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Topic: Communicating about mathematics 

Mathematics

 Standard 1.  Uses a variety of strategies in the problem-solving process
  Level I (Grade K-2)
   Benchmark 2.Uses discussions with teachers and other students to understand problems
    Knowledge/skill statements
     1.Discusses with peers to understand a numerical problem
   Benchmark 3.Explains to others how she or he went about solving a numerical problem
    Knowledge/skill statements
     1. Communicates the steps of a problem–solving process
  Level II (Grade 3-5)
   Benchmark 6.Understands the basic language of logic in mathematical situations (e.g., "and," "or," "not")
    Knowledge/skill statements
     1.Understands logic operator “and”
     2.Understands logic operator “or”
     3.Understands logic operator “not”
  Level III (Grade 6-8)
   Benchmark 8.Understands the role of written symbols in representing mathematical ideas and the use of precise language in conjunction with the special symbols of mathematics
    Knowledge/skill statements
     1. Understands how written symbols represent mathematical ideas
  Level IV (Grade 9-12)
   Benchmark 5.Uses formal mathematical language and notation to represent ideas, to demonstrate relationships within and among representation systems, and to formulate generalizations
    Knowledge/skill statements
     1.Explains relationships among different representations of problems
     2.Represents word problems using formal notation
 Standard 2.  Understands and applies basic and advanced properties of the concepts of numbers
  Level Pre-K (Grade Pre-K)
   Benchmark 7.Knows the common language for comparing quantity of objects (e.g., "more than," "less than," "same as")
    Knowledge/skill statements
     1.Understands the term "more than" for comparing quantity
     2.Understands the term "less than" for comparing quantity
     3.Understands the term "same as" for comparing quantity
 Standard 3.  Uses basic and advanced procedures while performing the processes of computation
  Level I (Grade K-2)
   Benchmark 3.Understands basic estimation strategies (e.g., using reference sets, using front-end digits) and terms (e.g., "about," "near," "closer to," "between," "a little less than")
    Knowledge/skill statements
     1.Understands the term "about"
     2.Understands the term "near"
     3.Understands the term "closer to"
     4.Understands the term "between"
     5.Understands the term "a little less than"
     6.Understands the concept of reference sets in estimation
     7.Understands the concept of front-end estimation
     8.Understands the concept of estimation as a strategy
  Level II (Grade 3-5)
   Benchmark 9.Knows the language of basic operations (e.g., "products," "multiplication")
    Knowledge/skill statements
     1.Understands the term "addend"
     2.Understands the term "sum"
     3.Understands the term "minuend"
     4.Understands the term "subtrahend"
     5.Understands the term "difference"
     6.Understands the term "product"
     7.Understands the term "divisor"
     8.Understands the term "dividend"
     9.Understands the term "quotient"
 Standard 5.  Understands and applies basic and advanced properties of the concepts of geometry
  Level Pre-K (Grade Pre-K)
   Benchmark 2.Understands the common language used to describe position and location (e.g., "up," "down," "below," "above," "beside," "inside," "outside")
    Knowledge/skill statements
     1.Understands the common language used to describe position
     2.Understands the common language used to describe location
     3.Understands the term "up"
     4.Understands the term "down"
     5.Understands the term "below"
     6.Understands the term "above"
     7.Understands the term "beside"
     8.Understands the term "inside"
     9.Understands the term "outside"
  Level I (Grade K-2)
   Benchmark 2.Understands the common language of spatial sense (e.g., "left," "right," "horizontal," "in front of")
    Knowledge/skill statements
     1.Understands the concept of "left"
     2.Understands the concept of "right"
     3.Understands the concept of "horizontal"
     4.Understands the concept of "in front of"
  Level II (Grade 3-5)
   Benchmark 1.Knows basic geometric language for describing and naming shapes (e.g., trapezoid, parallelogram, cube, sphere)
    Knowledge/skill statements
     1.Understands the concept of a trapezoid
     2.Understands the concept of a parallelogram
     3.Understands the concept of a sphere
     4.Understands the concept of a cube
 Standard 8.  Understands and applies basic and advanced properties of functions and algebra
  Level IV (Grade 9-12)
   Benchmark 1.Understands appropriate terminology and notation used to define functions and their properties (e.g., domain, range, function composition, inverses)
    Knowledge/skill statements
     1.Understands the concept of range as it relates to functions
     2. Understands the notation used to represent functions
     3.Understands the concept of inverse as it relates to functions
     4.Understands the concept of function composition
     5. Understands the concept of domain as it relates to functions