# AP* Calculus

#### We are pleased to welcome David Platt to the 2014 AP* Summer Institute!

### Registration is Now Open - Register before June 1 to get Early Bird Price!

### Instructor Bio

**David Platt** taught as a full time mathematics faculty member at Mesa Community College from 1990 to 2000 and has been a full time mathematics faculty member at Front Range Community College since 2000. He holds a Ph.D. in mathematics education from the University of Texas at Austin, an M.S. in mathematics from Colorado State University, and a B.A. in mathematics from Western Connecticut State College.

He has served as an AP Calculus Exam Reader or Table Leader since 2000. As a Certified College Board Consultant since 2002, he has presented weeklong AP Calculus AB Summer Institutes at California State University – Sacramento, Pacific Lutheran University, Carleton College, The University of Northern Colorado, and Vancouver, WA. He has taught a five week online summer institute for UCLA Extension since 2003. He has also presented numerous AP Calculus Professional Development Workshops in Washington, California, Nevada, Idaho, Utah, Colorado, Arizona, Missouri, Minnesota, Michigan, and Illinois.

### Course Information

The institute will cover all topics on the Calculus AB syllabus which includes limits and continuity; the concept of a derivative as a rate of change; computation of derivatives; the Mean Value Theorem; applications of derivatives including optimization and related rates; definite integrals and Riemann sums; techniques of antidifferentiation; applications of integrals including area, volume, average value, and accumulated change; the Fundamental Theorem of Calculus; slope fields; and separable differential equations.

We will focus on developing a conceptual understanding of content topics in the context of AP* Calculus questions, syllabus construction using AP* Audit guidelines, teaching strategies, and preparing for the AP* Calculus Exam. Several hands-on activities will be completed using graphical, numerical, analytic, and verbal representations to foster a more complete understanding of calculus. These handouts are designed to improve conceptual understanding of important topics to facilitate student success on the AP* Calculus Exam. A computer lab session will be conducted with hands-on practice with Mathematic demonstrations, screencasts, and learning styles inventories.

Sample free response questions as well as the entire 2003 and 2008 AP* Calculus AB multiple choice exams, indexed by topic, will be presented with detailed solutions to develop an understanding of the content and the College Board philosophy for choosing questions for the AP* Exam, and as well as strategies for embedding AP* questions in a Calculus AB course. Participants will receive a CD containing a variety of classroom tested activities and calculator programs to enhance their own teaching, a complete set of lecture notes and PowerPoint presentations for a college-level Calculus I class, and You-Tube videos useful in teaching calculus. Selected worksheets from AP* Calculus curriculum modules will be completed and discussed to address important areas of emphasis and common student difficulties on the AP* Calculus Exam. Strategies will be discussed to enhance student performance on the AP* Calculus Exam including tips for justifying answers, strategies for solving optimization problems, and strategies for choosing the correct branch of solutions to separable differential equations.

Participants will be trained to score free response questions using the scoring standards and actual student samples used at the AP* Calculus Reading. Detailed strategies for success on the AP* Calculus Exam will be discussed.

What To Bring:

- TI-83+ or TI-84+ graphing calculator
- 30 copies of a successful group activity for sharing best practices in teaching techniques
- The textbook that you will use (if known)

**Schedule:**

**Monday, July 7 –**

1. Introductions, packet materials

2. Equity and Access Policy

Discussion of College Board Equity and Access Policy Statement

Comment on Vertical Teams, Pre-AP Workshops

Look at AP Potential – https://appotential.collegeboard.com/loginGetAction.do

3. AP Central

Navigating AP Central - Calculus AB Homepage, sample syllabi, course description, curriculum modules,

Calculus AB Free-Response Exams, AP Calculus AB Teacher Community.

4. AP Free Response and Multiple Choice Exam Question Topic Index Files

5. Developing an AP Calculus AB Syllabus

AP Calculus Audit requirements, sample syllabi, block scheduling, timeline issues.

6. Technology

Graphing Calculator Capabilities Required for the AP Exam, technology restrictions, programs

TI SmartView graphing calculator presentation tool for the TI 84+ graphing calculator

TI Connect – Computer-Calculator Program Transfer

Calculator Activity

Computer Lab Activities – learning styles, screencasts, Wolfram demonstrations, Wolfram-Alpha,

Stewart animations, Great Websites for Calculus Teachers

7. Teaching Strategies - Share best teaching practices, Differentiated Instruction

8. Limits - AP Exam Questions

9. Continuity - Three-step definition, AP exam questions

10. Definition of the Derivative

Graphically, numerically, and analytically – programs on TI-83+

11. Derivative at a Point

Symmetric difference quotient

Special Focus on Approximation

Reasoning From Tabular Data Curriculum Module Activity

12. Derivative Rules

Product Rule, Quotient Rule, Chain Rule, inverse sine and inverse tangent functions, inverse

Functions, implicit differentiation

13. Graphs and Derivatives

Chain Rule Activity, Graphs of Derivatives Activity

**Tuesday, July 8 –**

1. Applications of Derivatives

Related Rates

Extrema Curriculum Module – Worksheet 1, Worksheet 2 Activity

Max/Min Optimization Problems (local vs global)

Properties of Graphs Activity

Sign Chart Activity

Textbook Controversies

Mean Value Theorem

Particle Motion - Motion Curriculum Module Worksheet 3 Activity

Integration Curriculum Module Lesson 3 Summative Assessment

Equation of a Tangent Line – Integration Curriculum Module Lesson 4

2. Riemann Sums - AP Questions, programs on the TI-83+

3. Area Using Trapezoidal Sum - intervals with unequal width

**Wednesday, July 9 –**

1. Fundamental Theorem of Calculus

Using FTC directly, Accumulation

Functions Defined By Integrals Curriculum Module Worksheet 3 Activity

FTC Curriculum Module Worksheet 5 Activity

2. MVT for Integrals, Average Value of a Function

Reasoning from Tabular Data Curriculum Module

3. Second Fundamental Theorem of Calculus

Special Case, General Case, FTC Curriculum Module Worksheet 4 Activity

4. Integration by Substitution

Integration Curriculum Module Lesson 4 Summative Assessment, Handouts 1 – 5

5. Slope fields and Separable Differential Equations

Content, Slope Fields Activity, separable differential equations handout

**Thursday, July 10 –**

1. Further Applications of Integration

Distance Concept

Area/Volume and Volumes of Solids of Revolution Curriculum Module

Calculus in Motion simulation demonstration using Geometer’s Sketchpad

Volumes of Solids With Known Cross-Sections Activity

2. The AP Calculus AB Exam

How the exams are developed

How the rubrics are prepared at the reading

The complete grading process

Test taking strategies for your students

Work Session on grading the 2014 Free Response Exam

3. What To Do After the AP Exam

4. College Board Resources

5. AP Quizzes

6. Additional Topics and Activities

**Note:**

The institute will include a review of content, completing activities stressing active participation using the

rule of four - graphical, numerical, analytic, and verbal representations, discussing teaching strategies,

solving multiple choice questions taken from the 2003 and 2008 exams, scoring actual student samples of

answers to free response questions taken from the 2014 exam, insights on common errors by students and

strategies to improve in these areas, and insights on changes in curriculum and the AP Exam.

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