Getting Started 
Misconception/Error The student does not demonstrate an understanding of reflections. 
Examples of Student Work at this Level The student asks, “What is a reflection?” and is unable to reflect the given figure.
The student:
 Confuses a reflection with a translation.
 Confuses a reflection with a dilation.

Questions Eliciting Thinking What are the basic rigid motions? Do you know other words to describe them?
What does it mean to reflect a figure? Does your image represent what you described?
How is a reflection different from a rotation? How is a reflection different from a translation? 
Instructional Implications Review the definition of each of the rigid transformations: translations, reflections, and rotations. To develop an intuitive understanding of rigid transformations, allow the student to experiment with a variety of transformations using transparent paper or interactive websites such as http://www.mathsisfun.com/flash.php?path=%2Fgeometry/images/reflection.swf&w=670.5&h=579&col=#FFFFFF&title=Geometry++Reflection, http://www.mathopenref.com/reflect.html, http://www.cuttheknot.org/Curriculum/Geometry/Reflection.shtml or http://www.shodor.org/interactivate/activities/TransmographerTwo/. Provide instruction on the conventional use of notation.
With regard to reflections, be sure the student understands that a reflection is a transformation of the plane. 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., line 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 additional opportunities to experiment with reflections using transparent paper and to perform reflections in the coordinate plane. Guide the student to check the image to ensure that it is congruent to the preimage and that the line of reflection is a line of symmetry for the two figures. 
Moving Forward 
Misconception/Error The student understands the concept of a reflection but demonstrates the reflection incorrectly. 
Examples of Student Work at this Level The student:
 Does not use the tracing paper correctly and plots one or more points incorrectly, most often point H' because the student assumes the preimage is a trapezoid.
 Does not plot the image the same distance from the line of reflection as the preimage.

Questions Eliciting Thinking Can you demonstrate how you reflected quadrilateral EFGH? What point on the image corresponds to point H on the preimage?
How would you compare the preimage to the image? Is quadrilateral E'F'G'H' congruent to quadrilateral EFGH?
What should be true of the location of points E and E' with regard to line m?
How would the vertices of quadrilateral E'F'G'H' be affected if line m were to be shifted one unit to the left? Can you demonstrate this reflection? 
Instructional Implications Review the definition of a reflection and provide numerous opportunities to experiment with reflections using transparent paper and to perform reflections in the coordinate plane. Vary the preimage (using points, segments, rays, angles, and polygons) and the location of the line of reflection with regard to the preimage. Be sure the student understands 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. When performing reflections, guide the student to always check the image to ensure that it is congruent to the preimage and that the line of reflection is a line of symmetry for the two figures.
Consider implementing the MFAS task Define a Reflection (GCO.1.4). 
Almost There 
Misconception/Error The student correctly reflects the figure but labels the image incorrectly. 
Examples of Student Work at this Level The student:
 Does not include the “prime” symbol ( ' ) when labeling the image.
 Does not label the image.
 Does not take into consideration the corresponding vertices and randomly labels the image or labels the image as if it were a translation.

Questions Eliciting Thinking Should E be used to label both a vertex of the preimage and a vertex of the image? Why do you think we might want to label these vertices differently?
Do you know the convention for labeling corresponding vertices of the preimage and image?
Can you identify the corresponding vertices of the preimage and image? 
Instructional Implications Discuss with the student the advantages to using the conventional approach to naming vertices of the image and preimage. Remind the student that corresponding vertices can be identified from the congruence statement (e.g., quadrilateral EFGH quadrilateral E'F'G'H').
Remind the student to always check the image to ensure that it is congruent to the preimage and that the line of reflection is a line of symmetry for the two figures. 
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 the preimage across the line of reflection. The student correctly labels the image using the notation indicated in the directions E', F', G', and H'.

Questions Eliciting Thinking What properties of the quadrilateral are preserved in the reflection? Is this true for rotations, reflections, and dilations? 
Instructional Implications Ask the student to explain how 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] ensure that:
 Reflections map angles to angles.
 Under a reflection, the image of a figure is always congruent to its preimage.
Ask the student to develop algebraic descriptions of the coordinates of point P(x, y) after reflections across each axis and after 90°,180°, and 270° clockwise and counterclockwise rotations about the origin. Then challenge the student to write an algebraic description of the coordinates of point P(x, y) after a composition of transformations such as a reflection across the xaxis followed by a 90° counterclockwise rotation about the origin. Encourage the student to check the descriptions by applying them to specific points. 