Calculus AB

AP Summer Institutes at Woodward Academy

June 5‐8

The AP Calculus Summer Institute provides an exciting week of technology intensive calculus. AP Calculus courses have recently undergone a redesign with updated courses being defined in a new curriculum framework that ties course content and mathematical practices to clearly stated learning objectives. It will take effect in the 2016-17 school year. There will be an increased emphasis on conceptual understanding through the Mathematical Practices for AP Calculus (MPACs). During the week, participants will become familiar with the new framework and its implications for teaching the AP Calculus courses. They will receive a notebook containing AP exam resource questions, reform questions, concept worksheets, grading samples and scoring standards, as well as, reference materials. Highlights of the week include discussions of pedagogy, use of technology, consideration of topics from a reformed perspective, a review of multiple choice and free response questions, how to prepare students for the AP Calculus AB exam and the grading of the 2017 AP exam.

About

Daily Schedule

Monday
  • Beginning the Course
  • Advanced Placement Program and Resources (AP Central)
  • What's New in AP Calculus?
  • Multiple Representations and its Implementation in Pre-AP as well as AP
  • Textbook Review & Notebook Tour
  • Pre-AP Curriculum
  • AP Audit Process and Samples/Pacing
  • Reformed Questioning
  • Limits and Continuity
  • Average Rates of Change, Local Linearity and the Development of the Concept of the Derivative
  • Issue: Technology
Tuesday
  • The Derivative as a Function & What does it tell us? f, f' and f''?
  • Local and Global Extrema: The First and Second Derivative Tests
  • AP Problem Review
  • Derive Shortcut Rules for Differentiation
  • Graphical Analysis including Derivative Tests
  • Linearization and Estimation
  • Optimization
  • Implicit Differentiation
  • Related Rates
  • Issue: Resources (including websites)
Wednesday
  • Rectilinear Motion
  • Inverse Functions and Derivatives
  • Rolle's Theorem/Mean Value Theorem
  • Calculator Lab Experience
  • Beginning Integration/Anti-differentiation
  • Left, Right, Midpoint and Trapezoid Sums
  • The Integral Function (ie. Definite Integral as an Accumulator)
  • The Fundamental Theorem including Reformed Version (Net Change)
  • Techniques of Integration including Substitution of Variables
  • The Average Value of a Function
  • Ways to Improve Your AP Score
  • Issue: Preparing for the AP Exam (Discuss Stand and Deliver/ AP Grading)
Thursday
  • Area
  • Calculus in Motion Computer Software
  • Calculator Interface
  • Volumes of Solids of Revolution (Disks, Washers, Shells) including Models
  • Volumes of Known Cross Sections
  • Slope Fields
  • Differential Equations and Initial Conditions
  • Issue: 2016 AP Exam Problems Review
  • Evaluations

July 17‐20

This AP Calculus AB workshop will focus on preparing teachers to teach the calculus topics covered in the AB curriculum framework, by familiarizing beginning teachers with the AB curriculum, familiarizing AP teachers to the updated Curriculum Framework, assisting in lesson planning, creating a syllabus for the new updated audit review, and assisting with technology interfacing. This workshop will also cover a materials and AP Exam review, and feature special topics, including slope fields, differential equations, the Fundamental Theorem of Calculus including integral functions, the Mean Value Theorem, and the derivative of the inverse of a function.

About

Daily Schedule

Monday
  • Welcome and Introductions
    • Overview of the Workshop
    • Let’s do some Calculus - overview of calculus activity
  • 2016 Curriculum Framework
  • Limits and Continuity
  • Definitions of the Derivative
    • Tangent Line Problems
    • Graph of the Derivative Activity
  • Derivative Rules
    • All derivative rules and the derivative of basic functions
    • Derivative of the Inverse of a function
    • The Mean Value Theorem
    • L'Hospital's Rule
Tuesday
  • Applications of the Derivative
    • Graph Theory
    • Functions defined implicitly
    • Applications of the Derivative
    • Related Rates
    • Motion along a Line
  • Anti-derivatives and the Definite Integral
    • Anti-derivatives of basic functions
    • Integration by u-substitution
    • Riemann Sums
    • Properties of Definite Integrals
  • Fundamental Theorem of Calculus
    • Average Value
Wednesday
  • Applications of the Definite Integral
    • Motion along a line.
    • Area Between Two Curves
    • Volume
      • Activities:
        • Constant Cross-Sections
        • Solid of Revolution
  • Functions defined by Integrals
    • Accumulation of a rate function
Thursday
  • Differential Equations
  • Slope Fields
  • Preparing a syllabus for the audit
  • The 2017 AP Exam ‐ Grading
  • Resources
  • Q&A
  • Evaluations
  • Certificates
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