Calculus One with iPads

Overview: In this lesson, students will continue to use their prior knowledge of derivatives in order to investigate how to differentiate the composite of two functions. 

 

Subject: Calculus One

 

Purpose: This lesson will enable students to differentiate complex functions that are formed from the composition of two functions. It will expand the students’ ability to compute slopes of functions and to write the equation of tangents at given points of the curve.

 

Prerequisite Knowledge

            Students should:

• already know and understand the concept of derivatives.

• know how to differentiate polynomials, products and quotients.

 

Learning Outcomes

 

By the end of this lesson, students will:

1. be able to apply the chain rule of derivatives and differentiate the composite of two functions.

2. be able to use Calculus resources in classroom as well as from home.

3. enrich their knowledge of differentiation techniques for the upcoming Calculus lessons.

 

Resources/Materials Needed

1. Internet access and Wi-Fi in classroom

2. iPads

3. Nearpod application installed on each device

4. Nearpod website; www.nearpod.com

5. Website: You Tube, www.youtube.com; Khan Academy, www.khanacademy.org; and Interactive Mathematics, www.intmath.com

6. Data projector

 

Description of students’ activities

 

Students will access the Nearpod lesson using their iPad devices and a PIN (QBZHT) provided by the teacher

 

Students already know how to differentiate polynomials and functions including products and quotients. After logging on the Nearpod app on their iPad devices and inserting the PIN of the Nearpod lesson, the instructor starts lesson activities by pushing presentation slides to students’ devices.

1) The instructor pushes a couple of slides, containing a reminder to composition of functions, to the students’ devices.

2) Students will engage in an activity to derive a formula for composite differentiation: students will be asked to write the function y=2(3x-5) as y=2u.

 

3) The instructor pushes to students’ devices the slide that prompts students to expand and differentiate the resulting polynomial.

4) Then, students will calculate the expression dy/du *du/dx. Students discuss in groups the relationship between y' and  dy/du *du/dx         .

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5) Using stylus pens on their iPad screens, students practice solving exercises by applying the chain rule of derivatives.

6) Students will watch an embedded You Tube tutorial video about differentiating the composite functions using the chain rule, and then they will practice applying the chain rule in the next slides.

7) The students will have access to online activities involving derivatives of functions. The teacher may share the screen of one student with the rest of the class.

8) Students will answer questions of a quiz and their results will be saved for comparison and analysis. The teacher wraps up the lesson by discussing students responses to questions. Students share their ideas about ways to differentiate composite functions. They can go online to explore suggested resources.

9) At the last stage, students will answer poll questions about their experience and satisfaction.

10) Finally, responding to an open-ended question, students will have the opportunity to write a couple of sentences to give feedback and comments to their teacher.