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Topic: Variables 

Mathematics

 Standard 6.  Understands and applies basic and advanced concepts of statistics and data analysis
  Level IV (Grade 9-12)
   Benchmark 3.Understands the concept of correlation (e.g., the difference between a "true" correlation and a "believable" correlation; when two variables are correlated)
    Knowledge/skill statements
     1.Understands the relationship between causality and correlation
     2.Understands the concept of spurious correlation
     3. Understands the concept of correlation
 Standard 8.  Understands and applies basic and advanced properties of functions and algebra
  Level II (Grade 3-5)
   Benchmark 3.Knows that a variable is a letter or symbol that stands for one or more numbers
    Knowledge/skill statements
     1.Understands that a letter or symbol can stand for one or more numbers
  Level III (Grade 6-8)
   Benchmark 1.Knows that an expression is a mathematical statement using numbers and symbols to represent relationships and real-world situations (e.g., equations and inequalities with or without variables)
    Knowledge/skill statements
     1.Understands the concept of a mathematical expression
     2.Understands the role of numbers in math expressions
     3.Understands the role of variables in math expressions
     4.Understands the concept of an inequality
     5.Understands the role of symbols in math expressions
   Benchmark 2.Understands that a variable can be used in many ways (e.g., as a placeholder for a specific unknown, such as x + 8 = 13; as a representative of a range of values, such as 4t + 7)
    Knowledge/skill statements
     1.Understands that variables can be used in many ways
     2.Understands variables can be placeholders for specific values
     3.Understands variables can represent ranges of values
   Benchmark 4.Understands the basic concept of a function (i.e., functions describe how changes in one quantity or variable result in changes in another)
    Knowledge/skill statements
     1.Understands the concept of a function
  Level IV (Grade 9-12)
   Benchmark 2.Uses expressions, equations, inequalities, and matrices to represent situations that involve variable quantities and translates among these representations
    Knowledge/skill statements
     1.Understands the relationship between inequalities and equations
     2.Transforms inequalities to equations
     3.Understands the relationship between equations and matrices
     4.Represents equations in matrix form
     5.Understands the relationship between expressions and equations
     6.Understands the relationship between expressions and inequalities
     7.Understands the relationship between expressions and matrices
     8.Understands the relationship between inequalities and matrices
     9.Understands the concept of an algebraic expressions
   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