Tangent Lines and Derivatives
Geometer's Sketchpad - Instantaneous Rate
This activity by Scott Steketee is designed into introduce students to instantaneous rates of change and the definition of a derivative. Students manipulate a pre-made sketch to see what happens to the rate of change as one point moves closer and closer to the second point.
Click on the image above to find the sketch and activity files.
Click on the image above to find the sketch and activity files.
geometers_sketchpad_instantaneous_rate_activity_review.docx | |
File Size: | 17 kb |
File Type: | docx |
Fathom - Rates of Change
This sample Fathom activity uses the derivative relationship between velocity and acceleration to help students explore the relationship between average and instantaneous rates of change. The program creates sample data that is graphed on scatter plots for students to make comparisons between the rates of change.
Click the image above to go to the Fathom Website.
Click the image above to go to the Fathom Website.
fathom_rates_of_change_activity_review.docx | |
File Size: | 17 kb |
File Type: | docx |
Secant and Tangent Lines Demo
This demo illustrates the relationship between secant lines and tangent lines. Students can adjust the point of tangency and the distance between the two points creating the secant line.
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Secant and Tangent Lines from the Wolfram Demonstrations Project by Joshua Fritz, Angela Sharp, |
secant_and_tangent_lines_online_activity_review.docx | |
File Size: | 17 kb |
File Type: | docx |
Calculus Grapher
PhET's applet allows students to play with drawing functions and seeing the resulting derivatives (or integrals). Students can explore what effect tilting the graph or shifting the graph vertically has on the derivative. The website also provides activities to accompany the applet written by other teachers.
Click on the image above to go to the Calculus Grapher page on the PhET website.
Click on the image above to go to the Calculus Grapher page on the PhET website.
calculus_grapher_online_activity_review.docx | |
File Size: | 18 kb |
File Type: | docx |
Moving Man - Position, Velocity, Acceleration and Derivatives
The Moving Man applet is really intended for physics classes, but the charts tab also works to see the relationship between a function and its first and second derivatives. It provides real world and cross-curriculum connections to the study of motion. Students can compare the types of functions (parabolic, linear, constant) to develop an understanding of relationships between derivatives.
Click on the image above to go to the Moving Man page on the PhET website.
Click on the image above to go to the Moving Man page on the PhET website.
moving_man_online_activity_review.docx | |
File Size: | 17 kb |
File Type: | docx |
Differentiation Using the Chain Rule
Duane Kouba's UC Davis website provides a brief description of the chain rule, and then 21 practice problems of various difficulty. Students can check their work (or peek if they get stuck) against the detailed solution provided for each problem.
Click on the image above to go to the website.
Click on the image above to go to the website.
chain_rule_website_online_activity_review.docx | |
File Size: | 17 kb |
File Type: | docx |