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Topic: Permutations/combinations 

Mathematics

 Standard 3.  Uses basic and advanced procedures while performing the processes of computation
  Level IV (Grade 9-12)
   Benchmark 7.Understands counting procedures and reasoning (e.g., use of the counting principles to find the number of ways of arranging objects in a set, the use of permutations and combinations to solve counting problems)
    Knowledge/skill statements
     1.Understands the concept of combinations
     2.Determines combinations
     3.Understands the concept of permutations
     4.Determines permutations
     5.Understands the concept of counting principles
     6.Uses counting principles to find ways of arranging items
 Standard 7.  Understands and applies basic and advanced concepts of probability
  Level III (Grade 6-8)
   Benchmark 1.Determines probability using mathematical/theoretical models (e.g., table or tree diagram, area model, list, sample space)
    Knowledge/skill statements
     1. Uses tables to determine probability
     2. Uses tree diagrams to determine probability
     3. Understands the concept of tree diagrams
     4. Uses sample spaces to determine probability
     5.Understands the concept of area models
     7.Understands the concept of modeling probability
     8.Uses area models to determine probability
     9.Uses lists to determine probability
  Level IV (Grade 9-12)
   Benchmark 3.Uses experimental and simulation methods (e.g., Monte Carlo simulations, statistical experiments, counting techniques) to determine probabilities
    Knowledge/skill statements
     1.Understands concept of Monte Carlo simulations
     2.Uses formulas to determine permutations
     3.Carries out a statistical experiment
     4.Uses Monte Carlo simulation to determine probability
     5.Understands the concept of a statistical experiment
     6.Uses formulas to determine combinations
     7.Uses counting principles to determine probability
     8.Uses permutations to determine probability
     9.Uses combinations to determine probability
   Benchmark 4.Understands the differences among experimental, simulation, and theoretical probability techniques and the advantages and disadvantages of each
    Knowledge/skill statements
     1.Understands the concept of experimental probability techniques
     2.Understands the concept of simulation probability techniques
     3.Understands the concept of theoretical probability techniques
     4.Understands the difference between experimental and simulation probability techniques
     5.Understands the difference between experimental and theoretical probability techniques
     6.Understands the difference between simulation and theoretical probability techniques
     7.Knows the advantages of experimental probability techniques
     8.Knows the advantages of simulation probability techniques
     9.Knows the advantages of theoretical probability techniques
     10.Knows the disadvantages of experimental probability techniques
     11.Knows the disadvantages of simulation probability techniques
     12.Knows the disadvantages of theoretical probability techniques