Getting Started 
Misconception/Error The student is unable to perform the given reflection. 
Examples of Student Work at this Level The student attempts to reflect point C across but is unable to do so correctly. The student may use a compass and straightedge but does not understand how to perform the necessary construction.

Questions Eliciting Thinking What does it mean to reflect a point? Does your image represent what you described?
Where, specifically, is the image of point C in your drawing? How do we usually name the image of a point under a reflection?
What is the relationship among point C, its image, and the reflection line? 
Instructional Implications Be sure the student understands that a reflection across line m (the line of reflection) assigns to each point not on line m, a point that is symmetric to itself with respect to line m (e.g., m is the perpendicular bisector of the segment whose endpoints are the point and its image). Also, a reflection assigns to each point on line m the point itself. Use grid paper to illustrate reflections of points and to demonstrate the relationship between a point, its image, and the line of reflection. Then illustrate reflections of more complex figures such as segments, angles, and polygons. Discuss the basic properties of reflections [e.g., (1) reflections map lines to lines, rays to rays, and segments to segments; (2) reflections are distance preserving; and (3) reflections are degree preserving] and how these properties ensure that the image of a figure under a reflection is always congruent to the preimage.
Provide opportunities to experiment with reflections of points. Guide the student to draw a line containing the preimage point that is perpendicular to the reflection line. Have the student locate the image point on this line so that the reflection line is the perpendicular bisector of the segment whose endpoints are the preimage and image points.
Assist the student in developing a concise but complete definition of reflection such as: is the reflection of point P if it lies on the line perpendicular to the reflection line that contains point P and if the reflection line is the perpendicular bisector of .
Consider implementing the MFAS task Demonstrating Reflections (GCO.1.2). 
Moving Forward 
Misconception/Error The student cannot develop a definition of a reflection. 
Examples of Student Work at this Level The student correctly reflects point C across . However, the student is unable to write a complete and coherent definition of reflection. For example, the student:
 Describes the steps used to locate the image of C.
 Describes the location of in the reflection performed in the first prompt.
 Writes a vague and imprecise statement.

Questions Eliciting Thinking How are definitions usually stated?
Do you think that someone who read your definition could perform a reflection? 
Instructional Implications Discuss with the student the qualities of a definition that make it precise and complete. Guide the student to write a concise but complete definition of reflection. Suggest to the student that he or she complete the statement that begins, “ is the reflection of point P if …” to define a reflection. 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 reflection.
Consider implementing the MFAS tasks Define a Translation and Define a Rotation (GCO.1.4). 
Almost There 
Misconception/Error The student develops a definition that is incomplete or imprecise. 
Examples of Student Work at this Level The student correctly reflects point C across and defines a reflection, but the definition lacks an important feature such as:
 Specifying that the reflection line bisects the segment whose endpoints are points C and its image.
 Specifying that the reflection line is perpendicular to the segment whose endpoints are points C and its image.
The student uses incorrect terminology, for example, referring to the line of reflection as a horizontal line or referring to a segment as a line.

Questions Eliciting Thinking How are the reflection line and the line containing point C and its image related?
What is true of the distance from point C to the reflection line and point to the reflection line? How are these distances related? 
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 reflection. 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 Rotation (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 reflects point C across and defines a reflection, for example, in the following way: is the reflection of point P if it lies on the line perpendicular to the reflection line that contains point P and if the reflection line is the perpendicular bisector of . 
Questions Eliciting Thinking What would happen if the point A were on the reflection line?
What would be the result if the reflected point were then reflected back across the reflection line? 
Instructional Implications Challenge the student to identify and describe in detail a transformation, other than a reflection, that will result in precisely the same image of point C as the reflection across .
Consider implementing the MFAS tasks Define a Translation and Define a Rotation (GCO.1.4). 