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Topic: Motion Geometry/Transformations 

Common Core Mathematics 9-12

 Cluster  Experiment with transformations in the plane
  Grade 9-12
   G.CO.2.Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
   G.CO.3.Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
   G.CO.4.Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
   G.CO.5.Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
 Cluster  Understand congruence in terms of rigid motions
  Grade 9-12
   G.CO.6.Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

Mathematics

 Standard 5.  Understands and applies basic and advanced properties of the concepts of geometry
  Level Pre-K (Grade Pre-K)
   Benchmark 4.Understands that a shape’s orientation in space can change
    Knowledge/skill statements
     1.Understands the basic concept of orientation in space
     2.Understands that even though a shape’s orientation changes, the shape itself does not change
  Level II (Grade 3-5)
   Benchmark 5.Uses motion geometry (e.g., turns, flips, slides) to understand geometric relationships
    Knowledge/skill statements
     1.Understands the concept of motion geometry
     2.Understands the concept of slides
     3.Understands the concept of turns
     4.Understands the concept of flips
  Level III (Grade 6-8)
   Benchmark 4.Understands geometric transformations of figures (e.g., rotations, translations, dilations)
    Knowledge/skill statements
     1. Understands the concept of rotations
     2.Understands the concept of transformation
     3.Understands the concept of translation
     4.Understands the concept of dilations
 Standard 8.  Understands and applies basic and advanced properties of functions and algebra
  Level IV (Grade 9-12)
   Benchmark 6.Understands the concept of a function as the correspondences between the elements of two sets (e.g., in algebra, functions are relationships between variables that represent numbers; in geometry, functions relate sets of points to their images under motions such as flips, slides, and turns; in the "real-world," functions are mathematical representations of many input-output situations)
    Knowledge/skill statements
     3.Understands that in geometry, functions relate points to images in motion (e.g., flips, slides, turns)