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OBJECTIVE - G.CO.A.4

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular line, parallel lines, and line segment.

INTERPRETATION OF OBJECTIVE - G.CO.A.4

This objective and the next one are the two BIGGEST OBJECTIVES OF THE UNIT!!! So slowdown and soak it all in.  The understanding of the isometric transformations is foundational to many topics that follow. This objective calls for the definition of each of these transformations and the identifying of their properties relating to angles, parallel, perpendicular, circles, etc... Within these properties we also need to discuss the distance and orientation between pre-image and image.

SKILLS

(1) The student will know the definitions of the isometric transformations (reflect, rotate, & translate).

(2) The student will be able to describe rotations, reflections and translations.

(3) The student will be able to determine and apply the properties of the isometric transformations.

(4) The student will be able to identify which transformation has taken place based on the properties found between the pre-image and image.

(5) The student will be able to identify the orientation relationship between the pre-image and image.

THE BIG IDEA

Transformations and their properties will unlock many geometric relationships to come. These transformations will help us find relationships in parallel lines and a transversal, in triangles, in quadrilaterals, in regular polygons and eventually in circles. As stated on the introductory webpage to this website - THE SPINE OF THE CORE IS TRANSFORMATIONS. These transformations will be used to connect many concepts and reveal many new relationships. The two biggest geometric relationships, Congruence and Similarity, come directly from transformations.

TRAPS & PITFALLS

The only trap I see here is moving too quickly and not allowing time to use the definitions to determine other properties found within the transformations. Having done the course now, I realize that these definitions play a big part of expressing how we know something in later proofs. A good grounding here will help us later.

PAST CONNECTIONS

Students will connect their informal understandings from early grades about flip (reflect), turn (rotate), and slide (translate) to the more formal presentation of transformations here. They will also connect the symmetry relationships of line symmetry (reflections) and rotate symmetry (rotations) to the more formal definitions.

FUTURE CONNECTIONS

Everything!! This is not an overstatement - so much hinges on these foundational concepts.

MY REFLECTIONS (over line l)

My general feeling is that I did a pretty good job of this area. I knew of its importance and so I gave it the time needed to establish a good foundation. We discussed orientation, distance and which points if any are not affected by the transformation. We looked at examples and determined what transformation produced them based on the properties found in the diagram.

What I didn't do well was breakdown more specifically the properties found in the relationship of pre-image and image such as after a translation all segments of the pre-image are parallel with their corresponding segments of the image or that a rotation of 180 degrees place all points on their opposite ray and equal distance thus also preserving a parallel relationships between corresponding parts. Emphasizing the resultant relationships of the transformation is critical to explaining those things later in a proof.