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I met with the other Pre-Calculus teachers yesterday for a planning meeting. A decision was made to assign a Pre-Calculus project to the students as an end of the year project. We also felt that the students really don't know the unit circle and would like to incorporate the unit circle in the project. I could use some help with ideas for this project. Can anyone suggest some?

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Comment by Kevin Hurley on April 6, 2010 at 12:43am
One thing our teachers and students have had great success with is to have the students create art using graphs of equations. This is a great way to reinforce the concept of transformation of functions - i.e. - a logarithmic graph can be shifted and stretched the same way a trigonometric one can, and the students are really motivated to produce nice drawings, and so they become very curious as to how they can model the various curves their art project will contain.

Here is the most recent version of the project I have given (please note that we had only studied polynomial, exponential and logarithmic functions at the point that I gave this). It could be easily modified to include the trig functions, rational functions, and "non-function" relations like the conic sections. You can also see my notes based on how I thought it went at the top.

An emphasis is placed on the use of a variety of functions, as well as restricting the domain and range of each relation (a nice byproduct of the project is strengthening their understanding of domain and range) to make the picture come out nice.

I would also recommend Win-Plot to aid the students in constructing their diagrams (if you are in a Windows environment that is). You can find it here.
Comment by Dylan Faullin on April 6, 2010 at 3:42am
What about the unit circle do you want your students to know? I have a project that I give my College Algebra students which involves using the unit circle to find the roots of unity of various degrees (for example, finding all the cube roots of 1, of which there are 3 or finding the sixth roots of 1, of which there are 6).

This project reinforces the concept that the number of roots to a polynomial equation is equal to the degree of the polynomial AND it gets the students working with the imaginary number AND trig functions (in the form of polar coordinates).

This is probably not very well written, as I tend to over-explain things. There may even be a typo or two. I've uploaded here for you to take a look at (see link below). Let me know if you have any questions.

colalgproject2.pdf
Comment by Myra Deister on April 6, 2010 at 11:05am
I have done a project before with conic sections where the students created a picture. Several years ago the students had to program their graphicing calculators to reproduce their pictures. The last time I assigned the project I was able to take the students into the computer lab and we used Geometer's Sketchpad. I had considered doing a similar project with the pre-Calculus students.
Thank you for your suggestions. We will be meeting again on Wednesday, so I will present both at our meeting.
Comment by Danny Clarke on November 6, 2010 at 8:00pm
Kevin, I read your post with interest. I had a similar idea (http://mathematics24x7.ning.com/forum/topics/form-following-functio...) and Colin gave me a link to your post. I plan to use my favorite tool, GeoGebra, for the project. I really like your form and grading scheme for your project and hope you don't mind if I copy it for mine. Including exponential and logarithmic functions makes sense and should make the project more interesting.

Form literally does follow function :-)

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