Getting Started 
Misconception/Error The student is unable to completely and correctly identify all of the rotations and reflections that carry the figure onto itself. 
Examples of Student Work at this Level The student:
 Describes only some of the rotations and reflections.
 Includes incorrect lines of reflection.
 Includes incorrect degrees of rotation.

Questions Eliciting Thinking About which point did you rotate this figure? Could you find more rotations if you used the point at which the diagonals intersect as the center of rotation?
How did you determine the degree of rotation?
Does a rotation of 360° satisfy the conditions of the problem?
Can you model the rotation (or reflection) that you described? Can you explain how the transformation you described will carry the figure onto itself? 
Instructional Implications Review the concepts of reflections and rotations. Have the student experiment with rotations and reflections on an interactive website such as http://www.cuttheknot.org/Curriculum/Geometry/Rotation.shtml or http://www.cuttheknot.org/Curriculum/Geometry/Reflection.shtml to help the student visualize the result of various transformations.
Provide tracing paper so the student can model rotations of regular polygons about the intersections of their diagonals. Assist the student in determining the degree of each rotation that carries the figure onto itself. Remind the student that rotations are described by specifying the center, the degree, and the direction (clockwise or counterclockwise) of rotation. Assist the student in precisely describing each rotation that was identified.
Provide regular polygons that can be cut out. Have the student fold each figure to identify lines of reflection that carry the figure onto itself. Guide the student to precisely describe these lines. Then ask the student to identify lines of symmetry for a variety of figures by both drawing and describing each line for each figure.
Consider implementing MFAS task Transformations of Rectangles and Squares (GCO.1.3). 
Making Progress 
Misconception/Error The student does not clearly and precisely describe transformations. 
Examples of Student Work at this Level The student identifies each rotation and reflection that will carry each figure onto itself. However, some identifications are not clearly stated or precisely described. For example, the student:
 Neglects to describe (or does not precisely describe) the center or direction of the rotation until prompted.
 Uses imprecise terminology to describe lines of reflection.
 Draws but does not describe lines of reflection

Questions Eliciting Thinking What is the direction of the rotations you described – clockwise or counterclockwise?
How could you precisely describe the center of this rotation?
How could you precisely describe the lines of reflection? 
Instructional Implications Remind the student that rotations are described by specifying the center, the degree, and the direction (clockwise or counterclockwise) of rotation. Assist the student in precisely describing each rotation that was identified.
Guide the student to draw and label lines of reflection for each figure and then refer to the lines by name. Encourage the student to use mathematical terms such as midpoint, vertex, parallel, perpendicular, and diagonal when describing lines of reflection.
Consider implementing MFAS task Transformations of Rectangles and Squares (GCO.1.3). 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level With regard to the regular hexagon, the student describes the center of rotation as the point where the diagonals intersect. The student indicates that rotations of degree 60, 120, 180, 240, 300, and 360 clockwise and counterclockwise about this point will carry the hexagon onto itself. The student also (upon questioning) indicates that any multiple of 60 will provide a degree of rotation that carries a regular hexagon onto itself. The student describes three lines of symmetry through pairs of opposite vertices and three lines of symmetry through midpoints of opposite sides.
With regard to the regular pentagon, the student describes the center of rotation as the point where the diagonals intersect. The student indicates that rotations of degree 72, 144, 216, 288, and 360 clockwise and counterclockwise about this point will carry the pentagon onto itself. The student also (upon questioning) indicates that any multiple of 72 will provide a degree of rotation that carries a regular pentagon onto itself. The student describes five lines of symmetry each with one endpoint at a vertex and the other endpoint at the midpoint of the opposite side.
The student may initially neglect to include the direction of rotation (clockwise and counterclockwise) but does so immediately upon questioning. 
Questions Eliciting Thinking Are there any rotations of degree larger than 360 that carry the figure onto itself? How can you describe these rotations? How can you describe, in general, the rotations that will carry a regular hexagon (or regular pentagon) onto itself?
Can you describe any rotations that will carry the figure onto itself using one of the vertices (or an exterior point) as the center?
Can you draw a hexagon that has no rotational symmetry (other than 360°) but still has line symmetry? 
Instructional Implications Challenge the student to describe the number of lines of symmetry and the rotations of a regular ngon that carry the figure onto itself, in terms of n. 