My Proposal for Major Project:

This fall I will again be teaching Informal Geometry. This class is for the un-motivated student who has struggled with Algebra, but needs another credit in math in order to graduate from high school. These students must be reached in a very different method than that of my "college-bound" math students.

I am proposing a unit for this course on Transformations. The purpose of this unit would be to better prepare the students for Congruence ideas and particularly proofs with congruent triangles.

I would begin with a Power Point presentation (for pizazz!) introducing the basic concepts of transformations, and isometries. I would introduce three types including reflection, translation and rotation. My thoughts are to present these concepts in as many different ways as possible. For each type, we would use hands-on experiences to create the day's isometry.

For example, we would create reflections of images using a MIRA, then create a reflection using graph paper and a ruler. Finally, we would demonstrate that a reflection can be created by tracing the figure after folding on a line of reflection.

The next day would be in the lab using Geometer's Sketchpad to create the given transformation thus reinforcing the concept. This program allows students to draw the pre-image, click the right sequence of buttons, and VOILA! the image of reflection appears. The student can change the colors of these images, add text labels identifying what each represents and print out a copy of their experience.

After learning the 3 types and doing appropriate practice problems for homework. We would combine the types of transformations and explore what new image results. For example, what happens when you reflect an image over 2 intersecting perpendicular lines?

I would spend one day on Transformations that are not Rigid, just to make students aware that the 2 figures will not ALWAYS be congruent. I plan to show dilation via hands-on paper methods and using the Lab.

Finally, a day to review.

Evaluation will be through examination of the results of the unit test. Also, examining the performance of students during the congruence unit to determine if this unit of preparation was worthwhile in helping students comprehend and achieve more.




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