# Three New Lessons for Calc BC!

This year we set out to make some new EFFL lessons for the big topics of AP Calc BC. Earlier this year we released lessons on __Integration by Parts__, __Improper Integrals__, and __Differentiating Parametric Equations____. __Today weâ€™re releasing some lessons from Unit 7 and Unit 9. Check them out!

__Topic 7.5: Approximating Solutions with Euler's Method__

__Topic 9.6: Solving Parametric and Vector Motion Problems __

__Topic 9.8: Areas of Polar Curve Regions__

With these lessons, we sought to develop deep conceptual understanding of topics that are generally reduced to formulas students have to memorize. For example, students may know how to set up a correct integral to find a particle's total distance traveled, but do they understand *why *speed is a scalar as opposed to a vector and how this connects to its geometric representation? (Speed is the absolute value--think magnitude-- of velocity, representing a distance from the origin, which in a 2-dimensional plane can be found using the Pythagorean Theorem). Many of these lessons build on topics in Calc AB and we've purposefully crafted and sequenced the questions to activate this prior knowledge.

Euler's Method builds on Tangent Line Approximations (

__Topic 4.6__)Parametric and Vector Motion builds on Particle Motion in 1-D (Topics

__4.2__and__8.2__)Areas of Polar Curve Regions builds on Riemann Sums (

__Topic 6.3__)

As always, these lessons are in our classic __Experience First, Formalize Later__ (EFFL) format. This means each lesson begins with students working collaboratively in small groups through a sequence of carefully crafted questions that slowly build in complexity (Experience First). Following this activity, the teacher facilitates a discussion connecting studentsâ€™ ideas with academic vocabulary and notation (Formalize Later). This approach encourages students to build strong math identities and take an active part in mathematical sense-making.

We believe in teaching students flexible thinking rather than rote memorization. Through our discovery-based activities and scaffolded questions, students uncover concepts and ideas on their own.