Calculus One with iPads

Overview: In this lesson, students will use their prior knowledge of slopes of functions and the definition of derivatives in order find a rule to differentiate polynomial functions.

 

Subject: Calculus One.

 

Purpose: This lesson will enable students to differentiate polynomial function. It will expand the students’ ability to write the equation of the slope of a function.

 

Prerequisite Knowledge:

            Students should:

• already know how to graph the slope and to write derivative function of some remarkable functions.

• know how to apply the definition of derivative.

 

Learning Outcomes

By the end of this lesson, students will:

1. be able to differentiate power functions and constant multiple functions.

2. be able to differentiate sum or difference of functions

3. be able to differentiate polynomial functions.

 

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. Tutorial websites: You Tube, www.youtube.com;

Khan Academy, www.khanacademy.org;

Interactive Mathematics, www.intmath.com

Bright Storm videos https://www.brightstorm.com/math/calculus/

Multiple applets Differentiation that are games and puzzles

    6. Data projector

 

Description of students’ activities

Students will access the Nearpod lesson using their iPad devices and a PIN (JXSRL) provided by the teacher. So far students have practised graphing slopes of functions, including polynomial and trigonometric functions. After logging on the Nearpod app on their mobile devices and inserting the PIN of the Nearpod lesson, the instructor starts lesson activities by pushing presentation slides to students’ devices.

 

1) Students will study the constant function graphically and analytically, they will have the opportunity to discuss in groups why the derivative of a constant function is zero.

2) The instructor pushes the next slide. Students discuss in groups the steps of differentiating the functions y=x2 and y=x3 by applying the definition of derivatives and using Pascale’s triangle to expand powers of a binomial. Receiving a ‘Draw It’ slide, students use their stylus to write on their iPad’s screen.

• Students continue the pattern for differentiating y=x4, y=x5, ………….., y=xn.

• Students fill in the blank:

3) Students in groups practice applying the power rule for differentiating power functions.

4) Students go over the next two slides and solve exercises, including the constant multiple property.

5) Instructor displays on students’ devices sum and difference rule for differentiation.

6) Now students are ready to differentiate a complete polynomial. The instructor displays on students’ devices and example for differentiating a polynomial by applying the rules they have just practiced.

7) Students individually watch an embedded video about finding the derivative of polynomial functions. Then, the students will go online to solve exercises on the Math tutorial website intmath.com.

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