative- Multiple Representation Reference Sheet

I pinned this picture years ago when I started teaching calculus and it's stuck with me every year. It's so simple and clean, but shows exactly where we came from and where we're going. Math is so elegant sometimes *sighhhhhhh*. 

I really want my students this year to make concrete connections between representations as often as possible. The limit definition of the derivative is such a foundational and, at its core, simple concept. It's slope. We know slope. 

I made this reference sheet for my kids to get them talking, thinking, and connecting between representations of the derivative. I have them start with their Algebra I definition of slope, then progress through notational changes to derive the formula for slope of the tangent line. I've included the general formula on the front and the definition at a point on the back. 

I'm  giving this as a warm up in class tomorrow so I know I'll be tweaking, but if you see anything you think should be tweaked leave a comment! 

Limit Definition of Derivative- Multiple Representation Reference 

UPDATE: Here is my filled in key from class! I really liked this and will incorporate it again next year for sure! 

Limit Definition of Derivatives KEY

Intermediate Value Theorem Justifications Gallery Walk

One of my favorite parts of AP Calculus is seeing my students' ability to make mathematical arguments develop. This is a long and drawn out process that takes the length of the course to complete. One thing that I found really useful last year was having students critique others' arguments. 

To get students analyzing arguments for IVT, I used this gallery walk and a whole lot of post its. 

IVT Gallery Walk 

Students were asked to critique arguments around the room, offering feedback and identifying one they thought made the best argument. They started to give specific feedback on how things could be improved and identify which was really "true dat." 

We will do more like this throughout the year, but it's still one of my favorite ways to get into justifying!