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 |