Week 8: Internet Enriched Lesson Plan
The following lesson is an overview of learning activities to be used in a Calculus when curve sketching and graphing derivatives is discussed. The lesson plan includes a variety of online resources and links to help students learn this topic and demonstrate their understanding.
Lesson Title: Graphing Derviatives
Instructor: Marci Smith
Content Area: AP Calculus
Grade Level: 10-12
Lesson Overview: The purpose of this lesson is for students to practice and master the skill of graphing derivative functions. Curve sketching is a topic of calculus that incorporate skills acquired throughout the course and even prerequisite graphing knowledge. The cumulative nature of this subject lends itself well to using internet resources and websites to fully grasp the subject matter.
Objectives:
California State Educational Standards for [Mathematics]
Calculus Standard 9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Relative Advantage: This topic can be very difficult for some students to master because it is such a visual learning activity. By giving students access to internet resources and interactive practice sites, students can spend as much or as little time practicing as they need. Using screencasting technology to exhibit their understanding of the technology is a good way to ensure individual proficiency.
Timeline: Two 80 minute block periods to complete this lesson plan
Materials Needed: ·
Teacher computer, projector and internet access in the classroom;
Student access to computer and internet in school and at home;
Computer with a microphone;
Calculus in a Single Variable, 8th edition, by Larson;
Graphing Calculator;
Learning Activities:
1.) Students will be asked to complete this worksheet as a warm up activity and introduction to curve sketching.
2.) Instructor will teach about how properties of functions, first derivative test and second derivative test can be used to help students sketch the curves of graphs and relate the graphs of f, f’ and f”.
3.) Instructor will reference the Dartmouth Math Website to show students how the slope of the tangent line is used to graph the derivative function.
4.) Instructor will demonstrate several examples of graphing derivative functions.
5.) Students will be asked to practice graphing derivatives using the following websites to sketch the graph of the derivative from the given curve.
a. Calculus Grapher: http://phet.colorado.edu/en/simulation/calculus-grapher
b. USNA Online Calculus Lab: http://www.usna.edu/MathDept/_files/documents/labs/deriv/Deriv.html
c. WIMS Interactive Math Server: http://wims.unice.fr/wims/wims.cgi?session=NXC576D488.2&+lang=en&+module=U1%2Fanalysis%2Fgraphder.en
6.) Students will be asked to practice sketching derivative graphs using these sites, in addition to doing the nightly homework.
7.) After reviewing homework and quizzing themselves by using the websites, students will be asked to create a screencast video using Screencast-O-Matic detailing how to graph a derivative. Students can use one of the practice sites above when recording their simulation or use another site they find. The objective of this task is for students to display their knowledge and mastery of the graphing process.
8.) If necessary, students can use this tutorial to assist them when using screencast-o-matic.com
9.) Instructor will show students this example in class.
10.) Students will need to post their videos to the class website when they are finished for their peers to view.
Additional Resources:
Students will be given these additional resources online to assist them with this difficult topic. These sites provide good tutorials, notes and presentations to help a student struggling with this content.
Spark Notes: http://www.sparknotes.com/math/calcab/applicationsofthederivative/section8.rhtml
Interactive Mathematics: http://www.intmath.com/applications-differentiation/5-curve-sketching-differentiation.php
UC Davis Notes: https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/graphingdirectory/
Assessment Plan:
be available for additional tutoring to review prior concepts that are pivotal to success in the course.
Resources:
Larson, R., Hostetler & Edwards, B. (2006). Calculus of a Single Variable (8th Ed). Cengage Learning.
Instructor: Marci Smith
Content Area: AP Calculus
Grade Level: 10-12
Lesson Overview: The purpose of this lesson is for students to practice and master the skill of graphing derivative functions. Curve sketching is a topic of calculus that incorporate skills acquired throughout the course and even prerequisite graphing knowledge. The cumulative nature of this subject lends itself well to using internet resources and websites to fully grasp the subject matter.
