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 product of two functions. 

 

Subject: Calculus One

 

Purpose: This lesson will enable students to differentiate functions that involve products of two functions.  It will expand the students’ ability to compute slope 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.

 

Learning Outcomes

 

By the end of this lesson, students will:

1. be able to apply the product rule of derivatives and differentiate functions involving products.

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 (HKCXG) provided by the teacher.

 

So far students have dealt with slopes of functions and derivatives of polynomials. 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) Students will warm up their knowledge by applying basic derivative rules on polynomial functions. The teacher monitors students’ progress from his device.

2) Students will engage in two activities:

• Students will expand the product of two binomials, then they would differentiate the worked out polynomial.

• Students will find the derivative of each binomial, then the teacher would ask them to simplify the expression u’v + v’u.

3) After the two activities, the teacher pushes to the students’ devices the next slide where they conclude a formula to differentiate the product of two functions.

4) Students will watch an embedded You Tube tutorial video about differentiating the product of functions, then they will practice applying the product rule in the next slides.

5) 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.

6) 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 products of functions. They can go online to explore suggested resources.

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

8) Finally, students will have the opportunity to write a couple of sentences to give feedback and comments to their teacher