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Following benchmarks were found| Mathematics |
| | | Standard 1. Uses a variety of strategies in the problem-solving process
| | | | | Level III [Grade: 6-8] |
| | | | | 5. | Represents problem situations in and translates among oral, written, concrete, pictorial, and graphical forms |
| | | | Level IV [Grade: 9-12] |
| | | | | 7. | Understands connections between equivalent representations and corresponding procedures of the same problem situation or mathematical concept (e.g., a zero of a function corresponds to an x-intercept of the graph of the function, the correspondence of binary multiplication to a series electrical circuit and the logical operation "and") |
| | | Standard 2. Understands and applies basic and advanced properties of the concepts of numbers
| | | | | Level IV [Grade: 9-12] |
| | | | | 3. | Uses discrete structures (e.g., finite graphs, matrices, sequences) to represent and to solve problems |
| | | Standard 6. Understands and applies basic and advanced concepts of statistics and data analysis
| | | | | Level Pre-K [Grade: Pre-K] |
| | | | | 1. | Knows that concrete and pictorial graphs represent information |
| | | | Level I [Grade: K-2] |
| | | | | 1. | Collects and represents information about objects or events in simple graphs |
| | | | Level II [Grade: 3-5] |
| | | | | 4. | Organizes and displays data in simple bar graphs, pie charts, and line graphs |
| | | | | 5. | Reads and interprets simple bar graphs, pie charts, and line graphs |
| | | | Level III [Grade: 6-8] |
| | | | | 6. | Organizes and displays data using tables, graphs (e.g., line, circle, bar), frequency distributions, and plots (e.g., stem-and-leaf, box-and-whiskers, scatter) |
| | | | | 8. | Understands that the same set of data can be represented using a variety of tables, graphs, and symbols and that different modes of representation often convey different messages (e.g., variation in scale can alter a visual message) |
| | | | Level IV [Grade: 9-12] |
| | | | | 1. | Selects and uses the best method of representing and describing a set of data (e.g., scatter plot, line graph, two-way table) |
| | | | Level V [Grade: 13] |
| | | | | 3. | Identifies patterns in graphical displays of data |
| | | Standard 7. Understands and applies basic and advanced concepts of probability
| | | | | Level IV [Grade: 9-12] |
| | | | | 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 |
| | | Standard 8. Understands and applies basic and advanced properties of functions and algebra
| | | | | Level III [Grade: 6-8] |
| | | | | 3. | Understands various representations (e.g., tables, graphs, verbal descriptions, algebraic expressions, Venn diagram) of patterns and functions and the relationships among them |
| | | | | 5. | Solves linear equations using concrete, informal, and formal methods (e.g., using properties, graphing ordered pairs, using slope-intercept form) |
| | | | | 10. | Solves simple systems of equations graphically |
| | | | Level IV [Grade: 9-12] |
| | | | | 4. | Understands properties of graphs and the relationship between a graph and its corresponding expression (e.g., maximum and minimum points) |
| | | | | 7. | Uses a variety of models (e.g., written statement, algebraic formula, table of input-output values, graph) to represent functions, patterns, and relationships |
| | | | | 9. | Understands the effects of parameter changes on functions and their graphs |
| | | | | 10. | Understands the basic concept of inverse function and the corresponding graph |
| | | | | 11. | Uses a variety of methods (e.g., with graphs, algebraic methods, and matrices) to solve systems of equations and inequalities |
| | | | Level V [Grade: 13] |
| | | | | 3. | Understands graphs of solution sets of quadratic inequalities |
| | | | | 10. | Understands periodicity in the trigonometric functions and their graphs |
| | | | | 12. | Understands the graph of a function of the form f(t)=Asin(Bt+C)+D or g(t)=Acos(Bt+C)+D, in terms of amplitude, frequency, period, and vertical shift, and phase shift |
| | | Standard 9. Understands the general nature and uses of mathematics
| | | | | Level II [Grade: 3-5] |
| | | | | 2. | Understands that mathematical ideas and concepts can be represented concretely, graphically, and symbolically |
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