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 quotient of two functions. 

 

Subject: Calculus One

 

Purpose: This lesson will enable students to differentiate functions that involve quotient 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 and products.

 

Learning Outcomes

 

By the end of this lesson, students will:

1. be able to apply the quotient rule of derivatives and differentiate functions involving quotients 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

7. Trig Derivatives teaches the objectives which is to find the derivatives of the six trigonometric functions by using the product and quotient rules.

 

Description of students’ activities

 

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

 

So far students have dealt with derivatives of polynomials and products of functions. 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 deal with a simple quotient function , which can be re-written and derived as a polynomial function. The teacher monitors students’ devices from his device and expand the discussion to other quotient functions

2) Students will engage in an activity to derive a formula for quotient differentiation: students will be asked to write the quotient function as y=u/v and then to evaluate the expression:  u'v-v'u/v2

 

3) Students discuss in groups the relationship between the value of y’, the students have just found, and the value of the expression.

4) Using stylus pens on their iPad screens, students practice solving exercises by applying the quotient rule of derivatives. Students study the function

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

6) 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.

7) 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.

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

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

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