Calculus AB APSI 2015

Day 4

Professional Development

Workshop Handbook

Curriculum Framework

Calculus AB and BC

Professional Development

Integration, Problem Solving, and Multiple

RepresentationsCurriculum Module

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ThursdayMorning (Part 1)

Discussion of Homework Problems Break Morning (Part 2)Activity #2 Exploring the Mathematical PracticesSelected Curriculum ModuleRevising Assessment QuestionsBalancing Concept and Skill

Lunch

Afternoon (Part 1)Free Response 2007 AB3Discovering the Relationship between Slopes at Corresponding Points on Inverse FunctionsIntegration, Problem Solving and Multiple RepresentationsBreakAfternoon (Part 2)Activity #3 - Scaffolding the Mathematical Practices Discussion about classroom procedures, grading, homework, tests, and any other concernsClosure

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Wednesday Assignment - AB

Multiple Choice Questions on the 2014 test: 1, 4, 8, 12, 14, 18, 26, 76, 77, 70, 80, 81, 83, 84, 85

Free Response: 2014: AB4, AB6 2015: AB4, AB5

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2014 AB4

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Scoring Rubric 2014 AB4

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2014 AB6

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Scoring Rubric 2014 AB6

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Scoring Rubric 2014 AB6

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2015 AB4

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Scoring Rubric 2015 AB4

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Scoring Rubric 2015 AB4

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2015 AB5

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Scoring Rubric AB5

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Activity #2 Exploring the Mathematical Practices

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Think about this question with your group. Be prepared to share your

responses with the rest of the class.

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Revising Assessment Questions

One suggestion for preparing students for the types of questions they see on AP Exams is to use questions with similar structure, formatting, and scoring throughout the year. Using the information you have gained in this workshop, you will revise existing questions to be similar to the types of questions and scoring guidelines that are used on the AP Exams.

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1. Find the derivative of the function

 AP Conversion:

Scoring Guideline:

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2. Given , find the points at which has a local maximum, minimum or point of inflection.

 AP Conversion:

Scoring Guideline:

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3. Evaluate the integral

AP Conversion

Scoring Guideline:

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Balancing

Skill Concept

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Many students finish Calculus thinking about a derivative as a process that leads to

a number.

2I ff (x)=cos ,then '

4 2x f

They also think about a integration leading to a number.

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0I ff (x)=cos ,then cos 1x xdx

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But we already saw that a derivative is a function:

( ) sin( )

' ( ) cos( )f x x

f x x

So likewise, a function can be represented by an integral.

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Functions Defined by Integrals

Smartboard File

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Exploring Functions Defined by Integrals

Worksheet 1: Page 3-7

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Exploring Derivatives of Functions Defined by Integrals

Worksheet 2: Page 10-12

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Graphical Analysis of F(x) using F’(x)

Worksheet 3: Page 15-16

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Activity #3 – Scaffolding the Mathematical Practices

Different Learning Objectives could reference the same MPAC, providing multiple opportunities for students to practice that skill in different contexts. Think about the following prompts.

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1. Label each of the student tasks below to establish a sequence that would help to support students’ development of MPAC 5a: Know and use a variety of notations. Use each label only once.

Understanding Scaffolding

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2. MPAC 6c states that students will be able to explain the meaning of expressions, notations, and results in terms of a context (including units). What are some strategies you can use that will help students build that skill over the course of the year?

3. List three Learning Objectives where you could incorporate those strategies and provide opportunities for students to practice MPAC 6c in multiple contexts?

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Activity #4 – Exam Items

Course planning can incorporate instructional strategies that will target specific misunderstanding and support students’ ability to demonstrate mastery of the Learning Objective.

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• The overall design of the exam has not changed and the Learning Objectives in the Concept Outline are the target of assessment.

• Review the same item and respond to the given prompts. • Reference the Curriculum Framework

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1. How does this item require students to demonstrate an understanding that a function’s derivative, which is itself a function, can be used to understand the behavior of the function (EU2.2)?

2. How does this tem require students to demonstrate an understanding that the definite integral of a function over an interval is the limit of a Riemann Sum over an interval and can be calculated using a variety of strategies (EU3.2)?

3. How does this item require students to apply one of the subskills in MPAC 6?

4. What other MPACs would students need to apply in order to be successful on this item?

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Discussion about classroom procedures, grading, homework, tests, and any other concerns

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Integration, Problem Solving and Multiple Representations Curriculum Module

Lesson 1Lesson 2Lesson 3Lesson 4

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Jim Rahn

►Event Code:

►Consultant Code 0602

►Session Number:

Meeting Code/Consultant CodeLasalle University

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Meeting Code/Consultant CodeMiddlesex County College

Jim RahnEvent Code: Consultant Code 0602Session Number:

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Meeting Code/Consultant CodeOcean County College

Jim RahnEvent Code: Consultant Code 0602Session Number: