# Mathematics |

**Standard 7.** | Understands and applies basic and advanced concepts of probability |

| ** Level Pre-K (Grade Pre-K)** |

| 1. | Not appropriate at this level |

| ** Level I (Grade K-2)** |

| 1. | Understands that some events are more likely to happen than others |

| 2. | Understands that some events can be predicted fairly well but others cannot because we do not always know everything that may affect an event |

| ** Level II (Grade 3-5)** |

| 1. | Understands that the word "chance" refers to the likelihood of an event A |

| 2. | Recognizes events that are sure to happen, events that are sure not to happen, and events that may or may not happen (e.g., in terms of "certain," "uncertain," "likely," "unlikely") |

| 3. | Understands that when predictions are based on what is known about the past, one must assume that conditions stay the same from the past event to the predicted future event |

| 4. | Understands that statistical predictions are better for describing what proportion of a group will experience something (e.g., what proportion of automobiles will be involved in accidents) rather than which individuals within the group will experience something, and how often events will occur (e.g., how many sunny days will occur over a year) rather than exactly when they will occur |

| 5. | Uses basic sample spaces (i.e., the set of all possible outcomes) to describe and predict events A |

| ** Level III (Grade 6-8)** |

| 1. | Determines probability using mathematical/theoretical models (e.g., table or tree diagram, area model, list, sample space) A |

| 2. | Determines probability using simulations or experiments |

| 3. | Understands how predictions are based on data and probabilities (e.g., the difference between predictions based on theoretical probability and experimental probability) |

| 4. | Understands that the measure of certainty in a given situation depends on a number of factors (e.g., amount of data collected, what is known about the situation, how current data are) |

| 5. | Understands the relationship between the numerical expression of a probability (e.g., fraction, percentage, odds) and the events that produce these numbers A |

| ** Level IV (Grade 9-12)** |

| 1. | Knows that a random variable can be represented by a discrete or continuous probability distribution |

| 2. | Understands the concepts of independent and dependent events and how they are related to compound events and conditional probability |

| 3. | Uses experimental and simulation methods (e.g., Monte Carlo simulations, statistical experiments, counting techniques) to determine probabilities |

| 4. | Understands the differences among experimental, simulation, and theoretical probability techniques and the advantages and disadvantages of each |

| 5. | Understands the properties of the normal curve (i.e., the graph used to approximate the distribution of data for many real-world phenomena) and how the normal curve can be used to answer questions about sets of data |

| ** Level V (Grade (College Readiness))** |

| 1. | Calculates the probability for dependent, independent, and conditional events |

| 2. | Understands the relationship between the probability of an event and the probability of its complement |

| 3. | Uses Venn diagrams in probability situations |

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A = Assessment items available |