Topic: Analytic geometry |
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 3. | Uses synthetic (i.e., pictorial) representations and analytic (i.e., coordinate) methods to solve problems involving symmetry and transformations of figures (e.g., problems involving distance, midpoint, and slope; determination of symmetry with respect to a point or line) |
| | | | Knowledge/skill statements |
| | | | | 1. | Uses synthetic geometric models to solve slope problems |
| | | | | 2. | Uses synthetic geometric models to solve line symmetry problems |
| | | | | 3. | Uses synthetic geometric models to solve point symmetry problems |
| | | | | 4. | Uses synthetic geometric models to solve distance problems |
| | | | | 5. | Uses synthetic geometric models to solve midpoint problems |
| | | | | 6. | Understands the concept of a synthetic model (i.e., a pictorial representation) |
| | | | | 7. | Uses analytic methods to solve slope problems |
| | | | | 8. | Uses analytic methods to solve line symmetry problems |
| | | | | 9. | Uses analytic methods to solve point symmetry problems |
| | | | | 10. | Uses analytic methods to solve distance problems |
| | | | | 11. | Uses analytic methods to solve midpoint problems |
| | Level V (Grade (College Readiness)) |
| | | Benchmark 5. | Uses algebraic methods to solve geometric problems |
| | | | Knowledge/skill statements |
| | | | | 1. | Translates geometric shapes into algebraic equations |
| | | | | 2. | Translates algebraic equations into geometric shapes |