(Suitable for CAS extension)
This activity involves a curve "with history"; an excellent example of combining geometry and algebra. This function, the so-called "Witch of Agnesi" is defined by a geometric description. After implementing the construction, students are then challenged to find the equation of the constructed curve. This equation, in turn, allows further investigations and generalisations, including some from the field of analysis - an alternative to conventional curve sketching.
The first and second parts of the task are suitable for students of secondary school age with knowledge of the theorems of intersecting lines and the laws of similarity, as well as the Pythagorean theorem. Methods of differential calculus are required only for the final task.
http://compasstech.com.au/TNSINTRO/TI-NspireCD/Exemplary_Activities_PDF/Act10_WitchofAgnesi.pdf
Path Finder
Different topic posts on the site:
-Lesson
-Practice
-TI-NSPIRE
Click on the link/label of those names to see all the posts that are filed under that category.
Lessons are reviews of notes from the textbook.
Practice questions are extra material for students to use.
Lots of space is left between the question and answer to give students the opportunity to explore the question before jumping to the result.
TI-NSPIRE activities are fun problems to enhance the learning of graphing.
Links are given as lesson plans.
-Lesson
-Practice
-TI-NSPIRE
Click on the link/label of those names to see all the posts that are filed under that category.
Lessons are reviews of notes from the textbook.
Practice questions are extra material for students to use.
Lots of space is left between the question and answer to give students the opportunity to explore the question before jumping to the result.
TI-NSPIRE activities are fun problems to enhance the learning of graphing.
Links are given as lesson plans.
Tuesday, December 1, 2009
Activity 10: The Witch of Agnesi
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