Getting Started 
Misconception/Error The student is unable to correctly perform reflections. 
Examples of Student Work at this Level The student:
 Only identifies the coordinates of the vertices of the preimage.
 Attempts to reflect the figure but does so incorrectly.
 Performs some transformation other than a reflection. The student attempts to rotate or translate the figure.

Questions Eliciting Thinking I see that you listed the coordinates of the vertices of trapezoid UVWZ as the coordinates of the vertices of the image. Would you expect these to be the same after the reflection?
What is a reflection? Can you describe the reflection in words? What happens to the vertices of the figure?
Could you perform the reflection with tracing paper?
How is a reflection different from a translation or rotation? 
Instructional Implications Review the definition of reflection as a transformation of the plane. Explain 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.
Emphasize the basic properties of rigid motions:
 Lines are taken to lines, and line segments to line segments of the same length.
 Angles are taken to angles of the same measure.
 Parallel lines are taken to parallel lines.
Discuss how these properties ensure that the image of a figure under a rigid motion is always congruent to the preimage.
To develop an intuitive understanding of transformations, allow the student to experiment with a variety of transformations using transparent paper or interactive websites such as: .
Provide additional opportunities to experiment with reflections using transparent paper to perform reflections in the coordinate plane. Guide the student to always check the image to ensure that it is congruent to the preimage. 
Moving Forward 
Misconception/Error The student performs a reflection but makes significant errors. 
Examples of Student Work at this Level The student uses the wrong line of reflection and instead reflects the figure over:
 The yaxis rather than the xaxis.
 A side of the polygon itself.
 Some line other than that requested.
The student attempts to draw the reflection but makes some errors in locating the vertices of the reflected figure.

Questions Eliciting Thinking Can you show me how you reflected this figure?
What should happen if you fold your paper along the reflection line?
Will using different lines of reflection produce different results? 
Instructional Implications Encourage the student to be mindful of the location of the reflection line. 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. This can be used as a check on the accuracy of the reflection and the labeling of the vertices. Have the student use tracing paper to perform reflections and draw the image figure. Then ask the student to identify the coordinates of the vertices of the image figure.Â
Provide additional opportunities to experiment with reflections using transparent paper to perform reflections in the coordinate plane. Guide the student to always check the image to ensure that it is congruent to the preimage. 
Almost There 
Misconception/Error The student makes an error when describing the coordinates of the verticesÂ of the image. 
Examples of Student Work at this Level The student correctly draws the image figure, but identifies the coordinates of one or more vertices incorrectly. The student:
 Reverses the order of the coordinates in one ordered pair but writes all other ordered pairs correctly.
 Omits a negative symbol from a coordinate.
 Makes a systematic error with one of the coordinates.

Questions Eliciting Thinking I think you may have made a small error when you determined the coordinates of the vertices of the image figure. Can you check your work to find the error?
Can you show me how you determined the ycoordinates of the vertices of the image figure? 
Instructional Implications Provide feedback on the specific error made and allow the student to revise his or her work. Remind the student that 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. This can be used as a check on the accuracy of the reflection and the labeling of the vertices.
Provide additional opportunities to perform reflections in the coordinate plane. 
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 describes and labels the coordinates of the image figures:
 (5, 2), (3, 1), (3, 3), (5, 6).
 (9, 8), (6, 8), (6, 4).

Questions Eliciting Thinking Is there a combination of reflections that you can perform so the figure will end up entirely in Quadrant IV?
Is it possible to reflect a figure in such a way that some of the vertices remain the same? Explain. 
Instructional Implications Challenge the student to further explore reflections across the xaxis and reflections across the yaxis. Ask the student to describe each type of reflection in terms of the effect on the coordinates of points. For example, a reflection across the xaxis maps each point P(x, y) to (x, y). Guide the student to reflect figures across axes by calculating the coordinates of the vertices of the images and then graphing the vertices and drawing the sides of the figure.
Consider implementing the MFAS tasks Translation Coordinates, Rotation Coordinates and Dilation CoordinatesÂ to give the student practice with a variety of transformations. 