TITLE: Volumes of Revolutions Course: AP Calculus Instructor: Bo Greene Grade Level: 11-12 Created: March 8, 2010
OVERVIEW: This
Teaching & Learning Guide structures review and new learning of the
following calculus concepts: Area Between Two Curves, Volumes of
Revolution, and Volumes using Known Cross Sections. These are extremely
important topics and are ALWAYS tested on both exams, usually as a Free
Response (FR) question. Find a new partner in the class, discuss the following questions, and then make a combined
posting in the AP Calculus Discussion Forum answering these questions. - What is important when finding the area
between 2 curves as it relates to the position of the 2 functions
(which one is "on top")??
- When do we use disks vs. washers??
- Does Volume with Known Cross Sections makes more sense and if so what
strategies do you use to help solve these type of problems??
If you can do the homework problems below, then you truly understand these
concepts and will do well on these types of questions on the AP BC Exam. Read Sections 7.1, 7.2 in your textbook (pages 446-466) - Problems 1-6 (page 452)
- Problems 33-35 (page 453)
- Problems 65-66 (page 453)
- Problems 1-14 (page 463)
- Problem 62 (page 466)
If you're struggling with any of the odd problems, don't forget about www.hotmath.com
ESSENTIAL QUESTION(S): - How can integrals be used to find areas of complex figures?
- What are the practical applications of finding such areas?
- How can integrals be used to find volumes of complex figures?
- What are the practical applications of finding such volumes?
STANDARDS & OBJECTIVES (SUBJECT & NETS-S): - Students
will graph two curves, find their intersections, set up an integral for
the area between the curves, and compute the area.
- Students
will explain the difference between the disc, washer, and shell
methods. They will also determine which method is preferred in
particular cases and explain why only one method will work in certain
cases.
- Creativity & innovation (NETS-S): Students use models and simulations to explore complex systems and issues.
- Communication
& Collaboration (NETS-S): Students use digital media and
environments to communicate and work collaboratively, including at a
distance, to support individual learning and contribute to the learning
of others. (discussion forum).
- Digital Citizenship
(NETS-S): Students exhibit a positive attitude toward using technology
that supports collaboration, learning, and productivity.
DIFFERENTIATED INSTRUCTIONAL STRATEGIES:
- Learning tasks have different access points
- Students work in multiple groupings
- Varied pacing with anchor options
- Varied supplementary materials
- Use of Simulations
ASSESSMENTS- homework problem sets
- class discussion
- online discussion questions (partners)
- traditional quiz & test
- AP Exam practice test questions
STUDENT ARTIFACTS
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