Topic: Likelihood/chance/certainty |
Mathematics |
| Standard 7. Understands and applies basic and advanced concepts of probability |
| | Level I (Grade K-2) |
| | | Benchmark 1. | Understands that some events are more likely to happen than others |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the basic concept of chance |
| | | | | 2. | Understands that some events are more likely to happen than others |
| | Level II (Grade 3-5) |
| | | Benchmark 1. | Understands that the word "chance" refers to the likelihood of an event |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of "chance" |
| | | Benchmark 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") |
| | | | Knowledge/skill statements |
| | | | | 1. | Identifies events that are sure to happen |
| | | | | 2. | Identifies events that may or may not happen |
| | | | | 3. | Identifies events that are sure not to happen |
| | | | | 4. | Understands the term "certain" |
| | | | | 5. | Understands the term "uncertain" |
| | | | | 6. | Understands the term "likely" |
| | | | | 7. | Understands the term "unlikely" |
| | 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 |
| | | Benchmark 2. | Determines probability using simulations or experiments |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of a simulation |
| | | | | 2. | Understands the concept of an experiment |
| | | | | 3. | Uses simulations to determine probability |
| | | | | 4. | Uses experiments to determine probability |
| | | Benchmark 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) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that the certainty of conclusion(s) depend upon many factors |
| | | | | 2. | Understands that the certainty of conclusion(s) depends upon the currency of data |
| | | | | 3. | Understands that the certainty of conclusion(s) depend upon what is known about a situation |
| | | | | 4. | Understands that the certainty of conclusion(s) depend upon the amount of data |
| | | Benchmark 5. | Understands the relationship between the numerical expression of a probability (e.g., fraction, percentage, odds) and the events that produce these numbers |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of percents representing probability |
| | | | | 2. | Understands the concept of fractions representing probability |
| | | | | 3. | Understands the concept of odds |
| | | | | 4. | Understands the relationship between odds and probability |
| | | | | 5. | Understands the concept of decimals representing probability |
| | Level IV (Grade 9-12) |
| | | Benchmark 1. | Knows that a random variable can be represented by a discrete or continuous probability distribution |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands concept of a random variable |
| | | | | 2. | Knows that a random variable can be represented by a discrete probability distribution |
| | | | | 3. | Knows that a random variable can be represented by a continuous probability distribution |
| | | Benchmark 2. | Understands the concepts of independent and dependent events and how they are related to compound events and conditional probability |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the relationship between compound events and dependent events |
| | | | | 2. | Understands the concept of compound events |
| | | | | 3. | Understands the concept of independent events |
| | | | | 4. | Understands the concept of dependent events |
| | | | | 5. | Understands the concept of conditional probability |
| | | | | 6. | Understands the relationship between compound events and independent events |
| | | | | 7. | Understands the relationship between dependent events and conditional probability |
| | | | | 8. | Understands the relationship between independent events and conditional probability |
| | | 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 |
| | Level V (Grade (College Readiness)) |
| | | Benchmark 1. | Calculates the probability for dependent, independent, and conditional events |
| | | | Knowledge/skill statements |
| | | | | 1. | Calculates the probability of dependent events |
| | | | | 2. | Calculates the probability of independent events |
| | | | | 3. | Calculates the probability of conditional events |
| | | Benchmark 2. | Understands the relationship between the probability of an event and the probability of its complement |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of a complementary event |
| | | | | 2. | Understands the concept of determining the probability of an event |
| | | Benchmark 3. | Uses Venn diagrams in probability situations |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of a Venn diagram |
| | | | | 2. | Knows that Venn diagrams can be used to show relationships in probability situations |