Monday, November 20, 2017

WODB for First Derivative Test

Using this as a warm up after our first day of curve sketching. Feel free to use or offer feedback, if you have any! 

Wednesday, November 15, 2017

Find My Mistake Activity- CPCTC

A CPCTC activity where each proof has something wrong and students need to find and correct it! I usually have students work in teams at stations around the room and record what they find wrong with each. Often, I'll put in one "correct" proof so they have to find the one that has no mistakes, but I decided not to on this one. Since I'm using this for my Geometry with Lab class, I wanted to give them a chance to practice proof analysis without the extra confusion. I'll add in that layer as we move on into more sophisticated proofs. 

Side Note: I don't let my kids say CPCTC until like February. By that time, some tutor or another has told them my well-kept secret and they're begging to use it. Until they can perfectly explain to me what it means, they don't touch it. You'll see no mention of it in these proofs! We instead talk about the fact that is triangles are congruent, the corresponding sides or corresponding angles. 

Mean Value Theorem Free Response Critique

Every year the justification of Mean Value Theorem is something we spend a lot of time finessing (a new favorite word of the senior class here...any other schools seeing this?) over the course of a year in AP Calculus. The students understand the concept, but struggle with accurately justifying the situation. We started MVT last class and as a warm up today I did this activity with them. 

I gave each set of partners about 5 minutes to complete the front page and then we discussed- what are the "giveaways" that you should be thinking about MVT? What are the conditions that need to apply? How would YOU answer this? 

Then, I had them flip over to the back and do a critique of 3 arguments with their partner. Each one could some tweaking, although one did receive full credit on the AP Exam. 

The third section I left blank intentionally, so I could move around the room and see what students were putting on the front side of the page. This way they could critique their own answers in light of the responses they saw. Here's what I had them write in based on what they were writing with their partners:
We got to discuss the importance of using the same notation for the function in the problem (using g, not f) and the importance of the justification part. 

Here's the activity! 

We will be building on this next class as we spend an entire day trying to differentiate between when to use which existence theorem and looking at some more interesting AP style questions. Feel free to send any suggestions or other favorite MVT activities my way! 

Sunday, November 12, 2017

Basic Triangle Congruence Proof Tools

I'll be honest- I wasn't quite sure how the start of triangle proofs would go with my Geo with Lab students this year. Not because they aren't capable, but because they were so scared! With students who already have some math anxiety, the anticipation of starting a famously formidable topic was hanging ominously over the classroom our very first day. They had heard things from their older sibling and friends and judged proofs before they ever even gave them a chance. So far, so good, though. No tears. A few "why did everyone make such a big deal of this?" comments. I count all of those in the W column. 

I've been scaffolding proofs slowly, a little more each day. We've been using this super basic graphic organizer to plan before writing anything, making a constant analogy to how your English teacher asks you to outline a paper before you write the final draft. Knowing where your headed before you ever start makes the destination easier to get to, for sure. I printed about 8 of these to a page and have them in sheet protectors in my room so kids can write on them with dry erase markers with no commitment as they plan. I also have a bunch of extras that they can pick up for homework or use on quizzes/tests if it helps them. 

Here's how it looked in action on our first day:

Here's a link if you're interested in using or adapting: 

I also designed this really basic sorting activity for triangle congruence. I know there are a ton of these out there already, but I wanted something targeted for my type of kiddos, who need to build some confidence and hadn't been exposed to everything yet. I didn't even use this with my standard level class because they were ready for more open-ended activities more quickly. There are 3 proofs and all the statements and reasons scrambled for each. My students at this point hadn't seen HL or CPCTC yet, so these are really just getting them to engage with the very first steps of proof. It went well with my kiddos and made them feel some success, which is really half the battle in a lab class. 

Steal away if this would be helpful to you! And as always, feel free to offer suggestions if you see room for improvement! Happy proving!  

Sunday, October 29, 2017

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

Monday, October 9, 2017

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

Wednesday, October 4, 2017

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. 

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!