Topic: Graphs and graphing systems |
Mathematics |
| Standard 5. Understands and applies basic and advanced properties of the concepts of geometry |
| | Level IV (Grade 9-12) |
| | | Benchmark 1. | Understands that objects and relations in geometry correspond directly to objects and relations in algebra (e.g., a line in geometry corresponds to a set of ordered pairs satisfying an equation of the form ax + by = c) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands a line in geometry corresponds to a set of ordered pairs |
| | | | | 2. | Understands the connections between algebra and geometry |
| | | | | 3. | Knows that ax + by = c is the general equation for a line |
| | | | | 4. | Understands the concept of a coordinate plane |
| | | | | 5. | Knows that geometric figures can be described algebraically |
| | | Benchmark 9. | Understands the basic properties and uses of polar coordinates |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the properties of polar coordinates |
| | | | | 2. | Understands the uses of polar coordinates |
| Standard 8. Understands and applies basic and advanced properties of functions and algebra |
| | Level II (Grade 3-5) |
| | | Benchmark 6. | Knows basic characteristics and features of the rectangular coordinate system (e.g., the horizontal axis is the X axis and the vertical axis is the Y axis) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the horizontal axis is the X axis |
| | | | | 2. | Understands the vertical axis is the Y axis |
| | | | | 3. | Knows that the X axis and the Y axis are perpendicular |
| | | | | 4. | Knows the rectangular coordinate system is divided into four quadrants |
| | Level III (Grade 6-8) |
| | | Benchmark 3. | Understands various representations (e.g., tables, graphs, verbal descriptions, algebraic expressions, Venn diagram) of patterns and functions and the relationships among them |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands how algebraic expressions can represent functions |
| | | | | 2. | Represents functions using algebraic expressions |
| | | | | 3. | Understands how verbal descriptions can represent functions |
| | | | | 4. | Represents functions using tables |
| | | | | 5. | Understands how tables can represent functions |
| | | | | 6. | Understands how graphs can represent functions |
| | | | | 7. | Represents functions using graphs |
| | | | | 8. | Represents functions using verbal descriptions |
| | | | | 9. | Understands the concept of a Venn diagram |
| | | | | 10. | Represents patterns using Venn diagrams |
| | | | | 11. | Understands how Venn diagrams can represent patterns |
| | | | | 12. | Understands how algebraic expressions can represent patterns |
| | | | | 13. | Represents patterns using algebraic expressions |
| | | | | 14. | Understands how verbal descriptions can represent patterns |
| | | | | 15. | Represents patterns using tables |
| | | | | 16. | Understands how tables can represent patterns |
| | | | | 17. | Understands how graphs can represent patterns |
| | | | | 18. | Represents patterns using graphs |
| | | | | 19. | Represents patterns using verbal descriptions |
| | | | | 20. | Understands the relationship between tables and graphs |
| | | | | 21. | Understands the relationship between tables and verbal descriptions |
| | | | | 22. | Understands the relationship between tables and algebraic expressions |
| | | | | 23. | Understands the relationship between tables and Venn diagrams |
| | | | | 24. | Understands the relationship between graphs and verbal descriptions |
| | | | | 25. | Understands the relationship between graphs and algebraic expressions |
| | | | | 26. | Understands the relationship between graphs and Venn diagrams |
| | | | | 27. | Understands the relationship between verbal descriptions and algebraic expressions |
| | | | | 28. | Understands the relationship between verbal descriptions and Venn diagrams |
| | | Benchmark 5. | Solves linear equations using concrete, informal, and formal methods (e.g., using properties, graphing ordered pairs, using slope-intercept form) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of a linear equation |
| | | | | 2. | Solves linear equations using knowledge of properties |
| | | | | 3. | Solves linear equations by graphing ordered pairs |
| | | | | 4. | Solves linear equations using slope-intercept form |
| | | | | 5. | Solves linear equations using concrete methods |
| | | | | 6. | Solves linear equations using informal methods |
| | | | | 7. | Solves linear equations using formal methods |
| | | Benchmark 7. | Understands special values (e.g., minimum and maximum values, x- and y-intercepts, slope, constant ratio or difference) of patterns, relationships, and functions |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands x- and y-intercepts |
| | | | | 2. | Understands the concept of slope |
| | | | | 3. | Understands constant ratio or difference |
| | | | | 4. | Understands the concept of maximum |
| | | | | 5. | Understands the concept of minimum |
| | | Benchmark 9. | Uses the rectangular coordinate system to model and to solve problems |
| | | | Knowledge/skill statements |
| | | | | 1. | Determines whether a problem can be modeled by using rectangular coordinates |
| | | | | 2. | Determines whether a problem can be solved by using rectangular coordinates |
| | | Benchmark 10. | Solves simple systems of equations graphically |
| | | | Knowledge/skill statements |
| | | | | 1. | Solves simple systems of equations graphically |
| | | | | 2. | Understands the concept of systems of equations |
| | Level IV (Grade 9-12) |
| | | Benchmark 4. | Understands properties of graphs and the relationship between a graph and its corresponding expression (e.g., maximum and minimum points) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the relationship between the graphical and algebraic representations of minimum |
| | | | | 2. | Understands the relationship between graphs and corresponding expressions |
| | | | | 3. | Understands the relationship between the graphical and algebraic representations of maximum |
| | | Benchmark 7. | Uses a variety of models (e.g., written statement, algebraic formula, table of input-output values, graph) to represent functions, patterns, and relationships |
| | | | Knowledge/skill statements |
| | | | | 1. | Represents functions using graphs |
| | | | | 2. | Represents functions using table of input/output values |
| | | | | 3. | Represents functions using algebraic formula |
| | | | | 4. | Represents functions using written statements |
| | | | | 5. | Represents functions using models |
| | | | | 6. | Represents patterns using graphs |
| | | | | 7. | Represents patterns using table of input/output values |
| | | | | 8. | Represents patterns using algebraic formula |
| | | | | 9. | Represents patterns using written statements |
| | | | | 10. | Represents patterns using models |
| | | | | 11. | Represents relationships using graphs |
| | | | | 12. | Represents relationships using table of input/output values |
| | | | | 13. | Represents relationships using algebraic formula |
| | | | | 14. | Represents relationships using written statements |
| | | | | 15. | Represents relationships using models |
| | | Benchmark 9. | Understands the effects of parameter changes on functions and their graphs |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of a parameter |
| | | | | 2. | Understands how parameter changes affect functions |
| | | | | 3. | Understands how parameter changes affect graphs of functions |
| | | Benchmark 10. | Understands the basic concept of inverse function and the corresponding graph |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of inverse functions |
| | | | | 2. | Graphs inverse functions |
| | | Benchmark 11. | Uses a variety of methods (e.g., with graphs, algebraic methods, and matrices) to solve systems of equations and inequalities |
| | | | Knowledge/skill statements |
| | | | | 1. | Solves systems of equations using graphs |
| | | | | 2. | Solves systems of equations using matrices |
| | | | | 3. | Solves systems of equations using algebraic methods |
| | | | | 4. | Understands the concept of systems of inequalities |
| | | | | 5. | Solves systems of inequalities using algebraic methods |
| | | | | 6. | Solves systems of inequalities using graphs |
| | | | | 7. | Solves systems of inequalities using matrices |
| | Level V (Grade (College Readiness)) |
| | | Benchmark 2. | Understands graphs of solution sets of quadratic inequalities |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of solution sets |
| | | | | 2. | Identifies solution sets of quadratic inequalities |
| | | | | 3. | Interprets graphs of solution sets of quadratic inequalities |