Getting Started 
Misconception/Error The student is unable to perform and describe the steps of the given rotation. 
Examples of Student Work at this Level The student:
 Does not know what a rotation is and attempts to translate or reflect the points.
 Uses a compass to draw a circle centered at C and of radius AC but never specifically locates the image of point A.
 Constructs a perpendicular to at point C but does not specifically draw or precisely identify the location of the image of A.

Questions Eliciting Thinking What are the basic rigid motions? Do you know other words to describe them?
What does it mean to rotate a figure? Does your image represent what you described?
Where, specifically, is the image of point A in your drawing? How do we usually name the image of a point under a rotation? 
Instructional Implications Be sure the student understands that under a rotation, each point in the plane is rotated a specified number of degrees (given by the degree of rotation) either clockwise or counterclockwise (indicated by the sign of the degree of rotation) about a fixed point called the center of rotation. Use a unit circle to illustrate rotations of points about the origin. Then illustrate rotations of more complex figures such as segments, angles, and polygons. Discuss the basic properties of rotations [e.g., 1) rotations map lines to lines, rays to rays, and segments to segments; 2) rotations are distance preserving; and 3) rotations are degree preserving] and how these properties ensure the image of a figure under a rotation is always congruent to the preimage.
Be sure the student understands that a degree of rotation less than corresponds to the angle determined by the following three points: a preimage point, the center of rotation, and the corresponding image point (with the center of rotation the vertex of the angle). Illustrate this idea with a variety of rotations of figures varying the location of the center of rotation with regard to the figure (in the interior of the figure, on the figure, and exterior to the figure).
Assist the student in developing a concise but complete definition of rotation such as: A rotation about point C maps point A to its image, point A', if A' lies on a circle centered at point C and of radius AC, and . The rotation is counterclockwise if the degree of the rotation is positive and is clockwise if the degree of the rotation is negative.
Consider implementing the MFAS task Demonstrating Rotations (GCO.1.2). 
Moving Forward 
Misconception/Error The student cannot develop a definition of a rotation. 
Examples of Student Work at this Level The student correctly rotates point A about point C and describes the sequence of steps used. However, the student is unable to write a complete and coherent definition of rotation.

Questions Eliciting Thinking Do all rotations involve perpendicular lines?
How are AC and A'C related?
How did you use the center of rotation? How did you use the degree of the rotation?
Is it necessary to be given a direction for the rotation? 
Instructional Implications Review the steps the student described in performing the rotation and assist the student in generalizing the procedure to develop a definition of a rotation. Suggest to the student that he or she complete the statement that begins, “A rotation about point C maps point A to its image, point A', if ...” and provide feedback. Then ask the student to apply the definition to several pairs of points to determine if one could be the image of the other as a result of a given rotation.
Consider implementing the MFAS tasks Define a Translation and Define a Reflection (GCO.1.4). 
Almost There 
Misconception/Error The student develops a definition that is incomplete and imprecise. 
Examples of Student Work at this Level The student correctly rotates point A about point C and describes the sequence of steps used. The student defines a rotation but the definition lacks an important feature such as:
 The direction of the rotation,
 The relationship between AC and A'C, or
 A specific description of the circle (e.g., its center and radius).

Questions Eliciting Thinking Does your definition address the direction of the rotation?
How are AC and A'C related?
You referred to a circle in your definition. Where is its center? What is its radius? 
Instructional Implications Provide specific feedback to the student regarding any omissions or points that require clarification or elaboration in his or her definition. Ask the student to consider if his or her definition is complete enough that it can be used to determine if one figure is the image of another under a rotation. Have the student analyze definitions written by other students to determine if they are complete and precisely written.
Consider implementing the MFAS tasks Define a Translation and Define a Reflection (GCO.1.4). 
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 correctly rotates point A about point C and describes the sequence of steps used. The student defines a rotation, for example, in the following way:
A rotation about point C maps point A to its image, point A', if A' lies on a circle centered at point C and of radius AC, and . The rotation is counterclockwise if the degree of the rotation is positive and is clockwise if the degree of the rotation is negative. 
Questions Eliciting Thinking Does a rotation preserve distance? Angle measure?
Can you think of an example of a transformation that does not preserve distance or angle measure? 
Instructional Implications Challenge the student to identify and describe in detail a transformation, other than a rotation, that will result in precisely the same image of point A as that which resulted from a 90° clockwise rotation about point C.
Consider implementing the MFAS tasks Define a Translation and Define a Reflection (GCO.1.4). 