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:
 Is unable to describe any rotation.
 Includes incorrect degrees of rotation.
 Includes incorrect lines of reflection.

Questions Eliciting Thinking About which point did you rotate this figure?
What is the degree measure of a complete 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 trapezoids about the intersections of their diagonals, their vertices, and several exterior points. Assist the student in determining that only a 360° rotation (clockwise or counterclockwise) will carry a trapezoid 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 trapezoids that can be cut out. Include both isosceles and nonisosceles trapezoids. 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 Parallelograms and Rhombi (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:
 Does not describe all centers of rotation or the direction of the rotation.
 Uses imprecise terminology to describe the line of reflection of the isosceles trapezoid such as a “vertical line down the middle.”
 Draws but does not describe the line of reflection of the isosceles trapezoid.

Questions Eliciting Thinking Are there any other points that could be used as the center of rotation?
What is the direction of the rotation you described?
How could you more precisely describe the line of reflection? What exactly did you mean by the “middle of the trapezoid?”
If you could only rotate the trapezoid once, would there be a degree of rotation that would carry the trapezoid onto itself? 
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 understanding that any point could serve as the center of a 360° rotation and in precisely describing each rotation.
Guide the student to draw and label lines of reflection 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 Parallelograms and Rhombi (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 The student says that only a rotation of 360° about any point will carry each trapezoid onto itself, the nonisosceles trapezoid has no lines of reflection, and the isosceles trapezoid has only one  the line that contains the midpoints of the two parallel sides. 
Questions Eliciting Thinking Is there a trapezoid for which a rotation of degree less than 360° would carry the trapezoid onto itself?
Is there a trapezoid with more than one line of reflection?
Why did an isosceles trapezoid have a line of reflection but not a degree of rotation less than 360°? 
Instructional Implications Introduce the student to compositions of transformations. Challenge the student to find and precisely describe a reflection followed by a rotation that will carry a trapezoid onto itself.
On a coordinate plane, have the student graph a trapezoid ABCD with all four vertices in the first quadrant. Ask the student to reflect the trapezoid over the yaxis and then again over the xaxis. Challenge the student to describe a rotation that will result in the same image of the trapezoid. 