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Topic: Motion Geometry/Transformations 

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
  Level IV (Grade 9-12)
   Benchmark 3.Uses synthetic (i.e., pictorial) representations and analytic (i.e., coordinate) methods to solve problems involving symmetry and transformations of figures (e.g., problems involving distance, midpoint, and slope; determination of symmetry with respect to a point or line)
    Knowledge/skill statements
     1.Uses synthetic geometric models to solve slope problems
     2.Uses synthetic geometric models to solve line symmetry problems
     3.Uses synthetic geometric models to solve point symmetry problems
     4.Uses synthetic geometric models to solve distance problems
     5.Uses synthetic geometric models to solve midpoint problems
     6.Understands the concept of a synthetic model (i.e., a pictorial representation)
     7.Uses analytic methods to solve slope problems
     8.Uses analytic methods to solve line symmetry problems
     9.Uses analytic methods to solve point symmetry problems
     10.Uses analytic methods to solve distance problems
     11.Uses analytic methods to solve midpoint problems
 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
     1.Understands functions as fixed relationships between elements of two sets
     2. Understands that in the real world, functions relate inputs to outputs
     3.Understands that in geometry, functions relate points to images in motion (e.g., flips, slides, turns)
     4.Understands that in algebra, functions represent relationships between variables