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Topic: Sequences and series 

Mathematics

 Standard 2.  Understands and applies basic and advanced properties of the concepts of numbers
  Level IV (Grade 9-12)
   Benchmark 3.Uses discrete structures (e.g., finite graphs, matrices, sequences) to represent and to solve problems
    Knowledge/skill statements
     1.Determines whether a problem can be modeled by number sequences
     2.Determines whether a problem can be solved by identifying number sequences
     3.Understands the concept of a number sequence
     4.Understands the concept of finite graphs
     5.Determines whether a problem can be modeled by finite graphs
     6.Understands the concept of discrete structures
     7.Determines whether a problem can be solved by using finite graphs
     8.Determines whether a problem can be modeled using matrices
     9.Determines whether a problem can be solved by using matrices
     10.Determines whether a problem can be modeled using discrete structures
     11.Determines whether a problem can be solved by using discrete structures
 Standard 3.  Uses basic and advanced procedures while performing the processes of computation
  Level IV (Grade 9-12)
   Benchmark 6.Uses recurrence relations (i.e., formulas expressing each term as a function of one or more of the previous terms, such as the Fibonacci sequence or the compound interest equation) to model and to solve real-world problems (e.g., home mortgages, annuities)
    Knowledge/skill statements
     1.Understands Fibonacci sequence is a type of recurrence relationship
     2.Determines whether a problem can be modeled by a recurrence relation
     3.Understands the concept of a recurrence equation
     4.Determines whether a problem can be solved by a recurrence relation
 Standard 8.  Understands and applies basic and advanced properties of functions and algebra
  Level III (Grade 6-8)
   Benchmark 11.Understands the properties of arithmetic and geometric sequences (i.e., linear and exponential patterns)
    Knowledge/skill statements
     1. Understands the properties of geometric sequences
     2. Understands the properties of arithmetic sequences
     3. Understands the concept of a linear sequence
     4. Understands the concept of an exponential sequence
  Level IV (Grade 9-12)
   Benchmark 12.Understands formal notation (e.g., sigma notation, factorial representation) and various applications (e.g., compound interest) of sequences and series
    Knowledge/skill statements
     1.Understands the difference between a sequence and a series
     2.Understands the application of series to compound interest
     3.Understands the concept of a sequence
     4.Understands sigma notation
     5.Understands factorial representation of sequences
     6.Understands the concept of a series
     7.Understands the concept of compound interest
     8.Understands factorial representation of a series