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 |