[PDF] Lesson Plan: A Comprehensive Overview of the Derivative of a

40313_2UDL_online_lesson_plan.pdf PSQF: 6211 Final Project Le Tang 5/10/2021 Lesson Plan: A Comprehensive Overview of the Derivative of a

Function

Designer: Le Tang

Department of Mathematics

University of Iowa, Iowa City

Target Audience: Calculus I students

Grade level: Undergraduate

Subject area: Mathematics

Pre-requisites: Students enrolled in this lesson should have completed and passed a class equivalent to Math 1005: College Algebra at the University of Iowa with a C or higher. Materials: Course textbook (Steward 9th Ed.) purchased by the Department of Mathematics and shared on course webpage as a PDF file, two online videos, pre-class worksheet, in-class discussions and quiz, and homework. Timeframe: Approximately 3 hours are required for this lesson. Delivery method: Completely Online; both asynchronous and synchronous learning are applied. Communication: Should students have any questions regarding any parts of the lesson, they are encouraged to reach out to the instructor. A good way to contact the instructor is via authenticated email (such as writing emails with @uiowa domain). Questions or concerns can also be addressed during the in-class portion or during the instructors office hours. To request additional appointments, please contact your instructor via email. Communication though/via text messages or social media is not suggested for this lesson.

Basic Lesson Objectives:

Be comfortable with the definitions and ideas of limits. State the formal definition of the derivative of a function. Explain the relationship between multiple informal descriptions of the derivative of a function and the formal definition of the derivative if a function. Discuss the necessary conditions where the derivative of a function can be defined. Given a graph (provided by Desmos and other online graphing calculators) of a simple differentiable function, informally describe the meaning of the derivative at some point ݔ on the graph.

Advanced Lesson Objectives:

(Advanced) Give a list of the derivatives of most common continuous and differentiable functions. (Advanced) Understand the proof behind the derivative of a function. PSQF: 6211 Final Project Le Tang 5/10/2021

(Advanced) Understand the definitions and meanings of the ݊௧௛ derivative of a function if

it exists. Pre-Class Introduction and Review: Students are expected to complete the following activities prior to the class meeting (~60 minutes).

1. Watch the pre-recorded lecture videos (English captioned) on Limits (10 minutes) and

Derivatives (20 minutes) on course website.

2. Additional tutorial videos on Limits and Derivatives can be found at Khan Academy:

Limits and at Khan Academy: Derivatives

3. Read the chapter on Limits in the textbook and find associated notes on the course

website. Pay close attention to the limits at 0 or infinity.

4. Be prepared to answer the following questions during in-class meeting:

(a) Why is it necessary to have a good understanding on Limits before studying

Derivatives?

(b) What is an intuitive definition of derivative (there are many from different areas of science)? (c) What is a formal definition of derivative? Are there any alternatives? (d) What are the notations, in symbols, for derivatives? (e) What is the derivative of ݂ሺݔሻൌʹȁݔȁ at ݔൌͲ?

(f) Graph the derivative of the function ݂ሺݔሻൌݔଶ൅ʹݔെͳ. What does the graph

indicate? (g) What is the second derivative of a function at a point? (h) Be ready to compute the derivative of some common functions such as ݁௫ and polynomials.

5. Upload sketch of answers to the above questions on course webpage.

6. Complete the pre-class survey on the course website (5 minutes). Email with reminders if

needed. In-Class Discussions, Practice and Quiz: Students and the instructor are supposed to meet online via Zoom (or other online meeting apps) at a scheduled time (~60 minutes).

1. Form groups (each with 3-5 students) using the feature of Breakout rooms on Zoom and

have students share answers/ideas from the pre-class activities with others and critique; access students answers on course webpage and download each group members answer then share on Zoom in a breakout room. Write on a Whiteboard provided by Zoom whenever needed. It is okay to use curser, keyboard or on-screen keyboard to briefly write down ideas, but it is suggested to have touch screen devices ready.

2. Ask a representative of each group to share their findings about pre-class questions.

3. Give students some time to come up with questions.

4. Explain what the representatives did well and correct anything if they were incorrect

(with a while board online).

5. Ask additional questions if time allows:

(a) Use definitions of derivative to prove product rule and quotient rule. (b) Assign a problem about the chain rule on the homework. (c) Find the 5th derivative of a function, possibly a polynomial. (d) What is the derivative of a constant? PSQF: 6211 Final Project Le Tang 5/10/2021 (e) When cant a function have a derivative?

6. Complete the in-class quiz (15 minutes). As students work on problems, provide

reasonable hints and reminders where warranted.

7. Discuss solutions to the quiz.

Post-Class Homework and Evaluation (~60 minutes)

1. Complete the homework set and submit it as a scanned PDF file to the course webpage

under HW by 11:59pm on Sunday.

2. Provide office hours and additionally availability, when needed, for student questions and

concerns.

3. Complete the post-class survey (5 minutes). Email with reminders if needed.

Accessibility of Course Materials

For accessible documents: Ensure that documents (texts, assignments, quiz and homework etc. are made accessible to all students: alt-text for links and pictures; appropriate titles, fonts and colors; and well ordered. A good way to do this is to make accessible Word document and convert to PDF files before posting on course website. For accessible video: Ensure to speak slowly, have a talking head, and type up accurate captions in English. Pay special attention to those captions on mathematical syntax and symbols. For accessible websites: Use the Wave website to check the accessibility of any websites associated to the lesson such as course webpage.

Assessments:

Pre-class Survey (formative): Design a survey that asks basic knowledge prior to this lesson; typical questions include what students know about a function, a limit, and slopes. In-class Quiz (summative): Design a short quiz consisting of 3-4 questions based on pre- class questions. Post-class Survey (formative): Design a survey that asks for students feedback: what they learned, what they like or dislike about the class, and what can be improved. Assistive technology: Most of the following are free of charge or paid by the University. Please contact University Tech Support for more information on the availability of any assistive technology you require additionally. For reading: Snap&Read with text-speech feature. For writing: EquatIO (browser extension), Co:Writer with speech-text feature. For physical access: on-screen keyboard, Voice Control.

Disability Statement

The College of Liberal Arts and the department of Mathematics make reasonable accommodations for students with disabilities. Students are expected to notify their instructor at the beginning of the lesson of any disability related needs, including any academic adjustments or accommodations requested. Students may also choose to contact Student Disability Services PSQF: 6211 Final Project Le Tang 5/10/2021 (SDS) directly. SDS facilitates academic accommodations and services for students with disabilities to ensure everyone has equal access to course materials and activities.

Language Support

Students whose first language is not English, or have trouble understanding English, please refer to the University Language Center for appropriate translation on the course materials. Video lectures are captioned in English and can be easily translated by apps such as Google Translator. Please do not be hesitate to contact your instructor for language support.