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Topic: Expressions 

Mathematics

 Standard 3.  Uses basic and advanced procedures while performing the processes of computation
  Level IV (Grade 9-12)
   Benchmark 1.Adds, subtracts, multiplies, divides, and simplifies rational expressions
    Knowledge/skill statements
     1.Understands the concept of a rational expressions
     2.Adds rational expressions
     3.Subtracts rational expressions
     4.Multiplies rational expressions
     5.Divides rational expressions
     6.Simplifies rational expressions
   Benchmark 2.Adds, subtracts, multiplies, divides, and simplifies radical expressions containing positive rational numbers
    Knowledge/skill statements
     1.Divides radical expressions with positive rational numbers
     2.Adds radical expressions with positive rational numbers
     3.Understands concept of radical expression with positive rational numbers
     4.Subtracts radical expressions with positive rational numbers
     5.Multiplies radical expressions with positive rational numbers
   Benchmark 4.Uses a variety of operations (e.g., finding a reciprocal, raising to a power, taking a root, taking a logarithm) on expressions containing real numbers
    Knowledge/skill statements
     1.Understands the concept of raising real numbers to powers
     2.Determines the logarithms of real numbers
     3.Understands the concept of logarithm of real number
     4.Computes the reciprocals of real numbers
     5.Understands the concept of the reciprocal of a real numbers
     6.Takes the roots of real numbers
     7.Raises real numbers to powers
     8.Understand the concept of taking roots of real numbers
 Standard 8.  Understands and applies basic and advanced properties of functions and algebra
  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 3.Understands various representations (e.g., tables, graphs, verbal descriptions, algebraic expressions, Venn diagram) of patterns and functions and the relationships among them
    Knowledge/skill statements
     1. Understands how algebraic expressions can represent functions
     2. Represents functions using algebraic expressions
     3.Understands how verbal descriptions can represent functions
     4.Represents functions using tables
     5.Understands how tables can represent functions
     6.Understands how graphs can represent functions
     7.Represents functions using graphs
     8.Represents functions using verbal descriptions
     9.Understands the concept of a Venn diagram
     10.Represents patterns using Venn diagrams
     11.Understands how Venn diagrams can represent patterns
     12.Understands how algebraic expressions can represent patterns
     13.Represents patterns using algebraic expressions
     14.Understands how verbal descriptions can represent patterns
     15.Represents patterns using tables
     16.Understands how tables can represent patterns
     17.Understands how graphs can represent patterns
     18. Represents patterns using graphs
     19.Represents patterns using verbal descriptions
     20. Understands the relationship between tables and graphs
     21.Understands the relationship between tables and verbal descriptions
     22.Understands the relationship between tables and algebraic expressions
     23.Understands the relationship between tables and Venn diagrams
     24.Understands the relationship between graphs and verbal descriptions
     25.Understands the relationship between graphs and algebraic expressions
     26.Understands the relationship between graphs and Venn diagrams
     27.Understands the relationship between verbal descriptions and algebraic expressions
     28.Understands the relationship between verbal descriptions and Venn diagrams
   Benchmark 8.Understands basic operations (e.g., combining like terms, expanding, substituting for unknowns) on algebraic expressions
    Knowledge/skill statements
     1.Combines like terms of an algebraic expression
     2.Understands combining like terms of an algebraic expression
     3.Expands algebraic expressions
     4.Understands substituting for unknowns in an algebraic expression
     5. Understands expanding algebraic expressions
     6.Substitutes for unknowns in an algebraic expression
     7.Understands operations on algebraic expressions
  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 14.Understands the meaning of and writes equivalent forms of expressions, equations, inequalities, and relations, including all of their parts(e.g., terms, factors, coefficients).
    Knowledge/skill statements
     1.Understands the meaning of expressions.
     2.Understands the meaning of equations.
     3.Understands the meaning of inequalities.
     4.Understands the meaning of relations.
     5.Writes expressions in equivalent forms.
     6.Writes equations in equivalent forms.
     7.Writes inequalities in equivalent forms.
     8.Writes relations in equivalent forms.
     9.Understands the meanings of terms of an equation.
     10.Understands the meanings of terms of an expression.
     11.Understands the meanings of terms of an inequality.
     12.Understands the meanings of terms of a relation.
     13.Understands the meanings of factors of an equation.
     14.Understands the meanings of factors of an expression.
     15.Understands the meanings of factors of an inequality.
     16.Understands the meanings of factors of a relation.
     17.Understands the meanings of coefficient of an equation.
     18.Understands the meanings of coefficient of an expression.
     19.Understands the meanings of coefficient of an inequality.
     20.Understands the meanings of coefficient of a relation.