Monday, 2/22/16: Coordinate Relationships / Reflection Art

We are beginning Unit 4, which is on using transformations to establish congruence, using transformations to establish similarity, the Pythagorean theorem, angle relationships in parallel lines and triangles, and the volume of cylinders, cones, and spheres.

We're starting with transformations, of which there are four types:

• translations (slides)
• reflections (flips)
• rotations
• dilations (zooming in or out)

Students, parents / guardians, and tutors, as we move forward, there are going to be two key tools that will help students with transformations (in addition to the normal internet and textbook resources):
First, I've given each student a section of tracing paper (to be kept in the plastic sleeve with the class assignment sheet and used for the entire unit).  For many students this will be of significant help, using the tracing paper to mimic the motion.  Second, look for patterns in the ordered pairs (x and y combinations) pre-image (the before) to image (the after).  From the very beginning, I am going to be making my students record all of the ordered pairs, before-and-after.  The patterns they will discover there will really help them.

We have been reviewing the Lesson 9-1 homework (three simple translations), analyzing the coordinates pre-image to image.  We are also in the midst of a reflection art project.  Last Thursday when I was out at a meeting, I had students create artwork on a coordinate grid, which we are going to reflect across the x-axis.  (Later we are also going to do a rotation with the same art.).  Students are recording coordinates pre-image to image in this reflection of their art, and thus are discovering the important pattern associated with the reflection.  I would rather have my students do art work presently (as opposed to working solely out of the textbook), because this is how transformational geometry is used in the real world, by computer animators.  Tomorrow night for homework (Tuesday) students will be completing this project, but for tonight, no formal homework is assigned.  However, students can be studying Lessons 9-1 and 9-2, either from the textbook pages they have or online at my.hrw.com .