Topic: Motion Geometry/Transformations |
Mathematics |
| Standard 5. Understands and applies basic and advanced properties of the concepts of geometry |
| | Level Pre-K (Grade Pre-K) |
| | | Benchmark 4. | Understands that a shape’s orientation in space can change |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the basic concept of orientation in space |
| | | | | 2. | Understands that even though a shape’s orientation changes, the shape itself does not change |
| | Level II (Grade 3-5) |
| | | Benchmark 5. | Uses motion geometry (e.g., turns, flips, slides) to understand geometric relationships |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of motion geometry |
| | | | | 2. | Understands the concept of slides |
| | | | | 3. | Understands the concept of turns |
| | | | | 4. | Understands the concept of flips |
| | Level III (Grade 6-8) |
| | | Benchmark 4. | Understands geometric transformations of figures (e.g., rotations, translations, dilations) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of rotations |
| | | | | 2. | Understands the concept of transformation |
| | | | | 3. | Understands the concept of translation |
| | | | | 4. | Understands the concept of dilations |
| | Level IV (Grade 9-12) |
| | | 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 |
| Standard 8. Understands and applies basic and advanced properties of functions and algebra |
| | Level IV (Grade 9-12) |
| | | Benchmark 6. | Understands the concept of a function as the correspondences between the elements of two sets (e.g., in algebra, functions are relationships between variables that represent numbers; in geometry, functions relate sets of points to their images under motions such as flips, slides, and turns; in the "real-world," functions are mathematical representations of many input-output situations) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands functions as fixed relationships between elements of two sets |
| | | | | 2. | Understands that in the real world, functions relate inputs to outputs |
| | | | | 3. | Understands that in geometry, functions relate points to images in motion (e.g., flips, slides, turns) |
| | | | | 4. | Understands that in algebra, functions represent relationships between variables |