Justifications and Curve Sketching in AP Calc

Have I mentioned that I love curve sketching? (Yes, I know, only every 5 minutes). To me, it's a giant puzzle that students can approach from all different angles. There are so many small parts that individually contribute to the big picture and I love those moments when you see it all come together for a student. It's one of the only units in Calculus where I can look around on any given day actually see the lightbulbs lighting up for each kid- each one benefiting from a different perspective or activity. Today we did some serious curve sketching challenges!

#1: Justification Graphic Organizer

Students worked in small groups to complete the graphic organizer with calculus explanations for each of the features in the chart. 

We returned to their chart over and over throughout the lesson and it's something they can keep to study from in the future. Next year I think I'd like to revise it to to include explanations of what happens on f, f', and f''...maybe a sketch or description box?

#2: Quiz, Quiz, Trade

This is an activity that is right from the College Board modules and I love it! I gave the students time to work on their own problem silently and then check their answer. They needed to be prepared to teach it to another student. If they didn't feel prepared, they got to come hang out with me at a side table to go over it once the activity started. I set a timer for 5 minutes and told students to interact with as many other students as they could in that time. They worked diligently, explaining their problem to those who needed help and solving each others problems. It brought out common misconceptions, too (which is always vital).  

Quiz Quiz Trade Student

Quiz Quiz Trade Teacher

#3: AP Justification Challenges

Next we worked on scaffolded activities to get students building arguments. Here we discussed what implications f, f', and f'' all have on each other more specifically and began to see common AP style questions. We didn't finish all of these in class, but the nice thing is you can pick and choose what your kids need to most help with while you work. 

Here's the whole document that we used!  AP Style Justifications

Let me know if you have any other activities you love for this unit!