Topic: Motion Geometry/Transformations |
Common Core Mathematics 9-12 |
| Cluster Experiment with transformations in the plane |
| | Grade 9-12 |
| | | G.CO.2. | Represent transformations in the plane using, e.g., transparencies
and geometry software; describe transformations as functions that
take points in the plane as inputs and give other points as outputs.
Compare transformations that preserve distance and angle to those
that do not (e.g., translation versus horizontal stretch). |
| | | G.CO.3. | Given a rectangle, parallelogram, trapezoid, or regular polygon,
describe the rotations and reflections that carry it onto itself. |
| | | G.CO.4. | Develop definitions of rotations, reflections, and translations in terms
of angles, circles, perpendicular lines, parallel lines, and line segments. |
| | | G.CO.5. | Given a geometric figure and a rotation, reflection, or translation,
draw the transformed figure using, e.g., graph paper, tracing paper, or
geometry software. Specify a sequence of transformations that will
carry a given figure onto another. |
| Cluster Understand congruence in terms of rigid motions |
| | Grade 9-12 |
| | | G.CO.6. | Use geometric descriptions of rigid motions to transform figures and
to predict the effect of a given rigid motion on a given figure; given
two figures, use the definition of congruence in terms of rigid motions
to decide if they are congruent. |
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 |
| 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 |
| | | | | 3. | Understands that in geometry, functions relate points to images in motion (e.g., flips, slides, turns) |