Objectives:
- Students will use the derivative to find intervals of increasing/decreasing and
concavity to find all extrema and points of inflection to sketch the graph of f from f’. - Students will understand and apply the relationships between the graphs of f, f’ and f”.
- Students will demonstrate their knowledge of this subject using screencasting technology and post their
presentation to the class website.
California State Educational Standards for [Mathematics]
Calculus Standard 9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.
Relative Advantage: This topic can be very difficult for some students to master because it is such a visual learning activity. By giving students access to internet resources and interactive practice sites, students can spend as much or as little time practicing as they need. Using screencasting technology to exhibit their understanding of the technology is a good way to ensure individual proficiency.
Timeline: Two 80 minute block periods to complete this lesson plan
Materials Needed: ·
Teacher computer, projector and internet access in the classroom;
Student access to computer and internet in school and at home;
Computer with a microphone;
Calculus in a Single Variable, 8th edition, by Larson;
Graphing Calculator;
Learning Activities:
1.) Students will be asked to complete this worksheet as a warm up activity and introduction to curve sketching.
2.) Instructor will teach about how properties of functions, first derivative test and second derivative test can be used to help students sketch the curves of graphs and relate the graphs of f, f’ and f”.
3.) Instructor will reference the Dartmouth Math Website to show students how the slope of the tangent line is used to graph the derivative function.
4.) Instructor will demonstrate several examples of graphing derivative functions.
5.) Students will be asked to practice graphing derivatives using the following websites to sketch the graph of the derivative from the given curve.
a. Calculus Grapher: http://phet.colorado.edu/en/simulation/calculus-grapher
b. USNA Online Calculus Lab: http://www.usna.edu/MathDept/_files/documents/labs/deriv/Deriv.html
c. WIMS Interactive Math Server: http://wims.unice.fr/wims/wims.cgi?session=NXC576D488.2&+lang=en&+module=U1%2Fanalysis%2Fgraphder.en
6.) Students will be asked to practice sketching derivative graphs using these sites, in addition to doing the nightly homework.
7.) After reviewing homework and quizzing themselves by using the websites, students will be asked to create a screencast video using Screencast-O-Matic detailing how to graph a derivative. Students can use one of the practice sites above when recording their simulation or use another site they find. The objective of this task is for students to display their knowledge and mastery of the graphing process.
8.) If necessary, students can use this tutorial to assist them when using screencast-o-matic.com
9.) Instructor will show students this example in class.
10.) Students will need to post their videos to the class website when they are finished for their peers to view.
Additional Resources:
Students will be given these additional resources online to assist them with this difficult topic. These sites provide good tutorials, notes and presentations to help a student struggling with this content.
Spark Notes: http://www.sparknotes.com/math/calcab/applicationsofthederivative/section8.rhtml
Interactive Mathematics: http://www.intmath.com/applications-differentiation/5-curve-sketching-differentiation.php
UC Davis Notes: https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/graphingdirectory/
Assessment Plan:
- Students will complete the screencast presentation and post their video to the class website.
- Students will be given a rubric for this presentation specifying the necessary components of this
assignment including time limit, difficulty of curves and elements of curve sketching to explain. - Students will be given a Chapter 3 Test and curve sketching will be covered on this assessment.
- Students will take the AP Calculus Exam in May and the derivative graph relationships will be tested.
be available for additional tutoring to review prior concepts that are pivotal to success in the course.
Resources:
Larson, R., Hostetler & Edwards, B. (2006). Calculus of a Single Variable (8th Ed). Cengage Learning.
AECT Standards achieved: 1.2 Message Design, 1.3 Instructional Strategies, 1.4 Learner Characteristics, 2.1 Print Technologies, 2.2 Audiovisual
Technologies, 2.3 Computer-Based Technologies, 2.4 Integrated Technologies, 3.1 Media Utilization, 3.2 Diffusion of Innovations
Technologies, 2.3 Computer-Based Technologies, 2.4 Integrated Technologies, 3.1 Media Utilization, 3.2 Diffusion of Innovations