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Topic: Exponents/logarithms/roots 

Mathematics

 Standard 2.  Understands and applies basic and advanced properties of the concepts of numbers
  Level III (Grade 6-8)
   Benchmark 1.Understands the relationships among equivalent number representations (e.g., whole numbers, positive and negative integers, fractions, ratios, decimals, percents, scientific notation, exponentials) and the advantages and disadvantages of each type of representation
    Knowledge/skill statements
     1.Understands the equivalence of decimals and percents
     2.Understands the equivalence of whole numbers and fractions
     3.Understands the equivalence of fractions and ratios
     4.Understands the equivalence of whole numbers and ratios
     5.Understands the equivalence of whole numbers and decimals
     6.Understands the equivalence of whole numbers and percents
     7.Understands the equivalence of whole numbers and scientific notation
     8.Understands the equivalence of integers and fractions
     9.Understands the equivalence of integers and ratios
     10.Understands the equivalence of integers and decimals
     11.Understands the equivalence of integers and percents
     12.Understands the equivalence of integers and scientific notation
     13.Understands the equivalence of integers and exponents
     14.Understands the equivalence of fractions and decimals
     15.Understands the equivalence of ratios and decimals
     16.Understands the equivalence of ratios and percents
     17.Understands the equivalence of decimals and scientific notation
     18.Understands the equivalence of decimals and exponents
     19.Understands the equivalence of scientific notation and exponents
     20.Understands the advantages and disadvantages of different number representations
   Benchmark 5.Understands the characteristics and uses of exponents and scientific notation
    Knowledge/skill statements
     1. Understands the concept of exponents
     2. Understands the concept of scientific notation
  Level IV (Grade 9-12)
   Benchmark 2.Understands the properties and basic theorems of roots, exponents (e.g., [bm][bn] = bm+n), and logarithms
    Knowledge/skill statements
     1.Understands the concept of a theorem
     2.Understands theorems of exponents
     3.Understands basic theorems of roots
     4.Understands basic theorems of logarithms
  Level V (Grade (College Readiness))
   Benchmark 1.Understands the properties of rational exponents
    Knowledge/skill statements
     1.Understands the concept of rational exponents
 Standard 3.  Uses basic and advanced procedures while performing the processes of computation
  Level III (Grade 6-8)
   Benchmark 3.Understands exponentiation of rational numbers and root-extraction (e.g., squares and square roots, cubes and cube roots)
    Knowledge/skill statements
     1.Understands the concept of square roots
     2.Understands the concept of roots
     3.Understands the concept of cubes
     4.Understands the concept of squares
     5.Understands the concept of cube roots
  Level IV (Grade 9-12)
   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 IV (Grade 9-12)
   Benchmark 5. Solves polynomial equations (e.g., find the real or complex roots of a quadratic equation) using a variety of methods (e.g., symbolically, graphically, numerically).
    Knowledge/skill statements
     1.Understands the concept of polynomials
     2.Understands the concept of roots
     3.Solves polynomial equations symbolically.
     4.Models real world problems using polynomial equations without the use of technology.
     5.Solves real world problems using polynomial equations with the use of technology.
     6.Solves polynomial equations by finding the real roots of a quadratic equation.
     7.Solves polynomial equations by finding the complex roots of a quadratic equation.