Calculus One with iPads

Overview: In this lesson, students will use their prior knowledge of functions and the properties of graphs in order to graph the slope of a given function (the derivative function)

 

Subject: Calculus One

Grade-level: Grade 12

 

Purpose: This lesson will enable students to graph the slope of a given 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 read graphs of functions.

• know how to sketch the graph of a given function by using the x-intercepts and the intervals

• where a function is monotone (increasing or decreasing)..

 

Learning Outcomes:

By the end of this lesson, students will:

1. Determine intervals where the slope of a function is positive, negative, and zero using graphical representations of a function.

2. be able to graph and interpret the slope of a function.

3. be able to write down the derivative function for some remarkable functions.

4. have their knowledge of differentiation techniques enriched 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. 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 activities

 

Students will have access to the Nearpod lesson using their mobile devices and a PIN (GDILN) provided by the teacher.

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So far students have practised graphing 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.

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1) Students will warm up their knowledge by analyzing a piecewise rectilinear graph and recognizing the corresponding graph of the slope function. The teacher leads group discussion and monitors students’ progress from his device.

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2) Students will engage in a ‘Draw It’ activity to plot the graph of the derivative function:

• Students identify the remarkable points of the graph (local maxima, minima, and turning points)

• Students locate the intervals where the function is increasing or decreasing

• Students then can sketch on their iPads, using ‘stylus pens’ the slope function after locating the x-intercepts and the intervals where the slope is positive or negative.

• Make connections between the graphs of f(x) and f'(x).

3) After the two activities, the instructor pushes to the students’ devices the next slide where they engage in groups in an online activity about graphs of functions.

4) Students will watch an embedded You Tube tutorial video from Khan Academy about graphing the derivative function given the graph of the function.

5) The students receive a ‘Draw It’ activity where they sketch on the screen of their iPads the slope function of sinx and cosx.and

6) Students individually watch an embedded video about finding the derivative function by applying the definition of derivative. Then, the students will go online to solve exercises on the Math tutorial website intmath.com.

7) Students will answer questions of a quiz, while the instructor can assess students’ understanding by reading their progress in an analysis table on his iPad. Students’ results will be saved for comparison and analysis.

8) 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) Students regroup to share their expertise with students from other groups. They work together to conjecture what the graphical connections are between a function and its derivative.

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

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