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Topic: Integers 

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 2.Understands the characteristics and properties (e.g., order relations, relative magnitude, base-ten place values) of the set of rational numbers and its subsets (e.g., whole numbers, fractions, decimals, integers)
    Knowledge/skill statements
     1.Understands the concept of "less than" with rational numbers
     2.Understands the concept of "greater than" with rational numbers
     3.Understands the concept of base 10
     4.Understands the concept of rational numbers
     5.Understands the concept of relative magnitude as it relates to rational numbers
     6.Understands the concept of relative magnitude as it relates to integers
   Benchmark 3.Understands the role of positive and negative integers in the number system
    Knowledge/skill statements
     1. Understands the concept of positive integers
     2. Understands the concept of negative integers
  Level IV (Grade 9-12)
   Benchmark 1.Understands the properties (e.g., relative magnitude, density, absolute value) of the real number system, its subsystems (e.g., irrational numbers, natural numbers, integers, rational numbers), and complex numbers (e.g., imaginary numbers, conjugate numbers)
    Knowledge/skill statements
     1.Understands the concept of density as it relates to the real number system
     2.Understands the concept of absolute value
     3.Understands the concept of relative magnitude as it relates to real numbers
     4.Understands the concept of real numbers
     5. Understands the concept of relative magnitude as it relates to irrational numbers
     6. Understands the concept of irrational numbers
     7.Understands the concept of integers
     8.Understands the concept of natural numbers
     9.Understands the concept of complex numbers
     10.Understands the concept of imaginary numbers
     11.Understands the concept of conjugate numbers
     12.Understands the concept of relative magnitude as it relates to complex numbers
 Standard 3.  Uses basic and advanced procedures while performing the processes of computation
  Level III (Grade 6-8)
   Benchmark 1.Adds, subtracts, multiplies, and divides integers, and rational numbers
    Knowledge/skill statements
     1.Adds rational numbers
     2.Subtracts rational numbers
     3.Multiplies rational numbers
     4.Divides rational numbers
     5.Adds integers
     6.Subtracts integers
     7.Multiplies integers
     8.Divides integers
     9.Understands the concept of integer addition
     10.Understands the concept of integer subtraction
     11.Understands the concept of integer multiplication
     12.Understands the concept of integer division