Calculus AB APSI 2015 Day 4 Professional Development Workshop Handbook Curriculum Framework Calculus AB and BC Professional Development Integration, Problem Solving, and Multiple Representations Curriculum Module

Thursday Morning (Part 1) Discussion of Homework Problems Break Activity #2 Exploring the Mathematical Practices Selected Curriculum Module Revising Assessment Questions Balancing Concept and Skill Lunch Afternoon (Part 1) Free Response 2007 AB3 Discovering the Relationship between Slopes at Corresponding Points on Inverse Functions Integration, Problem Solving and Multiple Representations Break Afternoon (Part 2) Activity #3 - Scaffolding the Mathematical Practices Discussion about classroom procedures, grading, homework, tests, and any other concerns Closure

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

2014 AB4

Scoring Rubric 2014 AB4

2014 AB6

Scoring Rubric 2014 AB6

Scoring Rubric 2014 AB6

2015 AB4

Scoring Rubric 2015 AB4

Scoring Rubric 2015 AB4

2015 AB5

Scoring Rubric AB5

Activity #2 Exploring the Mathematical Practices

Think about this question with your group Think about this question with your group. Be prepared to share your responses with the rest of the class.

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.

1. Find the derivative of the function 𝒚= 𝟑𝒙 𝟕 −𝟕 𝒙 𝟑 +𝟑 AP Conversion: Scoring Guideline:

AP Conversion: Scoring Guideline: 2. Given 𝒚 ′ =𝟔(𝒙+𝟏) (𝒙−𝟐) 𝟐 , find the points at which 𝒚=𝒇(𝒙) has a local maximum, minimum or point of inflection.  AP Conversion: Scoring Guideline:

3. Evaluate the integral 𝟐 𝟓 𝟒𝒙 𝒅𝒙 AP Conversion Scoring Guideline:

Balancing Skill Concept

They also think about a integration leading to a number. Many students finish Calculus thinking about a derivative as a process that leads to a number. They also think about a integration leading to a number.

But we already saw that a derivative is a function: So likewise, a function can be represented by an integral.

Functions Defined by Integrals Smartboard File

Exploring Functions Defined by Integrals Worksheet 1: Page 3-7

Exploring Derivatives of Functions Defined by Integrals Worksheet 2: Page 10-12

Graphical Analysis of F(x) using F’(x) Worksheet 3: Page 15-16

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.

Understanding Scaffolding 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.

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?

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.

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

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)? 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)? How does this item require students to apply one of the subskills in MPAC 6? What other MPACs would students need to apply in order to be successful on this item?

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

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Integration, Problem Solving and Multiple Representations Curriculum Module Lesson 1 Lesson 2 Lesson 3 Lesson 4

Meeting Code/Consultant Code Lasalle University Jim Rahn Event Code: Consultant Code 0602 Session Number:

Meeting Code/Consultant Code Middlesex County College Jim Rahn Event Code: Consultant Code 0602 Session Number:

Meeting Code/Consultant Code Ocean County College Jim Rahn Event Code: Consultant Code 0602 Session Number: